@unpublished {zeng2026IMAGEbjv,
	title = {Bayesian Joint Velocity and Impedance Inversion via Diffusion Models Conditioned on Common Image Gathers},
	year = {2026},
	month = {3},
	abstract = {We present a multi-parameter simulation-based inference framework for joint Bayesian recovery of subsurface velocity and acoustic impedance from seismic data. A score-based diffusion model is conditioned on two complementary Common Image Gathers (CIGs): an inverse-scattering CIG encoding reflectivity amplitude and an anti-ISIC CIG encoding kinematic velocity errors. The model simultaneously samples the posterior distributions of both parameters. Training labels are deliberately decoupled to prevent the model from exploiting the Gardner relationship: velocity targets are lightly smoothed to match the long-wavelength content of the anti-ISIC CIG, while impedance targets retain the unsmoothed ground truth. On the Compass benchmark the model achieves velocity SSIM of 0.967 (RMSE 0.050 km/s) and impedance SSIM 0.867 (RMSE 0.279 km/s{\textperiodcentered}g/cm{\textthreesuperior}), with velocity quality confirmed by CIG focusing.},
	keywords = {Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEbjv/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEbjv/IMAGE_Yunlin.pdf},
	author = {Yunlin Zeng and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@unpublished {deng2026IMAGEbag,
	title = {Bridging the Acoustic-Elastic Gap in Seismic Inversion via Robust Summary Statistics},
	year = {2026},
	month = {3},
	abstract = {Simulation-based seismic inversion provides a principled framework for uncertainty quantification, but its performance degrades when the physics used in simulation differ from those of observed data. In practice, seismic inversion is often misspecified because the true physics are only partially known or too costly to model at scale, making field observations out of distribution relative to the simulations used for training; here, we study this issue through the acoustic-elastic gap. We introduce ElasNet, a misspecification-robust probabilistic inversion framework that bridges acoustic simulations and elastic observations through physics-informed summary statistics. We use acoustically imaged common-image gathers (CIGs) as structured summaries of seismic data, compress them with an attention-based summary network, and use maximum mean discrepancy (MMD) to align acoustic and elastic feature distributions during training while learning a conditional normalizing flow for posterior estimation with only acoustic data. Experiments on 2D Compass models show that the proposed approach reduces acoustic-elastic discrepancies in inferred velocity models and improves structural consistency and uncertainty calibration. These results demonstrate that robust summary statistics and distribution matching provide a scalable pathway for simulation-based seismic inversion under realistic physics mismatch.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, IMAGE, Imaging, Inverse problems, mmd, SEG, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/deng2026IMAGEbag/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/deng2026IMAGEbag/IMAGE_Venice.pdf},
	author = {Zijun Deng and Abhinav Prakash Gahlot and Shiqin Zeng and Felix J. Herrmann}
}
@unpublished {gahlot2026IMAGEirs,
	title = {Improving reservoir state prediction in digital shadows using Radon-transformed subsurface common-offset gathers},
	year = {2026},
	month = {3},
	abstract = {Digital shadows for subsurface monitoring use simulation-based inference to map seismic and well-log observations to evolving reservoir states such as CO 2  saturation and pressure. When the simulation forward models rely on simplified or misspecified rock physics, predictions become biased and uncertainty quantification degrades. We address this by combining rock-physics-aware amortized Bayesian inference with inference in the Radon domain of common-image gathers (CIGs). Angle-dependent information from Radon-transformed subsurface offset gathers improves separation of fluid and stress effects: fluids exhibit distinct amplitude-variation-with-angle (AVA) signatures, so conditioning the digital shadow on angle gathers yields more accurate and physically consistent joint estimates of saturation and pressure than conditioning on migrated stacks or offset-domain gathers. We train a context-aware amortized posterior estimator that conditions on seismic data and rock-physics context, enabling robustness to model misspecification and structured what-if analysis at inference time without retraining. On a synthetic 2D geological carbon storage scenario, conditioning on Radon-transformed CIGs improves joint saturation and pressure prediction relative to reverse-time migrated images, while context conditioning preserves interpretability and calibration under rock physics uncertainty.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, GCS, IMAGE, Imaging, Inverse problems, permeability, reservoir simulation, rock physics, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/gahlot2026IMAGEirs/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/gahlot2026IMAGEirs/IMAGE_Abhinav.pdf},
	author = {Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@unpublished {park2026IMAGEnoa,
	title = {Neural Operators with Accurate Jacobian for High-Fidelity Image-Domain Seismic Inversion},
	year = {2026},
	month = {3},
	abstract = {Neural operators (NOs) provide efficient surrogates for wave-equation-based imaging operators, but accurate forward prediction alone does not guarantee reliable inversion. As inversion updates depend on the adjoint Jacobian, errors in learned sensitivities lead to unphysical updates and degraded quality in recovered models. To this end, we propose a Jacobian-informed training strategy that enforces accuracy in Jacobian in the directions where gradient descent occurs during Least-Squares. Numerical experiments with Fourier Neural Operators demonstrate that supervising only a small fraction ($0.1 \sim 0.01\%$) of Jacobian information significantly improves gradient quality and leads to more accurate subsurface velocity reconstruction. In particular, the proposed approach reduces mid to deep layer artifacts and improves structural continuity compared to models trained only with forward misfit term. These results highlight that learning inversion-relevant sensitivities, rather than forward mappings alone, is critical for reliable surrogate-assisted seismic inversion.},
	keywords = {deep learning, derivative-informed, Fisher-information, FNO, IMAGE, Imaging, Inverse problems, reduced-order modeling, RTM, SEG, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/park2026IMAGEnoa/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/park2026IMAGEnoa/IMAGE_Jayjay.pdf},
	author = {Jeongjin Park and Huseyin Tuna Erdinc and Grant Bruer and Richard Rex and Nisha Chandramoorthy and Felix J. Herrmann}
}
@unpublished {bhar2026IMAGEolr,
	title = {OpenSeisML: Open Large-Scale Real Seismic and well-log Dataset for Generative AI},
	year = {2026},
	month = {3},
	abstract = {The advent of machine learning (ML) and computer vision has significantly accelerated seismic inversion workflows by reducing the computational cost of traditionally expensive iterative methods. However, the development and evaluation of ML methods remains limited by the scarcity of realistic velocity models, as most high-quality data are privately owned by oil and gas companies. To address this gap, we present *OpenSeisML*, a collection of real seismic datasets designed to support generative AI (Gen-AI) workflows for seismic inversion. The datasets are curated from publicly available surveys in the UK National Data Repository (NDR). When seismic volumes are in the time domain and wells are in depth, a time-to-depth conversion is required. We use checkshot data to establish the time{\textendash}depth relationship and construct a velocity model through interpolation for accurate conversion of post-stack seismic data. Here, we present an automated data curation pipeline that enables seismic data preparation while ensuring reproducibility. The objective is to train a generative model that captures the statistical distribution of subsurface properties, enabling the synthesis of multiple statistically consistent realizations for uncertainty quantification which can act as a prior for seismic inversion.},
	keywords = {deep learning, generative model, IMAGE, Imaging, Inverse problems, real seismic data, SEG, time-to-depth conversion, well logs, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/bhar2026IMAGEolr/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/2026IMAGEolr/IMAGE_Ipsita.pdf},
	author = {Ipsita Bhar and Huseyin Tuna Erdinc and Thales Souza and Charles Jones and Felix J. Herrmann}
}
@unpublished {erdinc2026IMAGEsai,
	title = {SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posterior},
	year = {2026},
	month = {3},
	abstract = {Recent advances in generative networks have enabled new approaches to subsurface velocity model synthesis, offering a compelling alternative to traditional methods such as Full Waveform Inversion. However, these approaches predominantly rely on the availability of large-scale datasets of high-quality, geologically realistic subsurface velocity models, which are often difficult to obtain in practice. We introduce SAGE, a novel framework for statistically consistent proxy velocity generation from incomplete observations, specifically sparse well logs and migrated seismic images. During training, SAGE learns a proxy posterior over velocity models conditioned on both modalities (wells and seismic); at inference, it produces full-resolution velocity fields conditioned solely on migrated images, with well information implicitly encoded in the learned distribution. This enables the generation of geologically plausible and statistically accurate velocity realizations. We validate SAGE on both synthetic and field datasets, demonstrating its ability to capture complex subsurface variability under limited observational constraints. Furthermore, samples drawn from the learned proxy distribution can be leveraged to train downstream networks, supporting inversion workflows. Overall, SAGE provides a scalable and data-efficient pathway toward learning geological proxy posterior for seismic imaging and inversion. Repo link: https://github.com/slimgroup/SAGE."},
	keywords = {Bayesian inference, deep learning, generative model, IMAGE, Imaging, Inverse problems, RTM, SAGE, score, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/erdinc2026IMAGEsai/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/erdinc2026IMAGEsai/IMAGE_Tuna.pdf},
	author = {Huseyin Tuna Erdinc and Ipsita Bhar and Rafael Orozco and Thales Souza and Felix J. Herrmann}
}
@unpublished {zeng2026IMAGEssn,
	title = {Self-attention summary networks for subsurface velocity-model building from common-image gathers},
	year = {2026},
	month = {3},
	abstract = {Common-image gathers (CIGs) contain physically meaningful information about velocity-model errors through reflector focusing and residual moveout, but in conventional imaging workflows they are typically used only as diagnostic tools. In this work, we propose a multiscale self-attention summary network that maps high-dimensional 3D CIG volumes into compact conditioning embeddings for probabilistic subsurface velocity inversion. These learned embeddings preserve offset-dependent kinematic structure and spatial coherence while reducing variability caused by background-velocity mismatch. Conditioned on these summary embeddings, a flow-matching model learns a transport from a Gaussian source distribution to the posterior distribution of plausible velocity fields. Numerical experiments show that, compared with direct conditioning on raw CIGs, the proposed summary network improves posterior velocity inference. In particular, the multiscale attention design provides greater robustness to background-model mismatch, yielding more accurate posterior reconstructions and lower predictive uncertainty.},
	keywords = {attention, Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, learned summary statistics, RTM, SEG, uncertainty calibration, Uncertainty quantification, velocity model building, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEssn/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/zeng2026IMAGEssn/IMAGE_Shiqin.pdf},
	author = {Shiqin Zeng and Yunlin Zeng and Abhinav Prakash Gahlot and Zijun Deng and Felix J. Herrmann}
}
@unpublished {gahlot2025EAGEagc,
	title = {Advancing Geological Carbon Storage Monitoring with 3D Digital Shadow Technology},
	year = {2025},
	month = {6},
	keywords = {3D digital shadow, Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, FWI, GCS, Imaging, Inverse problems, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2025/gahlot2025EAGEagc/abstract.html},
	author = {Abhinav Prakash Gahlot and Rafael Orozco and Felix J. Herrmann}
}
@conference {herrmann2025IMSIafi,
	title = {Amortized Full-Waveform Inference w/ Learned Summary Statistics},
	booktitle = {Reduced Order and Surrogate Modeling for Digital Twins, IMSI, Chicago},
