@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}
}
@unpublished {orozco2023invnet,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 {louboutin2023lmi,
	title = {Learned multiphysics inversion with differentiable programming and machine learning},
	journal = {The Leading Edge},
	volume = {42},
	year = {2023},
	note = {(The Leading Edge)},
	month = {07},
	pages = {452-516},
	abstract = {We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, our software is designed to be both readable and scalable. This allows researchers to easily formulate their problems in an abstract fashion while exploiting the latest developments in high-performance computing. We illustrate and demonstrate our design principles and their benefits by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which aside from coupling of wave physics and multiphase flow, involves machine learning.},
	keywords = {CCS, deep learning, Fourier neural operators, GCS, Imaging, inversion, invertible networks, machine learning, monitoring, multiphysics, Normalizing flows, SLIM, software, time-lapse},
	url = {https://library.seg.org/doi/10.1190/tle42070474.1},
	presentation = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.html},
	author = {Mathias Louboutin and Ziyi Yin and Rafael Orozco and Thomas J. Grady II and Ali Siahkoohi and Gabrio Rizzuti and Philipp A. Witte and Olav M{\o}yner and Gerard J. Gorman and Felix J. Herrmann}
}
@conference {louboutin2023IMAGEloi,
	title = {Learned non-linear simultenous source and corresponding supershot for seismic imaging.},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2023},
	note = {(IMAGE, Houston)},
	month = {08},
	abstract = {Seismic imaging{\textquoteright}s main limiting factor is the scale of the involved dataset and the number of independent wave-equation solves required to migrate thousands of shots. To tackle this dimensionality curse, we introduce a learned framework that extends the conventional computationally reductive linear source superposition (e.g., via random simultaneous-source encoding) to a nonlinear learned source superposition and its corresponding learned supershot. With this method, we can image the subsurface at the cost of a one-shot migration by learning the most informative superposition of shots.},
	keywords = {deep learning, Imaging, SEG, simultaneous},
	url = {https://slimgroup.github.io/IMAGE2023/OneShot/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2023/louboutin2023IMAGEloi/louboutin2023IMAGEloi_pres.pdf},
	author = {Mathias Louboutin and Rafael Orozco and Ali Siahkoohi 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 {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}
}
@conference {yin2022SEGlci,
	title = {Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {Seismic monitoring of carbon storage sequestration is a challenging problem involving both fluid-flow physics and wave physics. Additionally, monitoring usually requires the solvers for these physics to be coupled and differentiable to effectively invert for the subsurface properties of interest. To drastically reduce the computational cost, we introduce a learned coupled inversion framework based on the wave modeling operator, rock property conversion and a proxy fluid-flow simulator. We show that we can accurately use a Fourier neural operator as a proxy for the fluid-flow simulator for a fraction of the computational cost. We demonstrate the efficacy of our proposed method by means of a synthetic experiment. Finally, our framework is extended to carbon sequestration forecasting, where we effectively use the surrogate Fourier neural operator to forecast the CO$_2$ plume in the future at near-zero additional cost.},
	keywords = {CCS, deep learning, Fourier neural operators, inversion, machine learning, multiphysics, SEG, time-lapse},
	doi = {10.1190/image2022-3722848.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/yin2022SEGlci/paper.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/yin2022SEGlci/index.html},
	software = {https://github.com/slimgroup/FNO4CO2},
	author = {Ziyi Yin and Ali Siahkoohi 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 {siahkoohi2022INTERSPEECHulbs,
	title = {Ultra-Low-Bitrate Speech Coding with Pretrained Transformers},
	booktitle = {Proceedings of INTERSPEECH},
	year = {2022},
	note = {International Speech Communication Association (ISCA)},
	month = {06},
