@unpublished {orozco2024IMAGEbeacon,
	title = {BEACON: Bayesian Experimental design Acceleration with Conditional Normalizing flows - a case study in optimal monitor well placement for CO2 sequestration},
	year = {2024},
	month = {3},
	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, Inverse problems, OED, Uncertainty quantification},
	doi = {10.48550/arXiv.2404.00075},
	author = {Rafael Orozco and Abhinav Prakash Gahlot and Felix J. Herrmann}
}
@unpublished {zeng2024IMAGEefw,
	title = {Enhancing Full-Waveform Variational Inference through Stochastic Resampling and Data Augmentation},
	year = {2024},
	month = {3},
	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://slimgroup.github.io/IMAGE2024/Yunlin_Zeng2024SEG/paper.html},
	author = {Yunlin Zeng and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@article {yin2023wise,
	title = {WISE: full-Waveform variational Inference via Subsurface Extensions},
	journal = {Geophysics},
	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}
}
@unpublished {yin2024IMAGEwiser,
	title = {WISER: full-Waveform variational Inference via Subsurface Extensions with Refinements},
	year = {2024},
	month = {3},
	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, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE, WISER},
	url = {https://slimgroup.github.io/IMAGE2024/yin2024SEG/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {orozco2022SPIEadjoint,
	title = {Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification},
	booktitle = {SPIE Medical Imaging Conference},
	year = {2023},
	note = {(SPIE, San Diego)},
	month = {02},
	abstract = {Machine learning algorithms such as Normalizing Flows, VAEs, and GANs are powerful tools in Bayesian uncertainty quantification (UQ) of inverse problems. Unfortunately, when using these algorithms medical imaging practitioners are faced with the challenging task of manually defining neural networks that can handle complicated inputs such as acoustic data. This task needs to be replicated for different receiver types or configurations since these change the dimensionality of the input. We propose to first transform the data using the adjoint operator {\textemdash}ex: time reversal in photoacoustic imaging (PAI) or back-projection in computer tomography (CT) imaging {\textemdash} then continue posterior inference using the adjoint data as an input now that it has been standardized to the size of the unknown model. This adjoint preprocessing technique has been used in previous works but with minimal discussion on if it is biased. In this work, we prove that conditioning on adjoint data is unbiased for a certain class of inverse problems. We then demonstrate with two medical imaging examples (PAI and CT) that adjoints enable two things: Firstly, adjoints partially undo the physics of the forward operator resulting in faster convergence of an ML based Bayesian UQ technique. Secondly, the algorithm is now robust to changes in the observed data caused by differing transducer subsampling in PAI and number of angles in CT. Our adjoint-based Bayesian inference method results in point estimates that are faster to compute than traditional baselines and show higher SSIM metrics, while also providing validated UQ.},
	keywords = {Amortized Inference, Bayesian inference, deep learning, Inverse problems, machine learning, medical imaging, Normalizing flows, SPIE, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2023/orozco2022SPIEadjoint/SPIE_2022_adjoint.html},
	author = {Rafael Orozco and Ali Siahkoohi and Gabrio Rizzuti and Tristan van Leeuwen and Felix J. Herrmann}
}
@presentation {yin2023CSEslim,
	title = {Introduction to Seismic Laboratory for Imaging and Modeling},
	year = {2023},
	note = {(CSE Student Recruiting Event)},
	month = {11},
	abstract = {We introduce the latest research developments in Seismic Laboratory for Imaging and Modeling (SLIM), including geological carbon storage monitoring, seismic and medical imaging and uncertainty quantification, and advancements in scientific machine learning and high performance computing.},
	keywords = {CCS, deep learning, Fourier neural operators, GCS, Inverse problems, learned constraints, learned surrogates, medical imaging, multiphysics, Normalizing flows, PDE, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CSE/2023/SLIM.pdf},
	author = {Ziyi Yin}
}
@unpublished {orozco2023invnet,
	title = {InvertibleNetworks.jl: A Julia package for scalable normalizing flows},
	year = {2023},
	month = {12},
	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 = {10.48550/arXiv.2312.13480},
	author = {Rafael Orozco and Philipp A. Witte and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Bas Peters and Felix J. Herrmann}
}
@article {siahkoohi2022ravi,
	title = {Reliable amortized variational inference with physics-based latent distribution correction},
	journal = {Geophysics},
	volume = {88},
	number = {3},
	year = {2023},
	note = {(Geophysics)},