	year = {2025},
	month = {11},
	keywords = {attention, Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, learned summary statistics, RTM, SEG, uncertainty calibration, Uncertainty quantification, velocity model building, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/IMSI/2025/herrmann2025IMSIafi},
	author = {Rafael Orozco and Ziyi Yin and Shiqin Zeng and Felix J. Herrmann}
}
@conference {herrmann20205IMAGEapg,
	title = {Attention Please: Getting the Most from CIGs with Learned Summary Statistics},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {attention, Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, learned summary statistics, RTM, SEG, uncertainty calibration, Uncertainty quantification, velocity model building, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/herrmann20205IMAGEapg},
	author = {Shiqin Zeng and Rafael Orozco and Yunlin Zeng and Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {zeng2025ML4SEISMICbde,
	title = {Background-Conditioned Diffusion Inversion for Seismic Velocity Models},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Accurate seismic imaging and velocity estimation are important for subsurface characterization, yet conventional full-waveform inversion remains computationally expensive and highly sensitive to initial velocity models. To address these challenges, we propose a simulation-based inference framework using conditional elucidated diffusion models for posterior velocity-model sampling. Our approach integrates both horizontal and vertical subsurface-offset common-image gathers to capture a wider range of reflector geometries, from gently dipping to steeply inclined layers. We further condition the model on the background-velocity field to improve generalization across diverse geological settings. Evaluations on the SEAM dataset, which includes complex salt geometries, demonstrate that this conditioning substantially improves performance, increasing SSIM from 0.717 to 0.733 and reducing RMSE from 0.381 km/s to 0.274 km/s. Uncertainty analysis further shows enhanced calibration, lowering uncertainty calibration error from 6.68 km/s to 3.91 km/s. These results confirm that our diffusion-based simulation framework enables robust seismic inversion with reliable uncertainty quantification.},
	keywords = {Bayesian inference, CIG, deep learning, diffusion models, FWI, Imaging, Inverse problems, ML4SEISMIC, MVA, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/zeng2025ML4SEISMICbde},
	author = {Yunlin Zeng and Huseyin Tuna Erdinc and Rafael Orozco and Felix J. Herrmann}
}
@conference {deng2025ML4SEISMICbag,
	title = {Bridging the Acoustic{\textendash}Elastic Gap in Seismic Inversion via Robust Summary Statistics},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Simulation-based Bayesian inference (SBI) enables uncertainty quantification in seismic inversion but typically assumes that simulated and observed data follow the same physics. In reality, this assumption does not hold. The Earth is elastic, yet large-scale simulations are often acoustic due to the prohibitive cost of elastic modeling. This acoustic{\textendash}elastic mismatch introduces model misspecification, leading to biased posterior estimates and reduced interpretability. We propose a robust conditional generative framework that mitigates this mismatch by learning a shared representation between acoustic and elastic domains. The approach integrates a robust summary network within a conditional normalizing flow, trained primarily on acoustic simulations and guided by limited elastic supervision. It enables elastic-consistent posterior inference from inexpensive acoustic simulations, balancing computational efficiency with physical realism. This framework offers a scalable path toward uncertainty-aware subsurface characterization under model misspecification, bridging the gap between fast acoustic modeling and physically accurate elastic data.},
	keywords = {Amortized Variational Inference, attention, Bayesian inference, CIG, deep learning, FWI, generative model, Imaging, Inverse problems, ML4SEISMIC, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/deng2025ML4SEISMICbag},
	author = {Zijun Deng and Abhinav Prakash Gahlot and Shiqin Zeng and Felix J. Herrmann}
}
@conference {li2025IMAGEceo,
	title = {CO2 Enhanced Oil Recovery Through Digital Shadow Modeling},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, EOR, experimental design, FWI, GCS, IMAGE, Imaging, Inverse problems, permeability, reservoir simulation, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/li2025IMAGEceo},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/li2025IMAGEceo/IMAGE_Haoyun.pdf},
	author = {Haoyun Li and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {herrmann2025SEGSPEcua,
	title = {Context- and uncertainty-aware Digital Twins for Integrated Reservoir Management},
	booktitle = {SEG/SPE 2nd Integrated Reservoir Characterization, Surveillance, and Management Workshop: Advances and Challenges},
	year = {2025},
	month = {7},
	abstract = {We present a new framework for Digital Twins (DTs) that supports uncertainty-aware monitoring, optimization, and risk management of underground storage operations, with a particular focus on Geological Carbon Storage (GCS) and Enhanced Oil Recovery (EOR). The proposed DT addresses key challenges in reservoir characterization, surveillance, and management by integrating generative AI methods with simulation-based inference, enabling scalable, probabilistic decision support under uncertainty. Our approach combines sensitivity-aware amortized Bayesian inference (SA-ABI) with ensemble-based data assimilation to efficiently incorporate multimodal time-lapse observations, such as seismic and well data, into dynamic reservoir models. By embedding context-awareness into neural networks, we account for variability in rock-physics relationships linking pressure, saturation, and seismic responses, and quantify uncertainties arising from model misspecifications{\textendash}-e.g. usage of patchy versus uniform saturation models. Computational efficiency is maintained through weight sharing across the network trained on different rock-physics scenarios, enabling rapid evaluation of the impact changing the underlying rock-physics model. The DT is built on industry-strength open-source software: {\textquoteleft}JutulDarcy.jl{\textquoteleft} for fully coupled multiphase flow simulations and {\textquoteleft}JUDI.jl{\textquoteleft}, a seismic inversion package leveraging the {\textquoteleft}Devito{\textquoteleft} finite-difference framework. This computational foundation allows scalable integration of physics-based simulations and data assimilation across large reservoir models, while retaining flexibility to adapt to varying physical contexts such as the inclusion of pressure-dependence of the compressional wavespeed. The resulting DT not only delivers posterior distributions for the reservoir{\textquoteright}s state (pressure/saturation) conditioned on available observations but also enables rapid {\textquotedblleft}what-if{\textquotedblright} scenario analysis by drawing posterior samples across a range of physical contexts without retraining. This capability supports proactive storage management, optimization of injection operations, and improved assurance of storage conformance.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, GCS, Imaging, Inverse problems, permeability, reservoir simulation, rock physics, RTM, SEG, SPE, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEGSPE/2025/herrmann2025SEGSPEcua},
	author = {Abhinav Prakash Gahlot and Ipsita Bhar and Haoyun Li and Felix J. Herrmann}
}
@conference {herrmann2025AIDT4EScad,
	title = {Context-aware Digital Twin for Underground Storage},
	booktitle = {Artificial Intelligence and Digital Twins for Earth Systems 2025, Austin, TX},
	year = {2025},
	month = {9},
	keywords = {AIDT4ES, Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, GCS, Imaging, Inverse problems, permeability, reservoir simulation, rock physics, RTM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/AIDT4ES/2025/herrmann2025AIDT4EScad},
	author = {Abhinav Prakash Gahlot and Haoyun Li and Ipsita Bhar and Huseyin Tuna Erdinc and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@conference {herrmann2025IMSIcad,
	title = {Context-Aware Digital Twin for Underground Storage Operations and Decision Making},
	booktitle = {Data Assimilation and Inverse Problems for Digital Twins Workshop 205, IMSI, Chicago},
	year = {2025},
	month = {10},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, decision making, digital twin, experimental design, GCS, Imaging, Inverse problems, permeability, reservoir simulation, rock physics, RTM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/IMSI/2025/herrmann2025IMSIcad},
	author = {Abhinav Prakash Gahlot and Haoyun Li and Ipsita Bhar and Huseyin Tuna Erdinc and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@conference {li2025ML4SEISMICdsc,
	title = {Digital Shadow for CO2-based Enhanced Oil Recovery (CO2-EOR)},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {We present a Digital Shadow for CO2-based Enhanced Oil Recovery (CO2-EOR), a data-driven surrogate model that predicts reservoir dynamics by conditioning on time-lapse seismic observations. Built upon conditional normalizing flows, the Digital Shadow learns the posterior distribution of subsurface states{\textemdash}CO2 and oil saturation{\textemdash}conditioned on seismic data generated through coupled multiphase flow and rock-physics modeling. The framework integrates high-fidelity simulations with JutulDarcy.jl, nonlinear seismic forward modeling and imaging with JUDI.jl, and nonlinear rock-physics mappings to relate saturation changes to changes in the acoustic properties. Trained on 128 stochastic realizations derived from a North Sea permeability distribution, the model achieves accurate posterior samples for the saturation fields with high structural similarity to the ground truth. This work demonstrates how integrating differentiable physics with generative modeling enables seismic-informed monitoring of CO2 plume evolution and oil recovery, laying the foundation for a Digital Twin of CO2-based EOR operations.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, EOR, experimental design, FWI, GCS, Imaging, Inverse problems, ML4SEISMIC, permeability, reservoir simulation, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/li2025ML4SEISMICdsc},
	author = {Haoyun Li and Abhinav Prakash Gahlot and Olav Moyner and Felix J. Herrmann}
}
@conference {cirakman2025IMAGEesp,
	title = {Efficient and scalable posterior surrogate for seismic inversion via wavelet score-based generative models},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Bayesian inference, deep learning, generative model, IMAGE, Imaging, Inverse problems, power-scaling, RTM, score, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/cirakman2025IMAGEesp},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/cirakman2025IMAGEesp/IMAGE_Ege.pdf},
	author = {Ege Cirakman and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@unpublished {gahlot2025EAGEerd,
	title = {Enhancing robustness of Digital Shadow for CO 2  Storage Monitoring with Augmented Rock Physics Modeling},
	year = {2025},
	month = {6},
	keywords = {Amortized Variational Inference, augmentation, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, FWI, GCS, Imaging, Inverse problems, rock physics, RTM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2025/gahlot2025EAGEerd/abstract.html},
	author = {Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {park2025ML4SEISMICftn,
	title = {Fisher-Informed Training of Neural Operators for Reliable PDE Inversion},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Neural operators have shown strong performance for PDE-solution learning; however, their effectiveness in PDE-constrained optimization, such as inversion, remains limited, in part because inaccurately learned derivatives can mislead gradient-based updates. Standard training typically optimizes only the forward least-squares fit, so during iterative inversion the optimization variable can drift outside the training distribution, further degrading quality of derivative information and inversion performance. To address this limitation, we propose a training algorithm designed for inversion: the surrogate is trained not only to predict forward outputs but also to learn observation-relevant gradients, which leads to Fisher-information directed parameter updates. We evaluate forward and gradient accuracy, as well as the inversion trajectory, on problems governed by PDEs{\textemdash}Darcy flow and laminar (incompressible) Navier{\textendash}Stokes{\textemdash}which are relevant to porous-media fluid flow and energy-storage applications. Our results suggest that training for gradient fidelity with forward accuracy unlocks a pathway to reliable, efficient, neural operator{\textendash}based inversion.},
	keywords = {deep learning, derivatve-informed, Fisher-information, FNO, GCS, Inverse problems, ML4SEISMIC, permeability, reduced-order modeling, reservoir simulation, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/park2025ML4SEISMICftn},