	abstract = {Speech coding facilitates the transmission of speech over low-bandwidth networks with minimal distortion. Neural-network based speech codecs have recently demonstrated significant improvements in quality over traditional approaches. While this new generation of codecs is capable of synthesizing high-fidelity speech, their use of recurrent or convolutional layers often restricts their effective receptive fields, which prevents them from compressing speech efficiently. We propose to further reduce the bitrate of neural speech codecs through the use of pretrained Transformers, capable of exploiting long-range dependencies in the input signal due to their inductive bias. As such, we use a pretrained Transformer in tandem with a convolutional encoder, which is trained end-to-end with a quantizer and a generative adversarial net decoder. Our numerical experiments show that supplementing the convolutional encoder of a neural speech codec with Transformer speech embeddings yields a speech codec with a bitrate of 600 bps that outperforms the original neural speech codec in synthesized speech quality when trained at the same bitrate. Subjective human evaluations suggest that the quality of the resulting codec is comparable or better than that of conventional codecs operating at three to four times the rate.},
	keywords = {deep learning, GANs, INTERSPEECH, signal processing, Transformers},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/INTERSPEECH/2022/siahkoohi2022INTERSPEECHulbs/paper.pdf},
	author = {Ali Siahkoohi and Michael Chinen and Tom Denton and W. Bastiaan Kleijn and Jan Skoglund}
}
@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}
}
@conference {kumar2021SEGeuq,
	title = {Enabling uncertainty quantification for seismic data pre-processing using normalizing flows (NF){\textemdash}an interpolation example},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2021},
	note = {(IMAGE, Denver)},
	month = {09},
	pages = {1515-1519},
	abstract = {Seismic data go through a sequence of pre-processing steps before being made into an image. Although some work has been done to assess the uncertainties in the final images, how the uncertainty in the pre-processing affects the results remains largely unexplored. We use Normalizing Flows (NF), a type of deep neural network, to interpolate seismic data and quantify the associated uncertainty. A big advantage of NFs, over the more commonly used Markov Chain Monte Carlo methods, is that they can successfully sample a complex and high-dimensional probability space with fewer assumptions. We present the first application of NF in interpolating (synthetic) seismic data. The statistical measurements retrieved from the network can be used to better characterize the data as it is passed to the post-processing phase.},
	keywords = {deep learning, normalizing flow, SEG, wavefield reconstruction},
	doi = {10.1190/segam2021-3583705.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/kumar2021SEGeuq/kumar2021SEGeuq.pdf},
	software = {https://github.com/slimgroup/Software.SEG2021},
	author = {Rajiv Kumar and Maria Kotsi and Ali Siahkoohi and Alison Malcolm}
}
@conference {witte2021JULIACONmedlj,
	title = {InvertibleNetworks.jl - Memory efficient deep learning in Julia},
	booktitle = {JuliaCon},
	year = {2021},
	note = {(JuliaCon, virtual)},
	month = {07},
	abstract = {We present InvertibleNetworks.jl, an open-source package for invertible neural networks and normalizing flows using memory-efficient backpropagation. InvertibleNetworks.jl uses manually implement gradients to take advantage of the invertibility of building blocks, which allows for scaling to large-scale problem sizes. We present the architecture and features of the library and demonstrate its application to a variety of problems ranging from loop unrolling to uncertainty quantification.},
	keywords = {deep learning, Invertible network, Julia, Normalizing flows, segmentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/JuliaCon/2021/witte2021JULIACONmedlj/witte2021JULIACONmedlj.pdf},
	url2 = {https://www.youtube.com/watch?v=9M-zEGHY4i4},
	author = {Philipp A. Witte and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Bas Peters and Felix J. Herrmann}
}
@conference {siahkoohi2021SEGlbe,
	title = {Learning by example: fast reliability-aware seismic imaging with normalizing flows},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2021},
	note = {(IMAGE, Denver)},
	month = {09},
	pages = {1580-1585},
	abstract = {Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of ill-posed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for accurate Bayesian inference and are often computationally infeasible for large-scale inverse problems, such as seismic imaging. Our main contribution is a data-driven variational inference approach where we train a normalizing flow (NF), a type of invertible neural net, capable of cheaply sampling the posterior distribution given previously unseen seismic data from neighboring surveys. To arrive at this result, we train the NF on pairs of low- and high-fidelity migrated images. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image{\textquoteright}s reliability. To our knowledge, this is the first attempt to train a conditional network on what we know from neighboring images to improve the current and assess its reliability.},