	month = {05},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs of the forward operator and the selection of an appropriate prior distribution. Amortized variational inference addresses these challenges where a neural network is trained to approximate the posterior distribution over existing pairs of model and data. When fed previously unseen data and normally distributed latent samples as input, the pretrained deep neural network{\textendash}-in our case a conditional normalizing flow{\textendash}-provides posterior samples with virtually no cost. However, the accuracy of this approach relies on the availability of high-fidelity training data, which seldom exists in geophysical inverse problems because of the highly heterogeneous structure of the Earth. In addition, accurate amortized variational inference requires the observed data to be drawn from the training data distribution. As such, we offer a solution that increases the resilience of amortized variational inference when faced with data distribution shifts, e.g., changes in the forward model or prior distribution. Our method involves a physics-based correction to the conditional normalizing flow latent distribution to provide a more accurate approximation to the posterior distribution for the observed data at hand. To accomplish this, instead of a standard Gaussian latent distribution, we parameterize the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance. These unknown quantities are then estimated by minimizing the Kullback-Leibler divergence between the corrected and true posterior distributions. While generic and applicable to other inverse problems, by means of a seismic imaging example, we show that our correction step improves the robustness of amortized variational inference with respect to changes in number of source experiments, noise variance, and shifts in the prior distribution. This approach provides a seismic image with limited artifacts and an assessment of its uncertainty with approximately the same cost as five reverse-time migrations.},
	keywords = {Inverse problems, Normalizing flows, seismic imaging, Uncertainty quantification, Variational Inference},
	doi = {10.1190/geo2022-0472.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/siahkoohi2022ravi/paper.html},
	software = {https://github.com/slimgroup/ReliableAVI.jl},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@article {yin2023smi,
	title = {Solving multiphysics-based inverse problems with learned surrogates and constraints},
	journal = {Advanced Modeling and Simulation in Engineering Sciences},
	volume = {10},
	year = {2023},
	note = {(Advanced Modeling and Simulation in Engineering Sciences)},
	month = {10},
	abstract = {Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO2 plume predictions near, and far away, from the monitoring wells.},
	keywords = {AMSES, deep learning, Fourier neural operators, Inverse problems, learned constraints, learned surrogates, multiphysics, Normalizing flows},
	doi = {10.1186/s40323-023-00252-0},
	url = {https://doi.org/10.1186/s40323-023-00252-0},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/AMSES/2023/yin2023smi/paper.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {yin2023HOTCSEspi,
	title = {Solving PDE-based inverse problems with learned surrogates and constraints},
	year = {2023},
	note = {(HotCSE)},
	month = {11},
	abstract = {In this presentation, I will introduce a learned inversion algorithm for solving inverse problems with computationally expensive forward operators. We tackle this challenge by combining learned surrogates (Fourier neural operators) with learned constraints (normalizing flows). After jointly training these networks with the same samples, the learned surrogates lead to computationally efficient surrogate-assisted inversion. Meanwhile, the learned constraints safeguard the accuracy of the surrogates by forcing the model iterates to remain in-distribution. By combining the two, we come up with a homotopy / continuation scheme where the constraints are relaxed slowly so that the data misfit objective can be minimized while the model iterates always remain in the statistical distribution on which the surrogates are trained. We demonstrate the efficacy of our learned inversion algorithm through carefully selected experiments centered around the problem of geological carbon storage monitoring.},
	keywords = {deep learning, Fourier neural operators, Inverse problems, learned constraints, learned surrogates, multiphysics, Normalizing flows, PDE},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/HotCSE/2023/yin2023HOTCSEspi},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {orozco2022ML4SEISMICaos,
	title = {Adjoint operators as summary functions in amortized Bayesian inference frameworks},
	year = {2022},
	month = {11},