	author = {Jeongjin Park and Grant Bruer and Huseyin Tuna Erdinc and Richard Rex Arockiasamy and Nisha Chandramoorthy and Felix J. Herrmann}
}
@conference {zeng2025IMAGEfwi,
	title = {Full-waveform variational inference with common-image gathers},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Bayesian inference, CIG, deep learning, diffusion models, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/zeng2025IMAGEfwi/IMAGE_Yunlin.pdf},
	author = {Yunlin Zeng and Huseyin Tuna Erdinc and Rafael Orozco and Felix J. Herrmann}
}
@conference {orozco2025SIAMisu,
	title = {Industry-Scale Uncertainty-Aware Full Waveform Inference with Generative Models},
	booktitle = {SIAM Conference on Computational Science and Engineering (CSE25)},
	year = {2025},
	note = {(SIAM CSE25, Dallas)},
	month = {03},
	abstract = {In this talk, we address the challenge of Bayesian sampling for ill-posed inverse problems involving expensive PDE forward operators. To tackle this, we propose the use of generative models and discuss three key challenges along with our solutions. First, we address the constraints of GPU memory by introducing patch-based training and memory-efficient invertible networks, enabling the handling of large-scale data. Second, we demonstrate that these models can be effectively trained using only prior data available from acoustic observations and borehole well data, making the approach practical for real-world applications. Third, we explore various strategies to enhance the reliability of posterior samples by incorporating physics-based constraints through the wave operator. We conclude by presenting experiments that showcase the capabilities of these methods in field-data Full Waveform Inversion (FWI) workflows, scaling up to industry-scale problems with large 2D (512x7000 degrees of freedom) and 3D models.},
	keywords = {Bayesian sampling, FWI, Generative models, Inverse problems, Normalizing flows, SIAM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMCSE/2025/orozco2025SIAMisu},
	author = {Rafael Orozco and Huseyin Tuna Erdinc and Mathias Louboutin and Felix J. Herrmann}
}
@conference {gahlot2025SIAMiac,
	title = {It{\textquoteright}s All in the Context: Sensitivity-Aware Digital Twins for Underground Storage},
	booktitle = {SIAM Conference on Mathematical \& Computational Issues in the Geosciences, Baton Rouge},
	year = {2025},
	month = {10},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, decision making, digital twin, experimental design, GCS, Imaging, Inverse problems, permeability, reservoir simulation, rock physics, RTM, SIAM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2025/gahlot2025SIAMiac},
	author = {Abhinav Prakash Gahlot and Ipsita Bhar and Felix J. Herrmann}
}
@conference {gahlot2025ML4SEISMICmrm,
	title = {Mitigating Rock-Physics Model Misspecification in Digital Shadows via Amortized Bayesian Inference},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Digital shadows for subsurface monitoring rely on simulation-based inference to map seismic observations to evolving reservoir states. However, when the simulations are generated using simplified or different rock physics models than those governing the observed data, model misspecification leads to biased posterior estimates and degraded uncertainty quantification. We address this challenge through Bayesian frameworks including rock-physics marginalization and a context-aware amortized inference using conditional normalizing flows. The framework learns a mapping from seismic responses to pressure and saturation while accounting for variability across different randomly drawn models for the rock-physics. To enhance sensitivity to fluid and stress effects, we also incorporate pressure-dependent rock physics into the seismic forward model and perform inference in the Radon domain of Common Image Gathers (CIGs) instead of conventional RTM images. Because fluids exhibit distinct angle-dependent signatures in AVA responses, Radon-transformed CIGs are expected to provide improved separation between pressure and saturation effects, leading to more accurate and physically consistent state estimates. Thus, it enables an uncertainty-aware, physics-informed digital shadows under rock-physics model mismatch.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, GCS, Imaging, Inverse problems, ML4SEISMIC, permeability, reservoir simulation, rock physics, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/gahlot2025ML4SEISMICmrm},
	author = {Abhinav Prakash Gahlot and Ipsita Bhar and Felix J. Herrmann}
}
@conference {cirakman2025ML4SEISMICpss,
	title = {Multiscale Wavelet Score-based Posterior Approximations for Seismic Inversion},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {We present a cascaded conditional wavelet score{\textendash}based posterior surrogate (CWSGM) for seismic inversion that generates samples of subsurface velocity fields conditioned on physics-derived summaries (e.g., RTM images). Through multi-scale wavelet-based whitening, we specifically address ill-conditioning of the velocity model{\textquoteright}s covariance (due to its fractal-like 1/f power spectrum), whose long range correlations hamper training neural networks to approximate the score function. This strategy improves the conditioning of the score-learning problem and accelerates both training and sampling. Experiments on the North Sea BG Model demonstrate that CWSGM accurately captures long-range geological correlations while reducing GPU memory usage by approximately 50\% and sampling time by 73\% compared to a single-scale vanilla score model. Overall, our approach enables efficient multi-scale generation of subsurface velocities at lower computational cost and provides a foundation for exploring alternative multiscale transforms that are more optimally aligned with seismic observations.},
	keywords = {Bayesian inference, deep learning, generative model, Imaging, Inverse problems, ML4SEISMIC, power-scaling, RTM, score, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/cirakman2025ML4SEISMICpss},
	author = {Ege Cirakman and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@conference {erdinc2025ML4SEISMICpbi,
	title = {Power-scaled Bayesian inference for velocity-model estimation},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Score-based generative models have emerged as powerful tools for conditional generation in Bayesian inference. While promising, a common criticism of these methods is their reliance on strong, structured priors, which can dominate the inference process and limit the network{\textquoteright}s dependence on observed data. To address this issue, we propose a modification to the generative sampling algorithm that incorporates power scaling of both priors and likelihoods. Our approach enables flexible control over the relative influence of the prior and likelihood without requiring retraining for different scaling configurations. We demonstrate this in the context of synthesizing seismic velocity models conditioned on imaged seismic data. By sampling from intermediate power posteriors, our method naturally supports sensitivity analysis and allows us to assess how varying prior and likelihood weights determines the behavior of the posterior. Through a comprehensive set of experiments, we examine the impact of the power parameters in three scenarios: scaling only the prior, scaling only the likelihood, and scaling both simultaneously. The results show that increasing the likelihood power up to a certain threshold improves the fidelity of posterior samples to the conditioning data, while reducing prior power increases structural diversity in the generated models. Furthermore, moderate likelihood scaling leads to reduced shot data residuals, demonstrating its effectiveness for posterior refinement.},
	keywords = {Bayesian inference, deep learning, generative model, Imaging, Inverse problems, ML4SEISMIC, power-scaling, RTM, score, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/erdinc2025ML4SEISMICpbi},
	author = {Huseyin Tuna Erdinc and Yunlin Zeng and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {erdinc2025IMAGEpbi,
	title = {Power-scaled Bayesian inference with score-based generative models},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Bayesian inference, deep learning, generative model, IMAGE, Imaging, Inverse problems, power-scaling, RTM, score, SEG, Summary Statistics, Uncertainty quantification, WISE},
	doi = {10.48550/arXiv.2504.10807},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/erdinc2025IMAGEpbi},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/erdinc2025IMAGEpbi/IMAGE_Tuna.pdf},
	author = {Huseyin Tuna Erdinc and Yunlin Zeng and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {henriksson2025ML4SEISMICpss,
	title = {Predicting Subsurface CO2 Saturation using Late Fusion of Seismic and Streaming Well Data},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Determining subsurface flow of CO2 in porous rock formations is a challenging task especially when it involves intergration of multimodal data that are collected at disparate timescales. In this work, we investigate how data fushion can be used to integrate multimodal data consisting on infrequently collected active-source seismic surveys and continuous streaming data of saturation measurements collected at monitoring wells. For the purpose, we propose a data fusion framework based on late fusion, which combines seismic images, computed from seismic surveys, with time-series data collected at the wells. By integrating the spatial information from seismic data with high-resolution but sparce spatial-temporal patterns from wells, we aim to better approximate the complex CO2 flow patterns.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, GCS, Imaging, Inverse problems, late fusion, ML4SEISMIC, permeability, reservoir simulation, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/henriksson2025ML4SEISMICpss},
	author = {Victor Henriksson and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@unpublished {deng2025EAGEpjrm,
	title = {Probabilistic Joint Recovery Method for CO2 Plume Monitoring},
	year = {2025},
	month = {6},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, GCS, igm, image generative model, Imaging, Inverse problems, JRM, Summary Statistics, Uncertainty quantification},
	doi = {10.48550/arXiv.2501.18761},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2025/deng2025EAGEpjrm/EAGE_Venice.pdf},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {park2025IMAGErdn,
	title = {A reduced-order derivative-informed neural operator for subsurface fluid-flow},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {deep learning, derivatve-informed, Fisher-information, FNO, GCS, IMAGE, Inverse problems, permeability, reduced-order modeling, reservoir simulation, SEG, Uncertainty quantification},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/park2025IMAGErdn/IMAGE_Jayjay.pdf},
	author = {Jeongjin Park and Grant Bruer and Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {li2025ML4SEISMICric,
	title = {Risk-Aware Injectivity Control for Energy Storage},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {We introduce a digital-twin{\textendash}driven framework for real-time injectivity control that maximizes injected CO2 while enforcing reservoir safety. The forward model is a multiphase flow simulator evolving reservoir states under injectivity controls q; time-lapse seismic acts as the observation operator to reduce uncertainty of the the state (reservoir{\textquoteright}s saturation/pressure). Risk is handled via two complementary metrics: the Probability of Failure (POF) for exceedance likelihood and the less conservative CVaR (superquantile) for tail severity. For the optimization, we employ smooth surrogates{\textemdash}a logistic exceedance rate for POF and the Rockafellar{\textendash}Uryasev formulation for CVaR{\textemdash}enabling gradient-based control with constraints. Within a finite-horizon Model Predictive Control (MPC) loop, we optimize a trajectory per posterior sample and aggregate the ensemble of optimal rates into an empirical (KDE-kernel) Cumulative Density Function (CDF) with binomial confidence bands; the final controlled injectivity q is chosen as the largest rate whose upper confidence bound satisfies the target risk level. Case studies demonstrate that POF-constrained optimization is more conservative than CVaR-based optimization, In addition, sensitivity of the policy to the CVaR tail level, α, is reduced compared to POF{\textquoteright}s parameter sensitivity, allowing for adaptive, uncertainty-aware control that balances injectivity and fracture risk. The proposed framework also unifies time-lapse seismic-informed inference, risk metrics, and MPC into a practical approach for safe high-throughput underground energy storage.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, EOR, experimental design, FWI, GCS, Imaging, Inverse problems, ML4SEISMIC, permeability, reservoir simulation, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/li2025ML4SEISMICric},
