@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}
}
@presentation {rex2023ML4SEISMIClsp,
	title = {Large-scale parametric PDE approximations with model-parallel Fourier neural operators},
	year = {2023},
	month = {11},
	abstract = {Solving PDEs to simulate two-phase flow is expensive since it involves the inversion of large ill-conditioned matrices. FNOs represent a special type of neural network capable of approximating solutions to two-phase flow equations. In order to speed up this computation, we develop a high-level software abstraction tool to exploit the linearly separable property of Fourier Transforms via Kronecker products. We perform a series of all-to-all operations where we partition the data to apply the operations in a distributed fashion. We apply these FNOs to predict the evolution of CO2-plumes in subsurface environments. Our model takes an input permeability model, and outputs time-varying CO2 saturations in a quick and cost-effective manner. Additionally, our research involves developing a distributed matrix-free abstraction library that can be used to represent any generic linear and nonlinear operator. This library is scalable and auto-differentiable thanks to the hand-written customized AD rules, allowing us to represent and train any network. We provide an evaluation on the accuracy of FNO simulations compared to traditional PDE simulations in solving various classes of PDEs.},
	keywords = {CCS, deep learning, Fourier neural operators, HPC, ML4SEISMIC, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2023/rex2023ML4SEISMIClsp},
	author = {Richard Rex and Thomas J. Grady II and Rishi Khan and Ziyi Yin 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}
}
@article {grady2022SCtll,
	title = {Model-Parallel Fourier Neural Operators as Learned Surrogates for Large-Scale Parametric PDEs},
	journal = {Computers \& Geosciences},
	volume = {178},
	year = {2023},
	note = {(Computers \& Geosciences)},
	month = {07},
	pages = {105402},
	abstract = {Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. We demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO2 dynamics in the Earth{\textquoteright}s subsurface.},
	keywords = {CCS, Computers and Geosciences, deep learning, Fourier neural operators, HPC, large-scale, Model Parallelism, Multiphase Flow, Operator Learning},
	doi = {10.1016/j.cageo.2023.105402},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ComputersAndGeosciences/2023/grady2022SCtll/grady2022SCtll.pdf},
	software = {https://github.com/slimgroup/dfno},
	author = {Thomas J. Grady II and Rishi Khan and Mathias Louboutin and Ziyi Yin and Philipp A. Witte and Ranveer Chandra and Russell J. Hewett and Felix J. Herrmann}
}
@conference {herrmann2023SIAMCSEtns,
	title = {The Next Step: Interoperable Domain-Specific Programming},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2023},
	note = {(SIAM CSE, Amsterdam)},
	month = {02},
	abstract = {Even though domain-specific programming approaches allow for readable, scalable, and maintainable software without sacrificing performance, the new paradigm of learned physics-informed models calls for an interdisciplinary approach typically involving multiple domain-specific languages. Take for example the problem of inverting for the fluid-flow properties from time-lapse seismic data, which entails domain-specific programming on the intersection of wave simulators, matrix-free linear algebra, learned neural surrogates for two-phase flow, and prior and posterior distributions for the fluid-flow properties. While domain-specific solutions exist for each of these sub-disciplines, integrating these approaches {\textendash} which may involve different programming languages {\textendash} into a single coupled scalable inversion framework that supports algorithmic differentiation can be a challenge. However, we show that challenges like this can be met when working with proper abstractions. In our inversion example, this involves math-inspired symbolic abstractions for numerical solutions of the wave equation (Devito), matrix-free implementations for its Jacobians (JUDI.jl), abstractions for Automatic Differentiation (ChainRules.jl), and homegrown implementations for conditional Invertible Neural Networks (InvertibleNetworks.jl) and Fourier Neural Operators (ParametricOperators.jl).},
	keywords = {algorithms, deep learning, devito, end-to-end, Fourier neural operators, GCS, JUDI, Jutul, SIAM, software, workshop},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMCSE/2023/herrmann2023SIAMCSEtns/index.html},
	author = {Felix J. Herrmann and Mathias Louboutin and Thomas J. Grady II and Ziyi Yin and Rishi Khan}
}
@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}
}
@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 {yin2022ML4SEISMICavc,
	title = {Amortized velocity continuation with Fourier neural operators},
	year = {2022},
	month = {11},
	abstract = {Velocity continuation aims to map the migration image using one background model to the image using another background model. It is of great importance to quantify the uncertainty in seismic imaging result from various background models. With Fourier neural operators as a learned surrogate, this continuation from a given background model to an unseen background model can be quite accurately estimated with near-zero cost. However, the limitation of the prior art is that the input background model and the survey area are assumed to be fixed. The main contribution of this work is to extend the Fourier neural operator surrogate to be amortized over different given background models and survey areas. We verify the effectiveness of our learned surrogates by a realistic example on different areas of Parihaka dataset against different background models.},