	abstract = {An important concern in seismic inverse problems is the large and varying size of observed data. The large size can cause computational cost concerns and its varying size (such as when changing receiver geometries) implies the need to rerun inference algorithms from scratch for each new observation. Motivated by these two problems, we take inspiration from the statistics literature which commonly relies on summary statistic of observed data. Summary statistic compress the observed data leaving only information needed for inference. In this work, we argue that the adjoint operator provides a natural candidate for a summary function in the context of physics-based inverse problems. We first mathematically show that for certain general assumptions transforming data under the adjoint operator defines a new conditional distribution which preserves the expectations of the original posterior. We validate our hypothesis by evaluating our framework in a learned amortized inference algorithm. Our seismic and medical synthetic experiments show computational gains and increased quality of point estimates using our framework. We discuss statistical metrics that show our learned posterior is well calibrated therefore justifying its use in uncertainty quantification.},
	keywords = {Amortized Inference, Bayesian inference, deep learning, Inverse problems, machine learning, medical imaging, ML4SEISMIC, Normalizing flows, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/orozco2022ML4SEISMICaos/index.html},
	author = {Rafael Orozco and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@mastersthesis {siahkoohi2022THdgmf,
	title = {Deep generative models for solving geophysical inverse problems},
	year = {2022},
	note = {(PhD)},
	month = {07},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {My thesis presents several novel methods to facilitate solving large-scale inverse problems by utilizing recent advances in machine learning, and particularly deep generative modeling. Inverse problems involve reliably estimating unknown parameters of a physical model from indirect observed data that are noisy. Solving inverse problems presents primarily two challenges. The first challenge is to capture and incorporate prior knowledge into ill-posed inverse problems whose solutions cannot be uniquely identified. The second challenge is the computational complexity of solving inverse problems, particularly the cost of quantifying uncertainty. The main goal of this thesis is to address these issues by developing practical data-driven methods that are scalable to geophysical applications in which access to high-quality training data is often limited. There are six papers included in this thesis. A majority of these papers focus on addressing computational challenges associated with Bayesian inference and uncertainty quantification, while others focus on developing regularization techniques to improve inverse problem solution quality and accelerate the solution process. These papers demonstrate the applicability of the proposed methods to seismic imaging, a large-scale geophysical inverse problem with a computationally expensive forward operator for which sufficiently capturing the variability in the Earth{\textquoteright}s heterogeneous subsurface through a training dataset is challenging. The first two papers present computationally feasible methods of applying a class of methods commonly referred to as deep priors to seismic imaging and uncertainty quantification. I also present a systematic Bayesian approach to translate uncertainty in seismic imaging to uncertainty in downstream tasks performed on the image. The next two papers aim to address the reliability concerns surrounding data-driven methods for solving Bayesian inverse problems by leveraging variational inference formulations that offer the benefits of fully-learned posteriors while being directly informed by physics and data. The last two papers are concerned with correcting forward modeling errors where the first proposes an adversarially learned postprocessing step to attenuate numerical dispersion artifacts in wave-equation simulations due to coarse finite-difference discretizations, while the second trains a Fourier neural operator surrogate forward model in order to accelerate the qualification of uncertainty due to errors in the forward model parameterization.},
	keywords = {Bayesian inference, deep learning, Generative models, Geophysics, Inverse problems, PhD},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf_pres.pdf},
	author = {Ali Siahkoohi}
}
@presentation {siahkoohi2022ML4SEISMICluq,
	title = {Low-cost uncertainty quantification for large-scale inverse problems},
	year = {2022},
	month = {11},