	author = {Haoyun Li and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {herrmann2025EAGEssf,
	title = {SAGE {\textemdash} Subsurface foundational model with AI-driven Geostatistical Extraction},
	booktitle = {EAGE Workshop},
	year = {2025},
	month = {6},
	abstract = {In this talk, we introduce a novel diffusion-based generative modeling approach for synthesizing high-fidelity subsurface velocity models. Once trained, this foundational model serves as a prior or a generative tool, enabling the sampling of velocity models that closely match the statistical distribution of geologically relevant Earth models. To achieve this, we leverage geostatistical information derived from curated datasets provided by the UK National Data Repository. Our training set comprises check-shot-corrected migrated images intersected by well logs. Numerical experiments on multiple synthetic datasets, including the Compass model and Synthoseis, demonstrate the model{\textquoteright}s ability to generate realistic subsurface velocity models. This capability offers a data-driven prior for full-waveform inversion and facilitates the generation of training samples for amortized neural networks to improve full-waveform inference.},
	keywords = {Bayesian inference, deep learning, EAGE, foundation models, full waveform inference, generative model, Imaging, Inverse problems, RTM, score, Summary Statistics, UK-NDR, Uncertainty quantification},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2025/herrmann2025EAGEssf/EAGE_WS22_Foundation_Herrmann.mp4},
	author = {Huseyin Tuna Erdinc and Thales Souza and Felix J. Herrmann}
}
@conference {erdinc2025ML4SEISMICspm,
	title = {SAGE - Subsurface modeling with AI-driven Geostatistical Extraction and evaluation on North Sea Data},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Traditional machine learning based approaches often depend on large, high-quality and complete datasets of 2D Earth propety models, which can be difficult to obtain in subsurface applications. In this study, we leverage score-based generative models to synthesize high-fidelity geophysical properties (velocity, density, etc.) trained on a combination of sparse but tied well logs and seismic lines without relying on densely sampled velocity models and adress the sampling-density differences by enabling coherent integration of these complementary sources of information. With experiments on multiple synthetic datasets from subsurface models featuring diverse geological structures (e.g., faults, salt bodies), we demonstrate that our approach can accurately capture long-range geological correlations and align well with unseen ground-truth properties. Finally, we highlight the potential of our method to generalize to field data by conducting fine-tuning on a curated dataset derived from real well-log and seismic data currated from the UK Data Repository for the North Sea. This study represents an important step toward the development of foundational models for inverting physical properties and provides inputs for applications such as full-waveform inference (WISE/ASPIRE), supervised learning algorithms, and enhanced seismic-based subsurface modeling.},
	keywords = {Bayesian inference, deep learning, generative model, Imaging, Inverse problems, ML4SEISMIC, North-sea data, power-scaling, RTM, score, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/erdinc2025ML4SEISMICspm},
	author = {Huseyin Tuna Erdinc and Ipsita Bhar and Thales Souza and Rafael Orozco and Felix J. Herrmann}
}
@article {bruer2024smpd,
	title = {Seismic monitoring of CO2 plume dynamics using ensemble Kalman filtering},
	journal = {Transactions on Geoscience and Remote Sensing},
	year = {2025},
	note = {(Accepted in Transactions on Geoscience and Remote Sensing)},
	month = {5},
	abstract = {Monitoring carbon dioxide (CO2) injected and stored in subsurface reservoirs is critical for avoiding failure scenarios and enables real-time optimization of CO2 injection rates. Sequential Bayesian data assimilation (DA) is a statistical method for combining information over time from multiple sources to estimate a hidden state, such as the spread of the subsurface CO2 plume. An example of scalable and efficient sequential Bayesian DA is the ensemble Kalman filter (EnKF). We improve upon existing DA literature in the seismic-CO2 monitoring domain by applying this scalable DA algorithm to a high-dimensional CO2 reservoir using two-phase flow dynamics and time-lapse full waveform seismic data with a realistic surface-seismic survey design. We show more accurate estimates of the CO2 saturation field using the EnKF compared to using either the seismic data or the fluid physics alone. Furthermore, we test a range of values for the EnKF hyperparameters and give guidance on their selection for seismic CO2 reservoir monitoring.},
	keywords = {Ensebmle Kalman Filter, GCS, Inverse problems, non-linear dynamical systems, seismic},
	doi = {10.48550/arXiv.2409.05193},
	author = {Grant Bruer and Abhinav Prakash Gahlot and Edmond Chow and Felix J. Herrmann}
}
@conference {gahlot2025IMAGEsrp,
	title = {Sensitivity-aware rock physics enhanced digital shadow for underground-energy storage monitoring},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, GCS, IMAGE, Imaging, Inverse problems, permeability, reservoir simulation, rock physics, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	doi = {10.48550/arXiv.2504.14405},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/gahlot2025IMAGEsrp},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/gahlot2025IMAGEsrp/IMAGE_Abhinav.pdf},
	author = {Abhinav Prakash Gahlot and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@conference {deng2025ML4SEISMICtfi,
	title = {Time-lapse full-waveform inversion with uncertainty quantification},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Reliable management of underground energy storage systems, such as underground compressed Hydrogene or Air storage, rely on semi-continuous monitoring and rigorous quantification of subsurface uncertainty. Time-lapse seismic imaging provides valuable insights into fluid migration and storage integrity. However, traditional inversion techniques{\textemdash}particularly full-waveform inversion (FWI){\textemdash}are inherently ill-posed and deterministic, limiting their applicability for uncertainty-aware decision-making. The Joint Recovery Method (JRM) improves consistency across multiple surveys by jointly reconstructing shared structures, but does not capture uncertainty. We introduce the Probabilistic Joint Recovery Method (πJRM), which embeds uncertainty estimation within a joint inversion framework. πJRM leverages a shared generative model to infer wave-equation{\textendash}based posterior distributions for each monitoring survey, enabling probabilistic interpretation of time-lapse changes. Synthetic experiments demonstrate that πJRM accurately recovers dynamic reservoir evolution and provides uncertainty-aware reconstructions, offering a principled foundation for safe, efficient management of subsurface energy storage operations.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, GCS, igm, image generative model, Imaging, Inverse problems, jrm pjrm, ML4SEISMIC, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/deng2025ML4SEISMICtfi},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {deng2025IMAGEtfi,
	title = {Time-lapse full-waveform inversion with uncertainty quantification},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2025},
	month = {8},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, GCS, igm, IMAGE, image generative model, Imaging, Inverse problems, JRM, SEG, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/deng2025IMAGEtfi},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2025/deng2025IMAGEtfi/IMAGE_Venice.pdf},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@conference {herrmann2025SciMLtfm,
	title = {Towards foundation models for subsurface priors and posteriors},
	booktitle = {Workshop on Scientific Machine Learning 2025, Austin, TX},
	year = {2025},
	month = {9},
	keywords = {Bayesian inference, deep learning, foundation models, full waveform inference, generative model, Imaging, Inverse problems, RTM, SciML, score, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SciML/2025/herrmann2025SciMLtfm},
	author = {Huseyin Tuna Erdinc and Thales Souza and Shiqin Zeng and Rafael Orozco and Felix J. Herrmann}
}
@article {gahlot2024uads,
	title = {An uncertainty-aware Digital Shadow for underground multimodal CO2 storage monitoring},
	journal = {Geophysical Journal International},
	year = {2025},
	note = {(Geophysical Journal International)},
	month = {5},
	abstract = {As a society, we are faced with important challenges to combat climate change. Geological Carbon Storage (GCS), during which gigatonnes of super-critical CO2 are stored underground, is arguably the only scalable net-negative CO2-emission technology that is available. While promising, subsurface complexities and heterogeneity of reservoir properties demand a systematic approach to quantify uncertainty when optimizing production and mitigating storage risks, which include assurances of Containment and Conformance of injected supercritical CO2. As a first step towards the design and implementation of a Digital Twin for monitoring and control of underground storage operations, a machine-learning-based data-assimilation framework is introduced and validated on carefully designed realistic numerical simulations. Because our implementation is based on Bayesian inference, but does not yet support control and decision-making, we coin our approach an uncertainty-aware Digital Shadow. To characterize the posterior distribution for the state of CO2 plumes (its CO2 concentration and pressure), conditioned on multi-modal time-lapse data, the envisioned Shadow combines techniques from Simulation-Based Inference (SBI) and Ensemble Bayesian Filtering to establish probabilistic baselines and assimilate multi-modal data for GCS problems that are challenged by large degrees of freedom, nonlinear multiphysics, non-Gaussianity, and computationally expensive to evaluate fluid-flow and seismic simulations. To enable SBI for dynamic systems, a recursive scheme is proposed where the Digital Shadow{\textquoteright}s neural networks are trained on simulated ensembles for their state and observed data (well and/or seismic). Once training is completed, the system{\textquoteright}s state is inferred when time-lapse field data becomes available. Contrary to ensemble Kalman filtering, corrections to the predicted simulated states are not based on linear updates, but instead follow during the Analysis step of Bayesian filtering from a prior-to-posterior mapping through the latent space of a nonlinear transform. Starting from a probabilistic model for the permeability field, derived from a baseline surface-seismic survey, the proposed Digital Shadow is validated on unseen simulated ground-truth time-lapse data. In this computational study, we observe that a lack of knowledge on the permeability field can be factored into the Digital Shadow{\textquoteright}s uncertainty quantification. Our results also indicate that the highest reconstruction quality is achieved when the state of the CO2 plume is conditioned on both time-lapse seismic data and wellbore measurements. Despite the incomplete knowledge of the permeability field, the proposed Digital Shadow was able to accurately track the unseen physical state of the subsurface throughout the duration of a realistic CO2 injection project. To the best of our knowledge, this work represents the first proof-of-concept of an uncertainty-aware, in-principle scalable, Digital Shadow that captures the uncertainty arising from unknown reservoir properties and noisy observations. This framework provides a foundation for the development of a Digital Twin aimed at mitigating risks and optimizing the management of underground storage projects.},
	keywords = {Bayesian inference, conditional normalizing flows, deep learning, digital twin, GCS, Inverse problems, sequential Bayes, Summary Statistics, Uncertainty quantification},
	doi = {10.1093/gji/ggaf176},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2024/gahlot2024uads/paper.html},
	author = {Abhinav Prakash Gahlot and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@conference {park2025ML4SEISMICvmb,
	title = {Velocity Model Building with Jacobian-Informed Neural Operators},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	keywords = {deep learning, derivatve-informed, FNO, GCS, Inverse problems, ML4SEISMIC, permeability, reduced-order modeling, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/park2025ML4SEISMICvmb},
	author = {Jeongjin Park and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@article {yin2024wiser,
	title = {WISER: multimodal variational inference for full-waveform inversion without dimensionality reduction},
	journal = {Geophysics},
	volume = {90},
	year = {2025},
	note = {(GEOPHYSICS)},
	month = {03},
