@unpublished {gahlot2026IMAGEirs,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@unpublished {gahlot2025EAGEagc,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 {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}
}
@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 {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 {gahlot2025CCUSocs,
	title = {Optimizing CO2 Storage Monitoring with Enhanced Rock Physics Modeling and Optimal Pressure Control},
	booktitle = {CCUS 2025 - Carbon Capture, Utilization, and Storage Conference},
	year = {2025},
	month = {3},
	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 = {Bayesian inference, CCUS, conditional normalizing flows, control, deep learning, digital twin, GCS, rock physics, sequential Bayes, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CCUS/2025/gahlot2025CCUSocs},
	author = {Abhinav Prakash Gahlot and Haoyun Li 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}
}
@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 {herrmann2025SIAMrdt,
	title = {Robust Digital Twin for Geological Carbon Storage},
	booktitle = {SIAM Conference on Computational Science and Engineering (CSE25)},
	year = {2025},
	note = {(SIAM CSE25, Dallas)},
	month = {03},
	abstract = {While recent work has shown that conditional neural networks can be used to effectuate prior-to-posterior mappings during ensemble Kalman filtering, their accuracy relies on the quality of the training ensemble, consisting of the simulated time-advanced nonlinear state and possibly nonlinear observations. Its precision also depends on the generative neural networks{\textquoteright} ability to generalize. In this work, we will report progress on how to make our Digital Twin more robust with respect to distribution shifts and modeling errors, e.g. due to erroneous choices for the physics within the Forecast Step. To this end, we will follow a two-pronged approach consisting of augmenting the Forecast step, e.g. by including different models for the rock physics that map the Digital Twin{\textquoteright}s state to seismic properties, and by adding more physics during the prior-to-posterior mapping. In its current implementation, training of our Digital Twin{\textquoteright}s neural networks relies on relative low-fidelity amortization of the Forecast Ensemble, which is susceptible to distribution shifts. By conducting non-amortized inference informed by the physics and low-fidelity prior-to-posterior mapping, we propose an approach that is more robust than the current implementation of the Digital Twin.},
	keywords = {Bayesian inference, conditional normalizing flows, CSE25, digital twin, rock physics, sequential Bayes, SIAM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMCSE/2025/herrmann2025SIAMrdt},
	author = {Felix J. Herrmann and Abhinav Prakash Gahlot and Rafael Orozco and Ziyi Yin and Grant Bruer}
}
@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}
}
@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}
}
@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}
}
@conference {gahlot2024IMAGEdt,
	title = {A Digital Twin for Geological Carbon Storage with Controlled Injectivity},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2024},
	month = {8},
	abstract = {We present an uncertainty-aware Digital Twin (DT) for geologic carbon storage (GCS), capable of handling multimodal time-lapse data and controlling CO2 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 CO2 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., CO2 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 CO2 storage operations.},
	keywords = {Bayesian inference, conditional normalizing flows, control, deep learning, digital twin, GCS, IMAGE, SEG, sequential Bayes, Uncertainty quantification},
	doi = {10.48550/arXiv.2403.19819},
	url = {https://slimgroup.github.io/IMAGE2024/GahlotLi2024SEG/paper.html},
	author = {Abhinav Prakash Gahlot and Haoyun Li and 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}
}
@conference {herrmann2024PURDUEicon,
	title = {Digital Twins in the era of generative AI {\textemdash} Application to Geological CO2 Storage},
	booktitle = {ICON Seminar in IoT},
	year = {2024},
	month = {9},
	abstract = {As a society, we are faced with important challenges to combat climate change. Geological Carbon Storage, during which gigatonnes of super-critical CO2 are stored underground, is arguably the only scalable net-negative CO2-emission technology that is available. Recent advances in generative AI offer unique opportunities{\textemdash}especially in the context of Digital Twins for subsurface CO2-storage monitoring, decision making, and control{\textemdash}to help scale this technology, optimize its operations, lower its costs, and reduce its risks, so assurances can be made whether storage projects proceed as expected and whether CO2 remains underground. During this talk, it is shown how techniques from Simulation-Based Inference and Ensemble Bayesian Filtering can be extended to establish probabilistic baselines and assimilate multimodal data for problems challenged by large degrees of freedom, nonlinear multiphysics, and computationally expensive to evaluate simulations. Key concepts that will be reviewed include neural Wave-Based Inference with Amortized Uncertainty Quantification and physics-based Summary Statistics, Ensemble Bayesian Filtering with Conditional Neural Networks, and learned multiphysics inversion with Differentiable Programming.},
	keywords = {Bayesian inference, conditional normalizing flows, differential programming, digital twin, Ensemble Bayesian filtering, GCS, multiphyics, sequential Bayes, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/PURDUEicon/2024/herrmann2024PURDUEicon},
	url2 = {https://www.youtube.com/watch?v=GQT9CLA-DlU},
	author = {Abhinav Prakash Gahlot and Rafael Orozco and Haoyun Li and Huseyin Tuna Erdinc and Ziyi Yin and Mathias Louboutin 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 {gahlot2024MINESGIGACO2dtg,
	title = {DT4GCS {\textemdash} Digital Twin for Geological CO2 Storage and Control},