	abstract = {Bayesian inference for large-scale inverse problems is challenged by the computationally costly forward operator evaluations during posterior distribution sampling. Recent advances in variational inference and deep learning reduce these costs by pretraining a neural network capable of sampling the posterior distribution for previously unseen observed data. In geophysical applications, however, the accuracy of these methods depends on sufficiently capturing subsurface variability through a training dataset, which is challenging given the heterogeneity of the Earth{\textquoteright}s subsurface and our lack of access to it. Moreover, these methods may be unreliable in the presence of data distribution shifts, e.g., a change in the number of source experiments, noise distribution, or geological features to be imaged. As such, we present a solution that increases the robustness of deep-learning-based Bayesian inference approaches when faced with changes in data distribution. Our proposed method involves a physics-based adaptation to the latent distribution of a conditional normalizing flow that is pretrained to approximate the posterior distribution for previously unseen data. Instead of feeding standard Gaussian latent samples to the conditional normalizing flow, this method parameterizes the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, estimated by minimizing the Kullback-Leibler divergence between predicted and true posterior distributions. This method is applicable to a wide range of inverse problems and has the potential to significantly reduce the costs of Bayesian variational inference. By means of a realistic seismic imaging example we demonstrate that the proposed latent distribution adaptation method mitigates the Bayesian inference errors induced by data distribution shifts, including shifts in the forward model and prior distribution.},
	keywords = {Inverse problems, ML4SEISMIC, Normalizing flows, seismic imaging, SLIM, Uncertainty quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/siahkoohi2022ML4SEISMICluq/siahkoohi2022ML4SEISMICluq_pres.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@presentation {orozco2022ML4SEISMICnfr,
	title = {Normalizing flows for regularization of 3D seismic inverse problems},
	year = {2022},
	month = {11},
	abstract = {We present the first known exploration of a normalizing flow (NF) for generative 3D volumes. First, we tackle computational issues surrounding the high dimensionality of our desired 3D volume output. This is of particular concern in normalizing flows since their invertibility constraint implies equal dimension of output and input. Our findings show that by {\textquotedblleft}freezing{\textquotedblright} expensive layers we can efficiently train a normalizing flow on 3D volumes. Using this NF architecture, we train a generative model on volume sections of the 3D BG compass model. Our method produces visually plausible generative samples which are efficient to produce. We demonstrate its practical use by using our trained generative model as an implicit prior in a Maximum A Posteriori (MAP) framework. We evaluate this MAP framework by estimating the solution of a inverse problem in seismic imaging. Our method results in higher SNR estimates than the baseline and in less iterations, importantly saving the computational cost of evaluating the expensive 3D PDE solver during optimization. Finally, through scaling analysis of training cost, we show that NF convolutional layers allow this approach to scale favorably to larger volumes.},
	keywords = {3D, Bayesian inference, deep learning, Inverse problems, machine learning, ML4SEISMIC, Normalizing flows, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/orozco2022ML4SEISMICnfr/index.html},
	author = {Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@conference {siahkoohi2022SEGWSrav,
	title = {Reliable amortized variational inference with conditional normalizing flows via physics-based latent distribution correction},
	booktitle = {IMAGE Workshop on Subsurface Uncertainty Description and Estimation - Moving Away from Single Prediction with Distribution Learning},
	year = {2022},
	note = {(IMAGE Workshop, Houston)},
	month = {09},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs associated with the forward operator during posterior sampling, as well as the selection of an appropriate prior distribution that encodes our prior knowledge about the unknown. Amortized variational inference addresses these challenges by pretraining a conditional normalizing flow (cNF) that approximates the posterior distribution over the existing model and data joint samples where the prior is implicitly learned from the data. When fed data and normally distributed latent samples as input, the pretrained cNF provides posterior samples for previously unseen data virtually for free. The accuracy of this purely data-driven approach, however, is dependent on the availability of high-fidelity training data, which is rarely the case with geophysical inverse problems, due to the highly heterogeneous structure of the Earth. To overcome this challenge and to minimize the negative bias of data distribution shifts during inference, we propose learning a physics-based correction to the cNF latent distribution to provide a more accurate approximation to the posterior distribution. We accomplish this by parameterizing the cNF latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, which are estimated by minimizing the Kullback-Leibler divergence between the corrected posterior distribution estimate and the true posterior distribution. For a relatively well-trained cNF, this approach provides reliable posterior samples with a limited computational cost while remaining bound to data and physics. We showcase the computational gains of this approach on a "quasi" real seismic imaging example.},