	keywords = {deep learning, Normalizing flows, SEG, seismic imaging, Variational Inference},
	doi = {10.1190/segam2021-3581836.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/Tue-09-15-siahkoohi.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/Tue-09-15-siahkoohi.mp4},
	software = {https://github.com/slimgroup/Software.SEG2021},
	author = {Ali Siahkoohi and Felix J. Herrmann}
}
@conference {herrmann2021Microsoftrla,
	title = {ML@scale using randomized linear algebra},
	booktitle = {Microsoft},
	year = {2021},
	note = {Talk at Microsoft},
	month = {03},
	abstract = {Deep Learning for large-scale applications such as video encoding or seismic segmentation are challenged by the excessive amounts of memory that is required for training networks via backpropagation. In this talk, I will discuss how techniques from randomized linear algebra can be used to address these bottle necks and bring down the memory footprint of training CNNs by up to a factor of O(N) (where N is number of pixels) without increasing computational cost. Additionally, I will illustrate how the seemingly disparate technologies of deep learning and large-scale PDE-constrained optimization share important similarities that can be taken advantage of in the development of next-generation deep learning technologies, with possible applications in scientific computing and sustainability.},
	keywords = {deep learning, randomized linear algebra, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/Microsoft/2021/herrmann2021Microsoftrla/herrmann2021Microsoftrla_pres.pdf},
	author = {Felix J. Herrmann and Mathias Louboutin and Ali Siahkoohi}
}
@presentation {siahkoohi2021ML4SEISMICmcn,
	title = {Multifidelity conditional normalizing flows for physics-guided Bayesian inference},
	year = {2021},
	month = {11},
	abstract = {We introduce a scalable Bayesian inference approach that combines techniques from deep learning with a physic-based variational inference formulation. Bayesian inference for ill-posed inverse problems is challenged by the high-dimensionality of the unknown, computationally expensive forward operator, and choosing a prior distribution that accurately encodes prior knowledge on the unknown. To handle this situation and to assess uncertainty, we propose to approximate the posterior distribution using a pretrained conditional normalizing flow, which is trained on existing low- and high-fidelity estimations of the unknown. To further improve the accuracy of this approximation, we use transfer learning and finetune this normalizing flow by minimizing the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density. This amounts to minimizing a physic-based variational inference objective with respect to the network weights, which we believe might scale better than Bayesian inference with Markov Chain sampling methods. We apply the proposed Bayesian inference approach to seismic imaging where we use quasi-real data obtained from the Parihaka dataset.},
	keywords = {deep learning, ML4SEISMIC, Normalizing flows, seismic imaging, SLIM, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/siahkoohi2021ML4SEISMICmcn/Mon-11-45-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {siahkoohi2020SEGCHAPTERGTdlbuq,
	title = {A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification},
	year = {2020},
	note = {(SEG Student Chapter)},
	abstract = {Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is via formulating the posterior distribution. Unfortunately, it is often not possible to formulate a prior distribution that precisely encodes our prior knowledge about the unknown. Furthermore, adherence to handcrafted priors may greatly bias the outcome of the Bayesian analysis. To address this issue, we propose to use the functional form of a randomly initialized convolutional neural network as an implicit structured prior, which is shown to promote natural images and excludes images with unnatural noise. In order to incorporate the model uncertainty into the final estimate, we sample the posterior distribution using stochastic gradient Langevin dynamics and perform Bayesian model averaging on the obtained samples. Our synthetic numerical experiment verifies that deep priors combined with Bayesian model averaging are able to partially circumvent imaging artifacts and reduce the risk of overfitting in the presence of extreme noise. Finally, we present pointwise variance of the estimates as a measure of uncertainty, which coincides with regions that are more difficult to image.},
	keywords = {deep learning, seismic imaging, stochastic gradient Langevin dynamics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/SEGCHAPTERGT/2020/siahkoohi2020SEGCHAPTERGTdlbuq/siahkoohi2020SEGCHAPTERGTdlbuq.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {siahkoohi2020EAGEdlb,