	booktitle = {Geophysical Research for Gigatonnes CO2 Storage, Colorado School of Mines},
	year = {2024},
	month = {7},
	keywords = {Bayesian inference, conditional normalizing flows, control, deep learning, digital twin, GCS, sequential Bayes, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/MINESGIGACO2/2024/gahlot2024MINESGIGACO2dtg},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/MINESGIGACO2/2024/gahlot2024MINESGIGACO2dtg/DTCCUS24.docx},
	author = {Abhinav Prakash Gahlot and Rafael Orozco and Haoyun Li and Huseyin Tuna Erdinc and Ziyi Yin and Mathias Louboutin 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}
}
@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 {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}
}
@mastersthesis {orozco2024THgmf,
	title = {GENERATIVE MODELS FOR UNCERTAINTY QUANTIFICATION OF MEDICAL AND SEISMIC IMAGING},
	year = {2024},
	note = {(PhD)},
	month = {12},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {This thesis investigates the intersection of machine learning-based generative models with physics-based methods to address imaging problems, with an emphasis on accelerat- ing computations while incorporating uncertainty quantification. Throughout the chapters, a key conclusion emerges: machine learning methods, though powerful, are insufficient when used in isolation. They must be combined with the trusted domain knowledge con- tained in numerical physics simulations to achieve robust results. The methods presented bridge two of the most impactful areas in modern computer science: numerical simula- tions methods rooted in linear algebra and the transformative potential of deep learning, particularly as exemplified by recent advancements in generative modeling. The focus of this work is on scenarios where the underlying physics is computation- ally expensive, requiring frugal use of simulations. This is particularly relevant in high- dimensional, ill-posed inverse problems, such as those encountered in the applications shown in this thesis: medical imaging and seismic exploration, where the forward oper- ator is governed by complex partial differential equations (PDEs). To address these challenges, this thesis introduces techniques that blend practical ma- chine learning approaches with theoretical insights, particularly through the use of physics- based summary statistics. These statistics enable efficient extraction of meaningful in- formation from physics simulations, reducing computational overhead while preserving the critical elements of the physical model. Theoretical foundations underpin the design choices, ensuring that the methods are both efficient and ameliorate the potential bias that would arise from using physics-based summary statistics instead of raw observations. As an engineering-focused work, the thesis places a strong emphasis on practicality and robustness. The proposed methods are stress-tested through validation experiments, on increasingly complex scenarios with a clear pathway toward deployment in the real-world. This applied perspective reflects the ultimate goal of leveraging these methods to create tangible, impactful changes in domains such as healthcare and geophysics. By bridging the gap between advanced machine learning and trusted physics-based methods, this work contributes to the development of innovative tools that balance computational efficiency, uncertainty quantification, and practical applicability.},
	keywords = {Bayesian inference, CCS, CIG, conditional normalizing flows, FWI, GCS, Generative models, Inverse problems, medical imaging, monitoring, Normalizing flows, PhD, RTM, scientific machine learning, time-lapse, Uncertainty quantification, Variational Inference, WISE, WISER},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2024/orozco2024THgmf/Thesis_Orozco_pdf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2024/orozco2024THgmf/defense-real},
	author = {Rafael Orozco}
}
@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 {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}
}
@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 {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}
}
@mastersthesis {yin2024THsgi,
	title = {Solving geophysical inverse problems with scientific machine learning},
	year = {2024},
	note = {(PhD)},
	month = {06},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Solving inverse problems involves estimating unknown parameters of interest from indirect measurements. Specifically, geophysical inverse problems seek to determine various Earth properties critical for geophysical exploration, carbon control, monitoring, and earthquake detection. These problems pose unique challenges: the parameters of interest are often high-dimensional, and the mapping from parameters to observables is computationally demanding. Moreover, these problems are typically non-convex and ill-posed, meaning that multiple sets of model parameters can adequately fit the observations, and inversion algorithms depend on accurate initial model parameters. This thesis introduces several innovative methods to tackle these challenges using scientific machine learning techniques. It discusses algorithms and software frameworks that utilize surrogate and generative models to achieve scalable and reliable inversion. It also examines the integration of conditional generative models with physics for Bayesian variational inference and uncertainty quantification. These methods have been applied to two critical inverse problems in geophysical applications: monitoring geological carbon storage and full-waveform inversion, both of which are plagued by the aforementioned computational challenges. The thesis consists of six papers. The first two papers present a scalable, interoperable, and differentiable programming framework for learned multiphysics inversion, showcased through realistic synthetic case studies in geological carbon storage monitoring. The third paper introduces a computationally efficient and