	keywords = {Bayesian inference, deep learning, Generative models, Imaging, Inverse problems, SEG, Uncertainty quantification, workshop},
	url = {https://www.imageevent.org/Workshop/subsurface-uncertainty-description-estimation-moving-away-single-prediction-distribution-learning},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGWSrav/Thur-15-55-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {herrmann2021KAUSTdbi,
	title = {Deep Bayesian Inference for Task-based Seismic Imaging},
	booktitle = {KAUST},
	year = {2021},
	note = {(KAUST, virtual)},
	month = {03},
	abstract = {High dimensionality, complex physics, and lack of access to the ground truth make seismic imaging one of the most challenging inversion problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks conducted on these images. By making use of a Markov-chain Monte Carlo (McMC) sampling technique, we demonstrate how uncertainty in the data can be propagated to the task of seismic horizon tracking. While this example shows that uncertainty can in principle be handled in a systematic manner by using neural nets as deep priors, it unfortunately also reveals that the McMC method fundamentally lacks ability to scale to relevant problem sizes. To overcome this shortcoming, we introduce a variational formulation based on normalizing flows. In this approach, invertible neural networks are trained to generate samples from the posterior. There are strong indications that this approach has the capability to scale better to problems where the forward operator is expensive to evaluate.},
	keywords = {Bayesian inference, Inverse problems, seismic imaging, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2021/herrmann2021KAUSTdbi/Kaust.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Philipp A. Witte and Felix J. Herrmann}
}
@conference {siahkoohi2021AABIpto,
	title = {Preconditioned training of normalizing flows for variational inference in inverse problems},
	booktitle = {3rd Symposium on Advances in Approximate Bayesian Inference},
	year = {2021},
	note = {AABI},
	month = {01},
	abstract = {Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a preconditioning scheme involving a conditional normalizing flow (NF) capable of sampling from a low-fidelity posterior distribution directly. This conditional NF is used to speed up the training of the high-fidelity objective involving minimization of the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density for indirect measurements at hand. To minimize costs associated with the forward operator, we initialize the high-fidelity NF with the weights of the pretrained low-fidelity NF, which is trained beforehand on available model and data pairs. Our numerical experiments, including a 2D toy and a seismic compressed sensing example, demonstrate that thanks to the preconditioning considerable speed-ups are achievable compared to training NFs from scratch.},
	keywords = {Inverse problems, Normalizing flows, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2021/siahkoohi2021AABIpto/siahkoohi2020ABIfab.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2021/siahkoohi2021AABIpto/siahkoohi2021AABIpto_pres.pdf},
	url2 = {https://openreview.net/forum?id=P9m1sMaNQ8T},
	software = {https://github.com/slimgroup/Software.siahkoohi2021AABIpto},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Philipp A. Witte and Felix J. Herrmann}
}
@article {kukreja2019PASCccd,
	title = {Combining checkpointing and data compression to accelerate adjoint-based optimization problems},
	journal = {Euro-Par 2019: Parallel Processing},
	year = {2019},
	note = {(Euro-Par 2019: Parallel Processing)},
	pages = {87-100},
	publisher = {Springer International Publishing},
	abstract = {Seismic inversion and imaging are adjoint-based optimization problems that processes up to terabytes of data, regularly exceeding the memory capacity of available computers. Data compression is an effective strategy to reduce this memory requirement by a certain factor, particularly if some loss in accuracy is acceptable. A popular alternative is checkpointing, where data is stored at selected points in time, and values at other times are recomputed as needed from the last stored state. This allows arbitrarily large adjoint computations with limited memory, at the cost of additional recomputations. In this paper we combine compression and checkpointing for the first time to compute a realistic seismic inversion. The combination of checkpointing and compression allows larger adjoint computations compared to using only compression, and reduces the recomputation overhead significantly compared to using only checkpointing.},
	keywords = {Adjoint-state, checkpointing, compression, FD, HPC, Inverse problems},
	doi = {10.1007/978-3-030-29400-7_7},
	url = {https://slim.gatech.edu/Publications/Public/Journals/PASC/2019/kukreja2019PASCccd/kukreja2019PASCccd.pdf},
	author = {Navjot Kukreja and Jan H{\"u}ckelheim and Mathias Louboutin and Paul Hovland and Gerard Gorman}
}
@conference {peters2019SIAMGEOgmrip,