	abstract = {We present a semi-amortized variational inference framework designed for computationally feasible uncertainty quantification in 2D full-waveform inversion to explore the multimodal posterior distribution without dimensionality reduction. The framework is called WISER, short for full-Waveform variational Inference via Subsurface Extensions with Refinements. WISER leverages the power of generative artificial intelligence to perform approximate amortized inference that is low-cost albeit showing an amortization gap. This gap is closed through non-amortized refinements that make frugal use of acoustic wave physics. Case studies illustrate that WISER is capable of full-resolution, computationally feasible, and reliable uncertainty estimates of velocity models and imaged reflectivities.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, MVA, Summary Statistics, Uncertainty quantification, WISE, WISER},
	doi = {10.1190/geo2024-0483.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2024/yin2024wiser/WISER.html},
	author = {Ziyi Yin and Rafael Orozco and Felix J. Herrmann}
}
@conference {orozco2024IMAGEbeacon,
	title = {BEACON: Bayesian Experimental design Acceleration with Conditional Normalizing flows - a case study in optimal monitor well placement for CO2 sequestration},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2024},
	month = {8},
	abstract = {CO2 sequestration is a crucial engineering solution for mitigating climate change. However, the uncertain nature of reservoir properties, necessitates rigorous monitoring of CO2 plumes to prevent risks such as leakage, induced seismicity, or breaching licensed boundaries. To address this, project managers use borehole wells for direct CO2 and pressure monitoring at specific locations. Given the high costs associated with drilling, it is crucial to strategically place a limited number of wells to ensure maximally effective monitoring within budgetary constraints. Our approach for selecting well locations integrates fluid-flow solvers for forecasting plume trajectories with generative neural networks for plume inference uncertainty. Our methodology is extensible to three-dimensional domains and is developed within a Bayesian framework for optimal experimental design, ensuring scalability and mathematical optimality. We use a realistic case study to verify these claims by demonstrating our method{\textquoteright}s application in a large scale domains and optimal performance as compared to baseline well placement.},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, deep learning, GCS, IMAGE, Inverse problems, OED, SEG, Uncertainty quantification},
	doi = {10.48550/arXiv.2404.00075},
	author = {Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {herrmann2024ML4SEISMICdtg,
	title = {A Digital Twin for Geological Carbon Storage with Controlled Injectivity},
	year = {2024},
	month = {11},
	abstract = {We present an uncertainty-aware Digital Twin (DT) for geologic carbon storage (GCS), capable of handling multimodal time-lapse data and controlling CO 2  injectivity to mitigate reservoir fracturing risks. In GCS, DT represents virtual replicas of subsurface systems that incorporate real-time data and advanced generative Artificial Intelligence (genAI) techniques, including neural posterior density estimation via simulation-based inference and sequential Bayesian inference. These methods enable the effective monitoring and control of CO 2  storage projects, addressing challenges such as subsurface complexity, operational optimization, and risk mitigation. By integrating diverse monitoring data, e.g., geophysical well observations and imaged seismic, DT can bridge the gaps between seemingly distinct fields like geophysics and reservoir engineering. In addition, the recent advancements in genAI also facilitate DT with principled uncertainty quantification. Through recursive training and inference, DT utilizes simulated current state samples, e.g., CO 2  saturation, paired with corresponding geophysical field observations to train its neural networks and enable posterior sampling upon receiving new field data. However, it lacks decision-making and control capabilities, which is necessary for full DT functionality. This study aims to demonstrate how DT can inform decision-making processes to prevent risks such as cap rock fracturing during CO 2  storage operations.},
	keywords = {Amortized Variational Inference, augmentation, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, FWI, Imaging, Inverse problems, ML4SEISMIC, rock physics, RTM, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/herrmann2024ML4SEISMICdtg},
	author = {Abhinav Prakash Gahlot and Haoyun Li and Ziyi Yin and Rafael Orozco and Felix J. Herrmann}
}
@presentation {gahlot2024ICLdtg,
	title = {Digital Twins in the era of generative AI - Application to Geological CO2 Storage},
	year = {2024},
	month = {6},
	abstract = {Our industry is experiencing significant changes due to AI and the challenges of the energy transition. While some view these changes as threats, recent advances in AI offer unique opportunities, especially in the context of Digital Twins for subsurface monitoring and control. IBM defines "A digital twin is a virtual representation of an object or system that spans its lifecycle, is updated from real-time data, and uses simulation, machine learning and reasoning to help decision-making." During this talk, I will explore these concepts and their significance in addressing the challenges of monitoring \& control of geological CO2 storage projects. This talk also aims to illustrate how Digital Twins can serve as a platform to integrate the seemingly disparate and siloed fields of geophysics and reservoir engineering.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, control, data assimilation, deep learning, digital twin, FWI, GCS, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICL/2024/gahlot2024ICLdtg},
	author = {Abhinav Prakash Gahlot and Rafael Orozco and Haoyun Li and Huseyin Tuna Erdinc and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@conference {zeng2024IMAGEefw,
	title = {Enhancing Full-Waveform Variational Inference through Stochastic Resampling and Data Augmentation},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2024},
	month = {8},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slimgroup.github.io/IMAGE2024/Yunlin_Zeng2024SEG/paper.html},
	author = {Yunlin Zeng and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@presentation {zeng2024ML4SEISMICefv,
	title = {Enhancing Full-Waveform Variational Inference through Stochastic Resampling},
	year = {2024},
	month = {11},
	abstract = {Recent developments in simulation-based inference, like the full-waveform variational inference via subsurface extensions (WISE), enable rapid online estimation of subsurface velocities by leveraging pre-trained models. To achieve this, WISE employs subsurface-offset common image gathers to convert shot data into physics-informed summary statistics. While common image gathers effectively retain critical information even when initial velocity estimates are inaccurate, WISE{\textquoteright}s performance still depends on the assumption that the initial migration-velocity model is a single 1D velocity model. In this work, we present experiments using both 1D and 2D velocity models and develop a stochastic resampling method to generate variations of initial migration-velocity models. This technique allows us to systematically infer alternative velocity models that are consistent with the observed data, while enhancing the posterior sample quality and reducing dependency on the initial velocity model compared to the standard WISE approach.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/zeng2024ML4SEISMICefv},
	author = {Yunlin Zeng and Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {zeng2024ML4SEISMICepu,
	title = {Enhancing Performance with Uncertainty Estimation in Geological Carbon Storage Leakage Detection from Time-Lapse Seismic Data},
	year = {2024},
	month = {11},
	abstract = {Ensuring CO 2  non-leakage is a critical aspect of Geological Carbon Storage (GCS). While previous approaches that develop deep neural networks demonstrate promising automatic leakage detection and potential cost reduction in dataset collection from time-lapse seismic images, they face challenges, such as a limited ability to reduce false alarms in CO 2  leakage instances and a lack of uncertainty analysis in detection results. This paper introduced a framework aimed at enhancing the deep neural network model{\textquoteright}s ability to detect GCS leakage risk through a multi-criteria decision-making (MCDM)-based ensemble algorithm. The proposed method can improve the detection ability of leakage cases while accurately distinguishing them from non-leakage instances. Furthermore, the proposed uncertainty analysis method utilizing Monte Carlo (MC) dropout technique efficiently identifies misclassified non-leakage cases and categorizes them as undetermined for further investigation. This comprehensive approach enhances both the reliability and performance of the model in detecting GCS leakage risks.},
	keywords = {CAM, CCS, classification, explainability, GCS, Imaging, Inverse problems, JRM, ML4SEISMIC, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/zeng2024ML4SEISMICepu},
	author = {Shiqin Zeng and Huseyin Tuna Erdinc and Ziyi Yin and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {rex2024ML4SEISMICfca,
	title = {FNO-charged ASPIRE},
	year = {2024},
	month = {11},
	abstract = {During this talk, we will demonstrate how extended re-migrations{\textemdash}i.e, formation of subsurface-offset Common-Image Gathers (CIGs) for a new velocity model, can be avoided altogether by training Fourier Neural Operators during training of ASPIRE {\textemdash} Amortized posteriors with Summaries that are Physics-based and Iteratively REfined. In this approach, FNOs are trained as surrogates capable of mapping CIGs for one migration-velocity model to the other. The approach is computationally feasible because it uses the same training set as used during ASPIRE. As a result, additional training costs are small and the inference costs are reduced by a factor equal to the number of ASPIRE refinements.},
	keywords = {deep learning, FNO, hierarchical tucker tensor, Inverse problems, kronecker product, ML4SEISMIC, SLIM, two-phase flow},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/rex2024ML4SEISMICfca},
	author = {Richard Rex and Yunlin Zeng and Ziyi Yin and Rafael Orozco and Felix J. Herrmann}
}
@presentation {zeng2024ML4SEISMICiic,
	title = {Image Impeccable Challenge: An Effective Machine Learning Denoising Method for 3D Seismic Volumes},
	year = {2024},
	month = {11},
	abstract = {Seismic denoising is essential for enhancing the clarity, accuracy, and reliability of seismic data. Traditional seismic denoising methods, while effective for specific types of noise, often rely on well-established mathematical techniques that can be time-consuming, require manual tuning, and struggle with more complex noise patterns. Leveraging the 500 paired synthetic seismic datasets provided by the Think Onward community, we incorporate a 3D U-Net deep learning model with residual blocks and spatial attention to capture both local and global features for the seismic denoising task. During training, we apply the Laplacian operator to preserve edge details, followed by the Structural Similarity Index Measure (SSIM) loss to fine-tune the model, effectively removing concurrent noise and recovering the original seismic information. The resulting individual model achieves an SSIM of 0.99 compared to the ground truth seismic data. Additionally, we implement Langevin dynamics and Equivariant Bootstrapping techniques to estimate uncertainty during the training and inference phases, further improving the robustness of the denoising process.},
	keywords = {CAM, CCS, classification, explainability, GCS, Imaging, Inverse problems, JRM, ML4SEISMIC, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/zeng2024ML4SEISMICiic},
	author = {Shiqin Zeng and Rafael Orozco and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@article {orozco2023invnet,
	title = {InvertibleNetworks.jl: A Julia package for scalable normalizing flows},
	journal = {Journal of Open Source Software},
	volume = {9},
	year = {2024},
	month = {7},
	abstract = {InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging the inherent invertibility of normalizing flows, which significantly reduces memory requirements during backpropagation compared to existing normalizing flow packages that rely on automatic differentiation frameworks. InvertibleNetworks.jl has been adapted for diverse applications, including seismic imaging, medical imaging, and CO2 monitoring, demonstrating its effectiveness in learning high-dimensional distributions.},
	keywords = {Bayesian inference, computing, conditional normalizing flows, deep learning, HPC, Inverse problems, memory, Normalizing flows, software, Uncertainty quantification},
	doi = {10.21105/joss.06554},
	url = {https://doi.org/10.21105/joss.06554},