	title = {A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2020},
	note = {Accepted in EAGE},
	month = {1},
	abstract = {Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is via formulating the posterior distribution. Unfortunately, it is often not possible to formulate a prior distribution that precisely encodes our prior knowledge about the unknown. Furthermore, adherence to handcrafted priors may greatly bias the outcome of the Bayesian analysis. To address this issue, we propose to use the functional form of a randomly initialized convolutional neural network as an implicit structured prior, which is shown to promote natural images and excludes images with unnatural noise. In order to incorporate the model uncertainty into the final estimate, we sample the posterior distribution using stochastic gradient Langevin dynamics and perform Bayesian model averaging on the obtained samples. Our synthetic numerical experiment verifies that deep priors combined with Bayesian model averaging are able to partially circumvent imaging artifacts and reduce the risk of overfitting in the presence of extreme noise. Finally, we present pointwise variance of the estimates as a measure of uncertainty, which coincides with regions that are difficult to image.},
	keywords = {deep learning, EAGE, seismic imaging, stochastic gradient Langevin dynamics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2020/siahkoohi2020EAGEdlb/siahkoohi2020EAGEdlb.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@techreport {siahkoohi2020TRfuqf,
	title = {Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows},
	number = {TR-CSE-2020-2},
	year = {2020},
	month = {07},
	institution = {Georgia Institute of Technology},
	abstract = {In inverse problems, we often have access to data consisting of paired samples $(x,y)\sim p_X,Y(x,y)$ where $y$ are partial observations of a physical system, and $x$ represents the unknowns of the problem. Under these circumstances, we can employ supervised training to learn a solution $x$ and its uncertainty from the observations $y$. We refer to this problem as the "supervised" case. However, the data $y\sim p_Y(y)$ collected at one point could be distributed differently than observations $y{\textquoteright}\sim p_Y{\textquoteright}(y{\textquoteright})$, relevant for a current set of problems. In the context of Bayesian inference, we propose a two-step scheme, which makes use of normalizing flows and joint data to train a conditional generator $q_θ(x|y)$ to approximate the target posterior density $p_X|Y(x|y)$. Additionally, this preliminary phase provides a density function $q_θ(x|y)$, which can be recast as a prior for the "unsupervised" problem, e.g. when only the observations $y{\textquoteright}\sim p_Y{\textquoteright}(y{\textquoteright})$, a likelihood model $y{\textquoteright}|x$, and a prior on $x{\textquoteright}$ are known. We then train another invertible generator with output density $q{\textquoteright}_φ(x|y{\textquoteright})$ specifically for $y{\textquoteright}$, allowing us to sample from the posterior $p_X|Y{\textquoteright}(x|y{\textquoteright})$. We present some synthetic results that demonstrate considerable training speedup when reusing the pretrained network $q_θ(x|y{\textquoteright})$ as a warm start or preconditioning for approximating $p_X|Y{\textquoteright}(x|y{\textquoteright})$, instead of learning from scratch. This training modality can be interpreted as an instance of transfer learning. This result is particularly relevant for large-scale inverse problems that employ expensive numerical simulations.},
	keywords = {deep learning, invertible networks, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2020/siahkoohi2020TRfuqf/siahkoohi2020TRfuqf.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Philipp A. Witte and Felix J. Herrmann}
}
@conference {siahkoohi2020SIAMTXLAudg,
	title = {Unsupervised data-guided uncertainty analysis in imaging and horizon tracking},
	booktitle = {SIAM Texas-Louisiana},
	year = {2020},
	note = {SIAMTXLA},
	month = {10},
	abstract = {Imaging typically is the first stage of a sequential workflow, and uncertainty quantification becomes more relevant when applied to subsequent tasks. We propose a Bayesian approach to horizon tracking uncertainty analysis, where we deploy a deep prior instead of adhering to handcrafted priors. By passing samples from the posterior distribution obtained via stochastic gradient Langevin dynamics to an automatic horizon tracker, we are able to incorporate the uncertainty on model parameters into horizon tracking.},
	keywords = {deep learning, horizon tracking, McMC, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMTXLA/2020/siahkoohi2020SIAMTXLAudg/siahkoohi2020SIAMTXLAudg_pres.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Felix J. Herrmann}
}
@article {siahkoohi2019itl,