	keywords = {Fourier neural operators, ML4SEISMIC, SLIM, Uncertainty quantification, velocity continuation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/yin2022ML4SEISMICavc/index.html},
	author = {Ali Siahkoohi and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@conference {herrmann2022EAGEcvm,
	title = {Capturing velocity-model uncertainty and two-phase flow with Fourier Neural Operators},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2022},
	note = {(EAGE, Madrid)},
	month = {06},
	pages = {AI in Geoscience and Geophysics: Current Trends and Future Prospects (Dedicated Session)},
	keywords = {CCS, EAGE, Fourier neural operators, JRM, seismic imaging, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/herrmann2022EAGEcvm/index.html},
	author = {Ali Siahkoohi and Thomas J. Grady II and Abhinav Prakash Gahlot and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@presentation {grady2022ML4SEISMICesn,
	title = {Effective scaling of numerical surrogates via domain-decomposed Fourier neural operators},
	year = {2022},
	month = {11},
	abstract = {Numerical surrogates are models which learn to mimic a complex physical process (such as the solution to a PDE produced by a solver) from a set of input/output pairs. Fourier neural operators (FNOs) are a specific type of numerical surrogate which use a learned matched filter to quickly approximate solutions to relatively smooth complex physical processes. In the case of carbon capture sequestration (CCS) technology, FNOs have been shown to well-approximate solutions to the two-phase flow equations, with speedups of 1,000 to 10,000 times at inference time versus a tradtitional solver. This speed combined with the fact that FNOs are differentiable with respect to their input parameters allows for inverse and uncertainty quantification problems to theoretically be solved on real 3D data, a previously intractible task. However, due to the size of the input data, network weights, and optimizer state, FNOs have thus far been limited to small to medium 2D and 3D problems, well below the size of an industry standard such as the Sleipner benchmark. Here we alleviate this problem by proposing a model-parallel FNO which makes use of domain decomposition of the input data and network weights, and exploits architectural features of FNOs to also include a natural form of asynchronous pipeline parallelism. Our network can scale to arbitrary problem sizes on CPU and GPU systems.},
	keywords = {CCS, deep learning, Fourier neural operators, HPC, ML4SEISMIC, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/grady2022ML4SEISMICesn/index.html},
	author = {Thomas J. Grady II and Rishi Khan and Mathias Louboutin and Ziyi Yin and Philipp A. Witte and Ranveer Chandra and Russell J. Hewett and Felix J. Herrmann}
}
@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}
}
@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 {siahkoohi2022SEGvcw,
	title = {Velocity continuation with Fourier neural operators for accelerated uncertainty quantification},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies{\textendash}-due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that maps seismic images associated with one background model to another virtually for free. While being trained with only 200 background and seismic image pairs, this surrogate is able to accurately predict seismic images associated with new background models, thus accelerating seismic imaging uncertainty quantification. We support our method with a realistic data example in which we quantify seismic imaging uncertainties using a Fourier neural operator surrogate, illustrating how variations in background models affect the position of reflectors in a seismic image.},
	keywords = {Fourier neural operators, SEG, Uncertainty quantification, velocity continuation},
	doi = {10.1190/image2022-3750475.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGvcw/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGvcw/Tue-16-30-Siahkoohi.pdf},
	software = {https://github.com/slimgroup/fno4vc},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {grady2021ML4SEISMICdfn,
	title = {Distributed Fourier Neural Operators},
	year = {2021},
	month = {11},
	abstract = {Fourier Neural Operators (FNOs) are a class of neural operator, which use weightings on the Fourier transform of their inputs to approximate infinite-dimensional mappings between function spaces. They are particularly useful in approximating the solutions of smooth parametric (e.g. by permeability) partial differential equations (PDEs), and once trained are capable of producing a nearly identical output to a traditional numerical solver roughly three orders of magnitude faster, making them very useful in a wide variety of engineering applications that require repeated PDE solves (e.g. during uncertainty quantification). Until now, FNOs have been limited to small problems, as their memory intensive design makes them difficult to scale in a traditional machine learning setting on a single computer or GPU. In this work, a decomposition scheme is described and implemented in PyTorch using the DistDL distributed deep learning framework, which is capable of scaling FNOs to arbitrary dimension and input size running on many nodes in a distributed memory system. This parallel implementations allows FNOs to be trained and run on problems of a practical scale on both CPU and GPU clusters.},
	keywords = {CCS, deep learning, Fourier neural operators, ML4SEISMIC, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/grady2021ML4SEISMICdfn/Tue-12-10-Grady.pdf},
	author = {Thomas J. Grady II and Rishi Khan and Felix J. Herrmann}
}