	author = {Rafael Orozco and Philipp A. Witte and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Bas Peters and Felix J. Herrmann}
}
@presentation {orozco2024ML4SEISMICmev,
	title = {Machine-learning enabled velocity-model building with uncertainty quantification},
	year = {2024},
	month = {11},
	abstract = {Accurately characterizing subsurface properties is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional characterization methods such as Full-Waveform Inversion (FWI) represent powerful tools but often struggle with the inherent complexities of the inverse problem, including noise, limited bandwidth and aperture of data, limited azimuth and computational constraints. To address these challenges, we propose a scalable methodology that integrates generative modeling with physics-informed summary statistics, making it suitable for complicated imaging problems potentially including field datasets. Our approach leverages the power of conditional diffusion networks, and methodologically incorporates physics in the form of summary statistics, allowing for the computationally efficient generation of Bayesian posterior samples that offer an useful assessment of uncertainty of the inferred migration-velocity models. To validate our approach, we introduce a battery of tests that measure the quality of the image estimates as well as the quality of the inferred uncertainties. With modern synthetic datasets, we maximally leverage the advantages of using subsurface-offset Common Image Gathers (CIGs) as the conditioning observable. Next, we tackle the challenging SEAM salt model that requires incorporating salt flooding into our approach based on the iterative refinements of ASPIRE {\textemdash} Amortized posteriors with Summaries that are Physics-based and Iteratively REfined.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, diffusion models, FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/orozco2024ML4SEISMICmev},
	author = {Rafael Orozco and Huseyin Tuna Erdinc and Thales Souza and Yunlin Zeng and Ziyi Yin and Felix J. Herrmann}
}
@conference {orozco2024IPMSnwi,
	title = {Neural wave-based imaging with amortized uncertainty quantification},
	booktitle = {Inverse Problems: Modelling and Simulation},
	year = {2024},
	month = {5},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, IPMS, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/IPMS/2024/orozco2024IPMSnwi},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/IPMS/2024/orozco2024IPMSnwi/herrmann2024.pdf},
	author = {Rafael Orozco and Ziyi Yin and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {orozco2024ICLnwi,
	title = {Neural wave-based imaging with amortized uncertainty quantification},
	year = {2024},
	month = {6},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICL/2024/orozco2024ICLnwi},
	author = {Rafael Orozco and Ziyi Yin and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {gahlot2024ML4SEISMICosm,
	title = {Optimizing CO2 Storage Monitoring with Enhanced Rock Physics Modeling},
	year = {2024},
	month = {11},
	abstract = {Based on the latest data-assimilation and machine-learning techniques, Digital Twins (DTs) have shown promise for high-fidelity monitoring and control of underground CO2​ storage. While the use of these techniques have important advantages, they do rely on certain assumptions. If these assumptions are not met, the DT{\textquoteright}s neural networks may no longer infer the state of the CO2 plume (pressure/saturation) accurately. By augmenting the forecast ensemble, we address this issue.},
	keywords = {Amortized Variational Inference, augmentation, Bayesian inference, conditional normalizing flows, data assimilation, deep learning, FWI, Imaging, Inverse problems, ML4SEISMIC, rock physics, RTM, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/gahlot2024ML4SEISMICosm},
	author = {Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {park2024ML4SEISMICpbi,
	title = {Physical Bayesian Inference for Two-Phase Flow Problems},
	year = {2024},
	month = {11},
	abstract = {Previous research on surrogate modeling of multiphase flow systems has shown that even models with low generalization error in forward predictions can generate posterior estimates that are out of distribution and physically unrealistic. To address this, we propose a regularization method that leverages the Fisher Information Matrix (FIM) to guide the training process. By integrating the FIM into a differentiable optimization framework, we aim to improve the reliability of surrogate models, such as Fourier Neural Operators (FNO), for both forward predictions and posterior inference. Our experiments on benchmark problems, including the Lorenz-63 system and Navier-Stokes equations, demonstrate that our approach significantly enhances physical consistency throughout time evolution, keeping predictions within the correct spatial distribution. Looking ahead, we plan to extend our framework to more complex applications, such as Geological Carbon Storage, with an emphasis on scaling FIM computations for high-dimensional problems.},
	keywords = {Bayesian inference, deep learning, Fisher Information Matrix, FNO, Inverse problems, ML4SEISMIC, SLIM, two-phase flow, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/park2024ML4SEISMICpbi},
	author = {Jeongjin Park and Huseyin Tuna Erdinc and Haoyun Li and Richard Rex and Nisha Chandramoorthy and Felix J. Herrmann}
}
@presentation {deng2024ML4SEISMICpjr,
	title = {Probabilistic Joint Recovery Method for CO2 plume monitoring},
	year = {2024},
	month = {11},
	abstract = {Accurately predicting fluid flow patterns in Carbon Capture and Storage (CCS) is a challenging task, particularly due to uncertainties in CO 2  plume dynamics and reservoir properties. While previous deterministic methods such as the Joint Recovery Method (JRM) have provided valuable insights, their effectiveness is limited as tools for decision-making since they do not communicate uncertainty. To address this, we propose a Probabilistic Joint Recovery Method (PJRM) that computes the posterior distribution at each monitoring survey while leveraging the shared structure among surveys through a common generative model. By efficiently computing posterior distributions for each monitoring survey, this method aims to provide valuable uncertainty information to decision-makers in CCS projects, augmenting their workflow with principled risk minimization.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, FWI, igm, image generative model, Imaging, Inverse problems, JRM, ML4SEISMIC, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/deng2024ML4SEISMICpjr},
	author = {Zijun Deng and Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {li2024ML4SEISMICrps,
	title = {Reconstructing Permeability and Saturation in Reservoir Simulation Using Diffusion PDE Models},
	year = {2024},
	month = {11},
	abstract = {This study explores the application of a diffusion partial differential equation (PDE) model for reservoir simulation, particularly aimed at reconstructing permeability and saturation fields within a saline aquifer. Focusing on pairs of input permeability and output saturation, the model is trained to capture the underlying dynamics governing fluid flow in porous media. Post-training, the model is capable of inferring or recovering the complete permeability and saturation distributions when provided with limited vertical pixel data of permeability and saturation. This approach offers a novel pathway for enhancing the resolution of subsurface characteristics, contributing to more accurate predictions in reservoir engineering and carbon storage simulations.},
	keywords = {augmentation, Bayesian inference, deep learning, diffusion models, Inverse problems, ML4SEISMIC, SLIM, Summary Statistics, two-phase flow, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/li2024ML4SEISMICrps},
	author = {Haoyun Li and Shiqin Zeng and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {erdinc2024ML4SEISMICsfm,
	title = {SAGE {\textendash} Subsurface foundational model with AI-driven Geostatical Extraction},
	year = {2024},
	month = {11},
	abstract = {In this study, we present a novel approach for synthesizing diverse subsurface velocity models using diffusion-based generative models. Traditional methods often depend on large, high-quality datasets of 2D velocity models, which can be difficult to obtain in subsurface applications. In contrast, our method leverages incomplete well and seismic data to generate high-fidelity velocity samples without requiring fully sampled training datasets.The results demonstrate that the generative model accurately captures long-range geological structures and aligns well with unseen ground-truth velocity models. Furthermore, it is shown that the diversity of generated velocity models can be increased through prior guidance in the training phase, and model uncertainties can be reduced with well conditioning during inference.Experiments conducted with multiple datasets (BG, Synthoseis, and North Sea data) and velocity models featuring various geological structures (e.g., faults, salt bodies) suggest that our approach facilitates realistic subsurface velocity synthesis, providing valuable inputs for full-waveform inversion and enhancing seismic-based subsurface modeling.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, diffusion models, FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/erdinc2024ML4SEISMICsfm},
	author = {Huseyin Tuna Erdinc and Rafael Orozco and Felix J. Herrmann}
}
@presentation {bruer2024ML4SEISMICsmp,
	title = {Seismic monitoring of CO2 plume dynamics using ensemble Kalman filtering},
	year = {2024},
	month = {11},
	abstract = {Monitoring CO 2  injected and stored in subsurface reservoirs is critical for avoiding failure scenarios and enables real-time optimization of CO 2  injection rates. Sequential Bayesian data assimilation (DA) is a statistical method for combining information over time from multiple sources to estimate a hidden state, such as the spread of the subsurface CO 2  plume. An example of scalable and efficient sequential Bayesian DA is the ensemble Kalman filter (EnKF). We improve upon existing DA literature in the seismic-CO 2  monitoring domain by applying this scalable DA algorithm to a high-dimensional CO 2  reservoir using two-phase flow dynamics and time-lapse full waveform seismic data with a realistic surface-seismic survey design. We show more accurate estimates of the CO 2  saturation field using the EnKF compared to using either the seismic data or the fluid physics alone. Furthermore, we test a range of values for the EnKF hyperparameters and give guidance on their selection for seismic CO 2  reservoir monitoring.},
	keywords = {Bayesian inference, data assimilation, ensemble Kalman filter, FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SLIM, two-phase flow, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/bruer2024ML4SEISMICsmp},
	author = {Grant Bruer and Abhinav Prakash Gahlot and Edmond Chow and Felix J. Herrmann}
}
@presentation {bhar2024ML4SEISMICshs,
	title = {Sensitivity of Horizontal shear waves on Geological Carbon Storage},
	year = {2024},
	month = {11},
	abstract = {With the growing focus on Carbon Capture and Storage (CCS) activities, the significance of shear wave velocity (Vs) in monitoring CO2 is becoming increasingly important. Shear waves are instrumental in detecting CO2 leakage, evaluating CCS-induced seismicity, and identifying caprock failure. According to Biot-Gassmann rock physics models, changes in seismic velocity are expected during CO2 injection. This work specifically focuses on the horizontal component of shear wave velocity (Vsh). Shear (Sh) waves are more sensitive to density variations than P-wave or Sv wave velocities, leading us to anticipate changes in Sh velocity as CO2 saturation increases. While P-wave velocity tends to decrease with supercritical CO2 injection, the investigation of its effects on Sh waves presents a particularly compelling area of study. Therefore, we simulated the wave equation incorporating both P-wave and Sh wave velocities to better understand their impacts on imaging and CO2 injection processes.},
	keywords = {FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SH wave, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/bhar2024ML4SEISMICshs},
	author = {Ipsita Bhar and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@presentation {rex2024ML4SEISMIChtc,
	title = {Tucker Compression for Scalable Operator Learning in Large-Scale Parametric PDE Models},
	year = {2024},
	month = {11},
	abstract = {Simulating two-phase flow via PDEs is computationally expensive due to the inversion of large, ill-conditioned matrices. To accelerate these computations, we reformulate Hierarchical Tucker Tensor (HTT) decompositions into Kronecker products, enabling scalable Fourier Neural Operators (FNOs) for CO2 saturation predictions in subsurface environments. This reformulation allows efficient scaling across multiple GPUs while maintaining a large number of modes. Building on our existing matrix-free abstraction library, we extend its capabilities to support distributed tensor operators. The extended library is auto-differentiable, with customized AD rules for training complex networks. We demonstrate the performance and scalability of our approach by evaluating FNO simulations against traditional PDE solvers for predicting time-varying CO2 saturations from permeability models in large-scale subsurface environments.},