	title = {The importance of transfer learning in seismic modeling and imaging},
	journal = {Geophysics},
	year = {2019},
	note = {(GEOPHYSICS)},
	abstract = {Accurate forward modeling is essential for solving inverse problems in exploration seismology. Unfortunately, it is often not possible to afford being physically or numerically accurate. To overcome this conundrum, we make use of raw and processed data from nearby surveys. We propose to use this data, consisting of shot records or velocity models, to pre-train a neural network to correct for the effects of, for instance, the free surface or numerical dispersion, both of which can be considered as proxies for incomplete or inaccurate physics. Given this pre-trained neural network, we apply transfer learning to finetune this pre-trained neural network so it performs well on its task of mapping low-cost, but low-fidelity, solutions to high-fidelity solutions for the current survey. As long as we can limit ourselves during finetuning to using only a small fraction of high-fidelity data, we gain processing the current survey while using information from nearby surveys. We demonstrate this principle by removing surface-related multiples and ghosts from shot records and the effects of numerical dispersion from migrated images and wave simulations},
	keywords = {deep learning, Imaging, Modeling, SRME, transfer learning},
	doi = {10.1190/geo2019-0056.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2019/siahkoohi2019itl/siahkoohi2019itl.html},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {herrmann2019HOTCSEliwcuq,
	title = {Learned imaging with constraints and uncertainty quantification},
	year = {2019},
	note = {(HotCSE)},
	abstract = {We outline new approaches to incorporate ideas from convolutional networks into wave-based least-squares imaging. The aim is to combine hand-crafted constraints with deep convolutional networks allowing us to directly train a network capable of generating samples from the posterior. The main contributions include combination of weak deep priors with hard handcrafted constraints and a possible new way to sample the posterior.},
	keywords = {deep learning, Expectation Maximization, HotCSE, Imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/HotCSE/2019/herrmann2019HOTCSEliwcuq/herrmann2019HOTCSEliwcuq.pdf},
	author = {Felix J. Herrmann and Ali Siahkoohi and Gabrio Rizzuti}
}
@conference {herrmann2019NIPSliwcuc,
	title = {Learned imaging with constraints and uncertainty quantification},
	booktitle = {Neural Information Processing Systems (NeurIPS)},
	year = {2019},
	note = {(NIPS, Vancouver)},
	month = {12},
	abstract = {We outline new approaches to incorporate ideas from convolutional networks into wave-based least-squares imaging. The aim is to combine hand-crafted constraints with deep convolutional networks allowing us to directly train a network capable of generating samples from the posterior. The main contributions include combination of weak deep priors with hard handcrafted constraints and a possible new way to sample the posterior.},
	keywords = {constraint, deep learning, Imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2019/herrmann2019NIPSliwcuc/herrmann2019NIPSliwcuc.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2019/herrmann2019NIPSliwcuc/herrmann2019NIPSliwcuc_pres.pdf},
	url2 = {https://openreview.net/pdf?id=Hyet2Q29IS},
	author = {Felix J. Herrmann and Ali Siahkoohi and Gabrio Rizzuti}
}
@techreport {siahkoohi2019TRnna,
	title = {Neural network augmented wave-equation simulation},
	number = {TR-CSE-2019-1},
	year = {2019},
	month = {09},
	institution = {Georgia Institute of Technology},
	abstract = {Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of Laplacian in simulation of wave equation via finite-difference method. We exploit intrinsic one-to-one similarities between timestepping algorithm with Convolutional Neural Networks (CNNs), and propose to intersperse CNNs between low-fidelity timesteps. Augmenting neural networks with low-fidelity timestepping algorithms may allow us to take large timesteps while limiting the numerical dispersion artifacts. While simulating the wave-equation with low-fidelity timestepping algorithm, by correcting the wavefield several time during propagation, we hope to limit the numerical dispersion artifact introduced by a poor discretization of the Laplacian. As a proof of concept, we demonstrate this principle by correcting for numerical dispersion by keeping the velocity model fixed, and varying the source locations to generate training and testing pairs for our supervised learning algorithm.},
	keywords = {deep learning, finite difference, wave equation},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2019/siahkoohi2019TRnna/siahkoohi2019TRnna.html},
	url2 = {https://arxiv.org/pdf/1910.00925.pdf},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
