@unpublished {zeng2026IMAGEbjv,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@unpublished {deng2026IMAGEbag,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 {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 {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 {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 {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 {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 {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}
}
@conference {zeng2025ML4SEISMICssn,
	title = {Self-attention summary networks for velocity model building from common-image gathers},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {This study develops a self-attention-based summary network designed to efficiently encode and compress seismic information residing in subsurface-offset Common Image Gathers (CIGs) into low-dimensional latent representations suitable for conditional machine-learning enabled velocity-model building. The proposed network functions as a compact seismic encoder that captures global spatial dependencies through self-attention mechanisms while preserving essential local structural features critical for accurate reconstruction. When integrated within a flow matching generative network, the summary network learns to effectively summarize seismic information from CIGs via a new multi-scale attention mechanisms. This integration enables efficient training and inference, facilitating fast and physically consistent generation of seismic velocity models conditioned on CIGs.},
	keywords = {attention, CIG, deep learning, flow-matching, Generative models, ML4SEISMIC, SLIM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/zeng2025ML4SEISMICssn},
	author = {Shiqin Zeng and Abhinav Prakash Gahlot and Yunlin Zeng and Zijun Deng 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 {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 {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 {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}
}
@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}
}
@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 {yin2024GTwise,
	title = {Generative AI for full-waveform variational inference},
	year = {2024},
	month = {1},
	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 Bayes, conditional normalizing flows, deep learning, FWI, generative AI, GT, inversion, machine learning, Normalizing flows, SLIM, Summary Statistics, Uncertainty quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/GTseminar/2024/yin2024GTwise},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin 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 {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}
}
@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 {gahlot2023NIPSWSifp,
	title = {Inference of CO2 flow patterns {\textendash} a feasibility study},
	booktitle = {Neural Information Processing Systems (NeurIPS)},
	year = {2023},
	note = {(NeurIPS 2023 Workshop - Tackling Climate Change with Machine Learning (Spotlight))},
	month = {10},
	abstract = {As the global deployment of carbon capture and sequestration (CCS) technology intensifies in the fight against climate change, it becomes increasingly imperative to establish robust monitoring and detection mechanisms for potential underground CO$_2$ leakage, particularly through pre-existing or induced faults in the storage reservoir{\textquoteright}s seals. While techniques such as history matching and time-lapse seismic monitoring of CO$_2$ storage have been used successfully in tracking the evolution of CO$_2$ plumes in the subsurface, these methods lack principled approaches to characterize uncertainties related to the CO$_2$ plumes{\textquoteright} behavior. Inclusion of systematic assessment of uncertainties is essential for risk mitigation for the following reasons: (i) CO$_2$ plume-induced changes are small and seismic data is noisy; (ii) changes between regular and irregular (e.g., caused by leakage) flow patterns are small; and (iii) the reservoir properties that control the flow are strongly heterogeneous and typically only available as distributions. To arrive at a formulation capable of inferring flow patterns for regular and irregular flow from well and seismic data, the performance of conditional normalizing flow will be analyzed on a series of carefully designed numerical experiments. While the inferences presented are preliminary in the context of an early CO$_2$ leakage detection system, the results do indicate that inferences with conditional normalizing flows can produce high-fidelity estimates for CO$_2$ plumes with or without leakage. We are also confident that the inferred uncertainty is reasonable because it correlates well with the observed errors. This uncertainty stems from noise in the seismic data and from the lack of precise knowledge of the reservoir{\textquoteright}s fluid flow properties.},
	keywords = {Amortized Variational Inference, Bayesian inference, CCS, conditional normalizing flows, geological carbon storage, monitoring, NIPS, Summary Statistics},
	doi = {10.48550/arXiv.2311.00290},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2023/gahlot2023NIPSWSifp/paper.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2023/gahlot2023NIPSWSifp/poster.pdf},
	author = {Abhinav Prakash Gahlot and Huseyin Tuna Erdinc and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@conference {orozco2023AABIiter,
	title = {Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics},
	booktitle = {5th Symposium on Advances in Approximate Bayesian Inference},
	year = {2023},
	note = {(AABI, Honolulu)},
	month = {06},
	abstract = {We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in maximally informative summary statistics. Amortized variational inference is restricted by the expressive power of the chosen variational distribution and the availability of training data in the form of joint data and parameter samples, which often lead to approximation errors such as the amortization gap. To address this issue, we propose an iterative framework that refines the current amortized posterior approximation at each step. Our approach involves alternating between two steps: (1) constructing a training dataset consisting of pairs of summarized data residuals and parameters, where the summarized data residual is generated using a gradient-based summary statistic, and (2) training a conditional generative model {\textendash} a normalizing flow in our examples {\textendash} on this dataset to obtain a probabilistic update of the unknown parameter. This procedure leads to iterative refinement of the amortized posterior approximations without the need for extra training data. We validate our method in a controlled setting by applying it to a stylized problem, and observe improved posterior approximations with each iteration. Additionally, we showcase the capability of our method in tackling realistically sized problems by applying it to transcranial ultrasound, a high-dimensional, nonlinear inverse problem governed by wave physics, and observe enhanced posterior quality through better image reconstruction with the posterior mean.},
	keywords = {AABI, Amortization Gap, Amortized Variational Inference, Bayesian inference, conditional normalizing flows, Summary Statistics},
	url = {https://arxiv.org/abs/2305.08733},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2023/orozco2023AABIiter/aabi_poster.pdf},
	author = {Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {yin2023ML4SEISMICwise,
	title = {WISE: Full-waveform Inference with Subsurface Extensions},
	year = {2023},
	month = {11},
	abstract = {Quantifying uncertainty in full-waveform inversion is complex given the large sizes of both the model and data. A previous approach employed a variational inference framework, leveraging reverse-time migration to summarize observed data and approximate the posterior distribution through conditional normalizing flows. While reverse-time migration effectively summarizes the data when the background model is close to the true one, its accuracy diminishes with a less accurate background model. In our study, we suggest utilizing subsurface offset gathers as the summary statistics for the variational inference of full-waveform inversion. These gathers retain all the information in seismic data, even when the background model is cycle-skipped or fails to flatten the gathers. Through a case study on Compass model, we confirm our framework{\textquoteright}s effectiveness and show that subsurface offset gathers offer a better summary statistic than just reverse-time migration.},
	keywords = {amortized Bayes, conditional normalizing flows, deep learning, FWI, inversion, machine learning, ML4SEISMIC, Normalizing flows, SLIM, Summary Statistics, uncertain quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2023/yin2023ML4SEISMICwise},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