	keywords = {deep learning, FNO, hierarchical tucker tensor, Inverse problems, kronecker product, ML4SEISMIC, SLIM, two-phase flow},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/rex2024ML4SEISMIChtc},
	author = {Richard Rex and Srikanth Avasarala and Thomas Grady and Felix J. Herrmann}
}
@article {yin2023wise,
	title = {WISE: full-Waveform variational Inference via Subsurface Extensions},
	journal = {Geophysics},
	volume = {89},
	year = {2024},
	note = {(GEOPHYSICS)},
	month = {04},
	abstract = {We introduce a probabilistic technique for full-waveform inversion, employing variational inference and conditional normalizing flows to quantify uncertainty in migration-velocity models and its impact on imaging. Our approach integrates generative artificial intelligence with physics-informed common-image gathers, reducing reliance on accurate initial velocity models. Considered case studies demonstrate its efficacy producing realizations of migration-velocity models conditioned by the data. These models are used to quantify amplitude and positioning effects during subsequent imaging.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Geophysics, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	doi = {10.1190/geo2023-0744.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2024/yin2023wise/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {yin2024IMAGEwiser,
	title = {WISER: full-Waveform variational Inference via Subsurface Extensions with Refinements},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2024},
	month = {8},
	abstract = {We introduce a cost-effective Bayesian inference method for full-waveform inversion (FWI) to quantify uncertainty in migration-velocity models and its impact on imaging. Our method targets inverse uncertainty due to null-space of the wave modeling operators and observational noise, and forward uncertainty where the uncertainty in velocity models is propagated to uncertainty in amplitude and positioning of imaged reflectivities. This is achieved by integrating generative artificial intelligence (genAI) with physics-informed common-image gathers (CIGs), which greatly reduces reliance on accurate initial FWI-velocity models. In addition, we illustrate the capability of fine-tuning the generative AI networks with frugal physics-based refinements to improve the inference accuracy.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, IMAGE, Imaging, Inverse problems, MVA, RTM, SEG, Summary Statistics, Uncertainty quantification, WISE, WISER},
	url = {https://slimgroup.github.io/IMAGE2024/yin2024SEG/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {orozco2022SPIEadjoint,
	title = {Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification},
	booktitle = {SPIE Medical Imaging Conference},
	year = {2023},
	note = {(SPIE, San Diego)},
	month = {02},
	abstract = {Machine learning algorithms such as Normalizing Flows, VAEs, and GANs are powerful tools in Bayesian uncertainty quantification (UQ) of inverse problems. Unfortunately, when using these algorithms medical imaging practitioners are faced with the challenging task of manually defining neural networks that can handle complicated inputs such as acoustic data. This task needs to be replicated for different receiver types or configurations since these change the dimensionality of the input. We propose to first transform the data using the adjoint operator {\textemdash}ex: time reversal in photoacoustic imaging (PAI) or back-projection in computer tomography (CT) imaging {\textemdash} then continue posterior inference using the adjoint data as an input now that it has been standardized to the size of the unknown model. This adjoint preprocessing technique has been used in previous works but with minimal discussion on if it is biased. In this work, we prove that conditioning on adjoint data is unbiased for a certain class of inverse problems. We then demonstrate with two medical imaging examples (PAI and CT) that adjoints enable two things: Firstly, adjoints partially undo the physics of the forward operator resulting in faster convergence of an ML based Bayesian UQ technique. Secondly, the algorithm is now robust to changes in the observed data caused by differing transducer subsampling in PAI and number of angles in CT. Our adjoint-based Bayesian inference method results in point estimates that are faster to compute than traditional baselines and show higher SSIM metrics, while also providing validated UQ.},
	keywords = {Amortized Inference, Bayesian inference, deep learning, Inverse problems, machine learning, medical imaging, Normalizing flows, SPIE, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2023/orozco2022SPIEadjoint/SPIE_2022_adjoint.html},
	author = {Rafael Orozco and Ali Siahkoohi and Gabrio Rizzuti and Tristan van Leeuwen and Felix J. Herrmann}
}
@article {siahkoohi2022ravi,
	title = {Reliable amortized variational inference with physics-based latent distribution correction},
	journal = {Geophysics},
	volume = {88},
	number = {3},
	year = {2023},
	note = {(Geophysics)},
	month = {05},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs of the forward operator and the selection of an appropriate prior distribution. Amortized variational inference addresses these challenges where a neural network is trained to approximate the posterior distribution over existing pairs of model and data. When fed previously unseen data and normally distributed latent samples as input, the pretrained deep neural network{\textendash}-in our case a conditional normalizing flow{\textendash}-provides posterior samples with virtually no cost. However, the accuracy of this approach relies on the availability of high-fidelity training data, which seldom exists in geophysical inverse problems because of the highly heterogeneous structure of the Earth. In addition, accurate amortized variational inference requires the observed data to be drawn from the training data distribution. As such, we offer a solution that increases the resilience of amortized variational inference when faced with data distribution shifts, e.g., changes in the forward model or prior distribution. Our method involves a physics-based correction to the conditional normalizing flow latent distribution to provide a more accurate approximation to the posterior distribution for the observed data at hand. To accomplish this, instead of a standard Gaussian latent distribution, we parameterize the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance. These unknown quantities are then estimated by minimizing the Kullback-Leibler divergence between the corrected and true posterior distributions. While generic and applicable to other inverse problems, by means of a seismic imaging example, we show that our correction step improves the robustness of amortized variational inference with respect to changes in number of source experiments, noise variance, and shifts in the prior distribution. This approach provides a seismic image with limited artifacts and an assessment of its uncertainty with approximately the same cost as five reverse-time migrations.},
	keywords = {Inverse problems, Normalizing flows, seismic imaging, Uncertainty quantification, Variational Inference},
	doi = {10.1190/geo2022-0472.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/siahkoohi2022ravi/paper.html},
	software = {https://github.com/slimgroup/ReliableAVI.jl},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@article {yin2023smi,
	title = {Solving multiphysics-based inverse problems with learned surrogates and constraints},
	journal = {Advanced Modeling and Simulation in Engineering Sciences},
	volume = {10},
	year = {2023},
	note = {(Advanced Modeling and Simulation in Engineering Sciences)},
	month = {10},
	abstract = {Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2 plume predictions near, and far away, from the monitoring wells.},
	keywords = {AMSES, deep learning, Fourier neural operators, Inverse problems, learned constraints, learned surrogates, multiphysics, Normalizing flows},
	doi = {10.1186/s40323-023-00252-0},
	url = {https://doi.org/10.1186/s40323-023-00252-0},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/AMSES/2023/yin2023smi/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {yin2023HOTCSEspi,
	title = {Solving PDE-based inverse problems with learned surrogates and constraints},
	year = {2023},
	note = {(HotCSE)},
	month = {11},
	abstract = {In this presentation, I will introduce a learned inversion algorithm for solving inverse problems with computationally expensive forward operators. We tackle this challenge by combining learned surrogates (Fourier neural operators) with learned constraints (normalizing flows). After jointly training these networks with the same samples, the learned surrogates lead to computationally efficient surrogate-assisted inversion. Meanwhile, the learned constraints safeguard the accuracy of the surrogates by forcing the model iterates to remain in-distribution. By combining the two, we come up with a homotopy / continuation scheme where the constraints are relaxed slowly so that the data misfit objective can be minimized while the model iterates always remain in the statistical distribution on which the surrogates are trained. We demonstrate the efficacy of our learned inversion algorithm through carefully selected experiments centered around the problem of geological carbon storage monitoring.},
	keywords = {deep learning, Fourier neural operators, Inverse problems, learned constraints, learned surrogates, multiphysics, Normalizing flows, PDE},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/HotCSE/2023/yin2023HOTCSEspi},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {orozco2022ML4SEISMICaos,
	title = {Adjoint operators as summary functions in amortized Bayesian inference frameworks},
	year = {2022},
	month = {11},
	abstract = {An important concern in seismic inverse problems is the large and varying size of observed data. The large size can cause computational cost concerns and its varying size (such as when changing receiver geometries) implies the need to rerun inference algorithms from scratch for each new observation. Motivated by these two problems, we take inspiration from the statistics literature which commonly relies on summary statistic of observed data. Summary statistic compress the observed data leaving only information needed for inference. In this work, we argue that the adjoint operator provides a natural candidate for a summary function in the context of physics-based inverse problems. We first mathematically show that for certain general assumptions transforming data under the adjoint operator defines a new conditional distribution which preserves the expectations of the original posterior. We validate our hypothesis by evaluating our framework in a learned amortized inference algorithm. Our seismic and medical synthetic experiments show computational gains and increased quality of point estimates using our framework. We discuss statistical metrics that show our learned posterior is well calibrated therefore justifying its use in uncertainty quantification.},
	keywords = {Amortized Inference, Bayesian inference, deep learning, Inverse problems, machine learning, medical imaging, ML4SEISMIC, Normalizing flows, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/orozco2022ML4SEISMICaos/index.html},
	author = {Rafael Orozco and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@presentation {siahkoohi2022ML4SEISMICluq,
	title = {Low-cost uncertainty quantification for large-scale inverse problems},
	year = {2022},
	month = {11},
	abstract = {Bayesian inference for large-scale inverse problems is challenged by the computationally costly forward operator evaluations during posterior distribution sampling. Recent advances in variational inference and deep learning reduce these costs by pretraining a neural network capable of sampling the posterior distribution for previously unseen observed data. In geophysical applications, however, the accuracy of these methods depends on sufficiently capturing subsurface variability through a training dataset, which is challenging given the heterogeneity of the Earth{\textquoteright}s subsurface and our lack of access to it. Moreover, these methods may be unreliable in the presence of data distribution shifts, e.g., a change in the number of source experiments, noise distribution, or geological features to be imaged. As such, we present a solution that increases the robustness of deep-learning-based Bayesian inference approaches when faced with changes in data distribution. Our proposed method involves a physics-based adaptation to the latent distribution of a conditional normalizing flow that is pretrained to approximate the posterior distribution for previously unseen data. Instead of feeding standard Gaussian latent samples to the conditional normalizing flow, this method parameterizes the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, estimated by minimizing the Kullback-Leibler divergence between predicted and true posterior distributions. This method is applicable to a wide range of inverse problems and has the potential to significantly reduce the costs of Bayesian variational inference. By means of a realistic seismic imaging example we demonstrate that the proposed latent distribution adaptation method mitigates the Bayesian inference errors induced by data distribution shifts, including shifts in the forward model and prior distribution.},