reliable algorithm that employs surrogate models, particularly Fourier neural operators, to accelerate inversion. The reliability of this algorithm is ensured by using normalizing flows as learned constraints to safeguard the accuracy of the surrogate models throughout the inversion process. The subsequent paper explores a joint inversion approach and an explainable deep neural classifier for time-lapse seismic imaging and carbon dioxide leakage detection during geological carbon storage. The final two papers introduce amortized and semi-amortized variational inference approaches that employ information-preserving physics-informed summary statistics and refinements to provide computationally feasible and reliable uncertainty quantification in high-dimensional full-waveform inversion problems. They also assess the impact of the inherent uncertainty in these ill-posed inversion problems on subsequent imaging tasks.},
	keywords = {Bayesian inference, CCS, CIG, conditional normalizing flows, end-to-end, Fourier neural operators, FWI, GCS, Generative models, Inverse problems, JRM, monitoring, Normalizing flows, PhD, RTM, scientific machine learning, time-lapse, Uncertainty quantification, Variational Inference, WISE, WISER},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2024/yin2024THsgi/yin2024THsgi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2024/yin2024THsgi/yin2024THsgi_pres.pdf},
	author = {Ziyi Yin}
}
@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}
}
@conference {yin2023EMIutm,
	title = {Uncertainty-aware time-lapse monitoring of geological carbon storage with learned surrogates},
	booktitle = {Engineering Mechanics Institute Conference},
	year = {2023},
	note = {(EMI, Atlanta)},
	month = {06},
	abstract = {Time-lapse seismic monitoring of CO2 sequestration is computationally expensive as it involves modeling of both fluid-flow physics and wave physics. It also requires differentiation through the solvers with respect to properties of interest in the subsurface. In this talk, we present a learned end-to-end inversion framework, which uses a pre-trained Fourier neural operator as a learned surrogate for the fluid-flow simulator in order to greatly reduces the cost associated with fluid-flow modeling and differentiation through the solver. Through synthetic experiments, we demonstrate the efficacy of this framework on inverting the subsurface permeability of the reservoir and on monitoring CO2 plumes. We further quantify the uncertainty of the permeability and CO2 plumes with conditional normalizing flow. With this framework, we can also forecast the growth of CO2 plumes in the future with uncertainty estimation without any acquired seismic data.},
	keywords = {amortized Bayes, conditional normalizing flows, deep learning, EMI, end-to-end, Fourier neural operators, GCS, inversion, machine learning, Normalizing flows, time-lapse, uncertain quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EMI/2023/yin2023EMIutm/yin2023EMIutm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EMI/2023/yin2023EMIutm/index.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Ali Siahkoohi 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}
}
@presentation {yu2022ML4SEISMICmsb,
	title = {Monitoring with sequential Bayesian inference},
	year = {2022},
	month = {11},
	abstract = {For this study, we apply sequential Bayesian inference to monitor the time evolution of subsurface flow of CO2 from indirect acoustic measurements at the surface. Upon receiving new acoustic measurements, we infer the current state of the CO2 by sampling from a learned posterior. Using the incoming data, we then perform online updates of the current posterior. This is accomplished by using the fluid flow model to advance the estimated state variable forward in time in order to update the learned posterior. With a synthetic experiment, we demonstrate this method can track the flow evolution accurately as measured by PSNR metrics. Since the posterior is a learned network, we can compute estimates faster than traditional least squares methods. This method can also quantify the uncertainty due to stochasticity in fluid flow model and the limited-azimuth imaging configuration.},
	keywords = {CCS, conditional normalizing flows, GCS, ML4SEISMIC, monitoring, sequential Bayes, SLIM, time-lapse, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/yu2022ML4SEISMICmsb/index.html},
	author = {Ting-ying Yu and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@presentation {yin2022ML4SEISMICutc,
	title = {Uncertainty-aware time-lapse CO$_2$ monitoring with learned end-to-end inversion},
	year = {2022},
	month = {11},
	abstract = {Seismic monitoring of CO2 sequestration is computationally expensive as it involves modeling of both fluid-flow physics modeling and wave physics and differentiation through the solvers with respect to the subsurface properties of interest. In this talk, we demonstrate the effectiveness of learned coupled inversion framework using a pre-trained Fourier neural operator as a learned surrogate for the fluid-flow simulator, which greatly reduces the cost associated with fluid-flow modeling and differentiation through the solver. We study the effectiveness and correctness of inversion based on Fourier neural operator surrogate and a normalizing flow prior. We also demonstrate the efficacy of this framework on monitoring the growth of CO2 plumes during sequestration, and on uncertainty quantification of the permeability and CO2 plumes with conditional normalizing flow. With this framework, we can further forecast the CO2 plume in the future without any acquired seismic data with uncertainty estimation.},
	keywords = {amortized Bayes, conditional normalizing flows, deep learning, Fourier neural operators, GCS, inversion, machine learning, ML4SEISMIC, Normalizing flows, SLIM, time-lapse, uncertain quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/yin2022ML4SEISMICutc/index.html},
	author = {Ziyi Yin and Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