	title = {Generalized Minkowski sets for the regularization of inverse problems},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2019},
	note = {(SIAM)},
	month = {05},
	abstract = {We present a new algorithm to compute projections onto the intersection of constraint sets, designed particularly for multiple sets because we exploit similarities between constraint sets. When we do not know projections onto the individual sets in closed form, as is the case for total-variation constraints, our algorithm does not need other optimization algorithms to solve sub-problems. This a significant advantage in terms of computational cost and number of tuning parameters and stopping conditions, compared to classical algorithms to compute projections onto the intersection, such as Dykstra{\textquoteright}s algorithm. The proposed algorithm is suitable for problems with a large number of model parameters such as full-waveform inversion because it exploits coarse and fine-grained parallelism, and we also present a multilevel accelerated version. The corresponding software is open-source and implemented in Julia. We present strategies to use projections onto multiple constraints to regularize full-waveform inversion for models with salt domes or sedimentary geology.},
	keywords = {Intersections, Inverse problems, Minkowski set, Projections, Sets},
	url = {https://www.pathlms.com/siam/courses/11267/sections/14618/video_presentations/128671},
	url2 = {https://meetings.siam.org/sess/dsp_talk.cfm?p=97656},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {peters2018CMSWMissrip,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	booktitle = {Canadian Mathematical Society Winter Meeting},
	year = {2018},
	note = {(CMSWM)},
	month = {12},
	abstract = {We present new algorithms to compute projections onto the intersection of constraint sets. We focus on problems with multiple sets for which there is no simple and closed-form projection. Different from more classical methods such as Dykstra{\textquoteright}s algorithm, we do not need other algorithms to solve sub-problems. Our algorithms are based on the alternating direction method of multipliers and apply to models/images/video on small 2D and large 3D grids because we exploit computational similarity between constraint sets, coarse and fine-grained parallelism, and we also present a multilevel accelerated version. To obtain more flexible descriptions of prior knowledge, we introduce a formulation that allows constraint sets to be the sum of intersections of sets, which is essentially an extension of a Minkowski set. This formulation builds on the success of additive image descriptions that are usually based on penalty methods, such as cartoon-texture decomposition and robust principal component analysis. We show applications where we use multiple constraint sets to regularize partial-differential-equation based parameter estimation problems such as seismic waveform inversion, as well as various image and video processing and segmentation tasks.},
	keywords = {Intersections, Inverse problems, Projections, Sets},
	url = {https://cms.math.ca/Events/winter18/abs/ipi$\#$bp},
	author = {Bas Peters and Felix J. Herrmann}
}
@conference {herrmann2017SIAMdsa,
	title = {Domain-specific abstractions for full-waveform inversion},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2017},
	note = {(SIAM Conference on Computational Science and Engineering, Atlanta)},
	month = {02-03},
	keywords = {FWI, Inverse problems, SIAM, software},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2017/herrmann2017SIAMdsa/herrmann2017SIAMdsa_pres.pdf},
	author = {Felix J. Herrmann and Curt Da Silva}
}
@article {vanleeuwen2015IPpmp,
	title = {A penalty method for PDE-constrained optimization in inverse problems},
	journal = {Inverse Problems},
	volume = {32},
	number = {1},
	year = {2015},
	note = {(Inverse Problems)},
	month = {12},
	pages = {015007},
	abstract = {Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate.},
	keywords = {Inverse problems, Optimization, PDE, penalty method},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2015/vanleeuwen2015IPpmp/vanleeuwen2015IPpmp.pdf},
	url2 = {http://stacks.iop.org/0266-5611/32/i=1/a=015007},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@article {Aravkin11TRridr,
	title = {Robust inversion, dimensionality reduction, and randomized sampling},
	journal = {Mathematical Programming},
	volume = {134},
	number = {1},
	year = {2012},
	month = {08},
	pages = {101-125},
	abstract = {We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student{\textquoteright}s t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 \% corrupted data.},
	keywords = {FWI, Inverse problems, Optimization, Robust estimation, Seismic inversion, Stochastic optimization},
	doi = {10.1007/s10107-012-0571-6},
	url = {http://www.springerlink.com/content/35rwr101h5736340/},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/MathematicalProgramming/aravkin2012MPrid/aravkin2012MPrid.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander and Felix J. Herrmann and Tristan van Leeuwen}
}