	keywords = {Inverse problems, ML4SEISMIC, Normalizing flows, seismic imaging, SLIM, Uncertainty quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/siahkoohi2022ML4SEISMICluq/siahkoohi2022ML4SEISMICluq_pres.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@presentation {orozco2022ML4SEISMICnfr,
	title = {Normalizing flows for regularization of 3D seismic inverse problems},
	year = {2022},
	month = {11},
	abstract = {We present the first known exploration of a normalizing flow (NF) for generative 3D volumes. First, we tackle computational issues surrounding the high dimensionality of our desired 3D volume output. This is of particular concern in normalizing flows since their invertibility constraint implies equal dimension of output and input. Our findings show that by {\textquotedblleft}freezing{\textquotedblright} expensive layers we can efficiently train a normalizing flow on 3D volumes. Using this NF architecture, we train a generative model on volume sections of the 3D BG compass model. Our method produces visually plausible generative samples which are efficient to produce. We demonstrate its practical use by using our trained generative model as an implicit prior in a Maximum A Posteriori (MAP) framework. We evaluate this MAP framework by estimating the solution of a inverse problem in seismic imaging. Our method results in higher SNR estimates than the baseline and in less iterations, importantly saving the computational cost of evaluating the expensive 3D PDE solver during optimization. Finally, through scaling analysis of training cost, we show that NF convolutional layers allow this approach to scale favorably to larger volumes.},
	keywords = {3D, Bayesian inference, deep learning, Inverse problems, machine learning, ML4SEISMIC, Normalizing flows, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/orozco2022ML4SEISMICnfr/index.html},
	author = {Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {siahkoohi2022SEGWSrav,
	title = {Reliable amortized variational inference with conditional normalizing flows via physics-based latent distribution correction},
	booktitle = {IMAGE Workshop on Subsurface Uncertainty Description and Estimation - Moving Away from Single Prediction with Distribution Learning},
	year = {2022},
	note = {(IMAGE Workshop, Houston)},
	month = {09},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs associated with the forward operator during posterior sampling, as well as the selection of an appropriate prior distribution that encodes our prior knowledge about the unknown. Amortized variational inference addresses these challenges by pretraining a conditional normalizing flow (cNF) that approximates the posterior distribution over the existing model and data joint samples where the prior is implicitly learned from the data. When fed data and normally distributed latent samples as input, the pretrained cNF provides posterior samples for previously unseen data virtually for free. The accuracy of this purely data-driven approach, however, is dependent on the availability of high-fidelity training data, which is rarely the case with geophysical inverse problems, due to the highly heterogeneous structure of the Earth. To overcome this challenge and to minimize the negative bias of data distribution shifts during inference, we propose learning a physics-based correction to the cNF latent distribution to provide a more accurate approximation to the posterior distribution. We accomplish this by parameterizing the cNF latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, which are estimated by minimizing the Kullback-Leibler divergence between the corrected posterior distribution estimate and the true posterior distribution. For a relatively well-trained cNF, this approach provides reliable posterior samples with a limited computational cost while remaining bound to data and physics. We showcase the computational gains of this approach on a "quasi" real seismic imaging example.},
	keywords = {Bayesian inference, deep learning, Generative models, Imaging, Inverse problems, SEG, Uncertainty quantification, workshop},
	url = {https://www.imageevent.org/Workshop/subsurface-uncertainty-description-estimation-moving-away-single-prediction-distribution-learning},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGWSrav/Thur-15-55-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {herrmann2021KAUSTdbi,
	title = {Deep Bayesian Inference for Task-based Seismic Imaging},
	booktitle = {KAUST},
	year = {2021},
	note = {(KAUST, virtual)},
	month = {03},
	abstract = {High dimensionality, complex physics, and lack of access to the ground truth make seismic imaging one of the most challenging inversion problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks conducted on these images. By making use of a Markov-chain Monte Carlo (McMC) sampling technique, we demonstrate how uncertainty in the data can be propagated to the task of seismic horizon tracking. While this example shows that uncertainty can in principle be handled in a systematic manner by using neural nets as deep priors, it unfortunately also reveals that the McMC method fundamentally lacks ability to scale to relevant problem sizes. To overcome this shortcoming, we introduce a variational formulation based on normalizing flows. In this approach, invertible neural networks are trained to generate samples from the posterior. There are strong indications that this approach has the capability to scale better to problems where the forward operator is expensive to evaluate.},
	keywords = {Bayesian inference, Inverse problems, seismic imaging, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2021/herrmann2021KAUSTdbi/Kaust.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Philipp A. Witte and Felix J. Herrmann}
}
@conference {siahkoohi2021AABIpto,
	title = {Preconditioned training of normalizing flows for variational inference in inverse problems},
	booktitle = {3rd Symposium on Advances in Approximate Bayesian Inference},
	year = {2021},
	note = {AABI},
	month = {01},
	abstract = {Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a preconditioning scheme involving a conditional normalizing flow (NF) capable of sampling from a low-fidelity posterior distribution directly. This conditional NF is used to speed up the training of the high-fidelity objective involving minimization of the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density for indirect measurements at hand. To minimize costs associated with the forward operator, we initialize the high-fidelity NF with the weights of the pretrained low-fidelity NF, which is trained beforehand on available model and data pairs. Our numerical experiments, including a 2D toy and a seismic compressed sensing example, demonstrate that thanks to the preconditioning considerable speed-ups are achievable compared to training NFs from scratch.},
	keywords = {Inverse problems, Normalizing flows, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2021/siahkoohi2021AABIpto/siahkoohi2020ABIfab.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2021/siahkoohi2021AABIpto/siahkoohi2021AABIpto_pres.pdf},
	url2 = {https://openreview.net/forum?id=P9m1sMaNQ8T},
	software = {https://github.com/slimgroup/Software.siahkoohi2021AABIpto},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Philipp A. Witte and Felix J. Herrmann}
}
@conference {peters2019SIAMGEOgmrip,
	title = {Generalized Minkowski sets for the regularization of inverse problems},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2019},
	note = {(SIAM)},
	month = {05},
	abstract = {We present a new algorithm to compute projections onto the intersection of constraint sets, designed particularly for multiple sets because we exploit similarities between constraint sets. When we do not know projections onto the individual sets in closed form, as is the case for total-variation constraints, our algorithm does not need other optimization algorithms to solve sub-problems. This a significant advantage in terms of computational cost and number of tuning parameters and stopping conditions, compared to classical algorithms to compute projections onto the intersection, such as Dykstra{\textquoteright}s algorithm. The proposed algorithm is suitable for problems with a large number of model parameters such as full-waveform inversion because it exploits coarse and fine-grained parallelism, and we also present a multilevel accelerated version. The corresponding software is open-source and implemented in Julia. We present strategies to use projections onto multiple constraints to regularize full-waveform inversion for models with salt domes or sedimentary geology.},
	keywords = {Intersections, Inverse problems, Minkowski set, Projections, Sets},
	url = {https://www.pathlms.com/siam/courses/11267/sections/14618/video_presentations/128671},
	url2 = {https://meetings.siam.org/sess/dsp_talk.cfm?p=97656},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {peters2018CMSWMissrip,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	booktitle = {Canadian Mathematical Society Winter Meeting},
	year = {2018},
	note = {(CMSWM)},
	month = {12},
	abstract = {We present new algorithms to compute projections onto the intersection of constraint sets. We focus on problems with multiple sets for which there is no simple and closed-form projection. Different from more classical methods such as Dykstra{\textquoteright}s algorithm, we do not need other algorithms to solve sub-problems. Our algorithms are based on the alternating direction method of multipliers and apply to models/images/video on small 2D and large 3D grids because we exploit computational similarity between constraint sets, coarse and fine-grained parallelism, and we also present a multilevel accelerated version. To obtain more flexible descriptions of prior knowledge, we introduce a formulation that allows constraint sets to be the sum of intersections of sets, which is essentially an extension of a Minkowski set. This formulation builds on the success of additive image descriptions that are usually based on penalty methods, such as cartoon-texture decomposition and robust principal component analysis. We show applications where we use multiple constraint sets to regularize partial-differential-equation based parameter estimation problems such as seismic waveform inversion, as well as various image and video processing and segmentation tasks.},
	keywords = {Intersections, Inverse problems, Projections, Sets},
	url = {https://cms.math.ca/Events/winter18/abs/ipi$\#$bp},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {herrmann2017SIAMdsa,
	title = {Domain-specific abstractions for full-waveform inversion},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2017},
	note = {(SIAM Conference on Computational Science and Engineering, Atlanta)},
	month = {02-03},
	keywords = {FWI, Inverse problems, SIAM, software},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/herrmann2017SIAMdsa/herrmann2017SIAMdsa_pres.pdf},
	author = {Felix J. Herrmann and Curt Da Silva}
}
@article {vanleeuwen2015IPpmp,
	title = {A penalty method for PDE-constrained optimization in inverse problems},
	journal = {Inverse Problems},
	volume = {32},
	number = {1},
	year = {2015},
	note = {(Inverse Problems)},
	month = {12},
	pages = {015007},
	abstract = {Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate.},
	keywords = {Inverse problems, Optimization, PDE, penalty method},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2015/vanleeuwen2015IPpmp/vanleeuwen2015IPpmp.pdf},
	url2 = {http://stacks.iop.org/0266-5611/32/i=1/a=015007},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@article {Aravkin11TRridr,
	title = {Robust inversion, dimensionality reduction, and randomized sampling},
	journal = {Mathematical Programming},
	volume = {134},
	number = {1},
	year = {2012},
	month = {08},
	pages = {101-125},
	abstract = {We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student{\textquoteright}s t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 \% corrupted data.},
	keywords = {FWI, Inverse problems, Optimization, Robust estimation, Seismic inversion, Stochastic optimization},
	doi = {10.1007/s10107-012-0571-6},
	url = {http://www.springerlink.com/content/35rwr101h5736340/},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/MathematicalProgramming/aravkin2012MPrid/aravkin2012MPrid.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander and Felix J. Herrmann and Tristan van Leeuwen}
}
