A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs

Crestel, Benjamin; Stadler, Georg; Ghattas, Omar

doi:10.1088/1361-6420/aaf129

Cited by 17 publications

(15 citation statements)

References 36 publications

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“…Resulting capabilities have enabled the use of UQ methods in complex problems of physical relevance, including e.g. transport in porous media [110,111], seismic sensing [112], fluid dynamics [62,113,114], chemistry [115,116], reacting flow [117], and materials [118,119], spanning applications in geophysics, combustion, and climate.…”

Section: G Uncertainty Quantificationmentioning

confidence: 99%

2022 Review of Data-Driven Plasma Science

Archibald¹,

Asif²,

Becker³

et al. 2022

Preprint

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Data science and technology offer transformative tools and methods to science. This review article highlights latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS). A large amount of data and machine learning algorithms go hand in hand. Most plasma data, whether experimental, observational or computational, are generated or collected by machines today. It is now becoming impractical for humans to analyze all the data manually. Therefore, it is imperative to train machines to analyze and interpret (eventually) such data as intelligently as humans but far more efficiently in quantity. Despite the recent impressive progress in applications of data science to plasma science and technology, the emerging field of DDPS is still in its infancy. Fueled by some of the most challenging problems such as fusion energy, plasmaprocessing of materials, and fundamental understanding of the universe through observable plasma phenomena, it is expected that DDPS continues to benefit significantly from the interdisciplinary marriage between plasma science and data science into the foreseeable future. CONTENTSI. Introduction 6 II. Fundamental Data Science 6 A. Introduction 6 B. Data Reduction/Compression 7 C. Dimensional reduction and sparse modeling 8 D. ML-enhanced modeling and simulation 9 E. ML Hardware and integration with models 10 F. Workflow Automation 11 G. Uncertainty Quantification 12 H. Visualization and Data Understanding 13 I. ML Control Theory 15 III. Basic Plasma Physics and Laboratory Experiments A. Introduction B. Spectroscopy, imaging and tomography C. Sparse measurement and noise D. Synthetic instruments and data E. Experimental data visualization F. High-rep rate laser experiments G. Charged particle beams H. Control and Optimisation of Plasma Accelerator Experiments I. Dusty and complex plasmas J. Physics and machine learning K. Challenges and outlook 5 IV. Magnetic Confinement Fusion 36 A. Introduction 36 B. Data-Driven Physics Models 36 C. Optimizing experimental workflows with data-driven methods 37 D. Diagnostics and Fusion Data Streams 38 E. Prediction of Tokamak Disruption 39 F. Surrogate models of fusion plasma 40 G. Magnetic Fusion Energy Data Challenges and Solutions 41 H. Data Science for extreme scale simulation 43 I. Challenges and outlook 44 V. Inertial confinement fusion and high-energy-density physics 45 A. Introduction 45 B. Representation learning for multimodal data 45 C. Transfer learning for simulation and experimen 47 D. Uncertainty quantification and Bayesian inference 47 E. High-performance computing and simulation acceleration 49 F. Design exploration and optimization 49 G. Self-driving experimental facilities 51 H. Challenges and outlook 52 VI. Space and astronomical plasmas 52 A. Introduction 52 B. Space and ground instruments 53 C. Space weather prediction 55 D. Transfer learning to improve historic data 56 E. Surrogate models of fluid closures using machine learning 56 F. Magnetic reconnection 58 G. Challenges and outlook 60 VII. Plasma tec...

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Section: G Uncertainty Quantificationmentioning

confidence: 99%

2022 Review of Data-Driven Plasma Science

Archibald¹,

Asif²,

Becker³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Notable examples are PET and MRI (PET/MRI) [50–52], PAT and US [53], geophysics applications with multiple data (e.g. electromagnetic waves, seismic waves, radar, DC resistivity, groundwater flow) [54–61]. MMMI: Coupled Physics Imaging (CPI).…”

Section: A Taxonomy Of Problemsmentioning

confidence: 99%

(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods

Arridge

Ehrhardt

Thielemans

2021

Phil. Trans. R. Soc. A.

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Imaging is omnipresent in modern society with imaging devices based on a zoo of physical principles, probing a specimen across different wavelengths, energies and time. Recent years have seen a change in the imaging landscape with more and more imaging devices combining that which previously was used separately. Motivated by these hardware developments, an ever increasing set of mathematical ideas is appearing regarding how data from different imaging modalities or channels can be synergistically combined in the image reconstruction process, exploiting structural and/or functional correlations between the multiple images. Here we review these developments, give pointers to important challenges and provide an outlook as to how the field may develop in the forthcoming years. This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 1’.

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“…We note that this function and its gradients are additive, leading to an optimization procedure that is uncoupled in theory, and the different parameter updates and the forward problem solutions do not mutually influence each other. Recent studies (Crestel et al 2018) have suggested introducing an explicit coupling via, e.g. cross-gradient or density-norm regularization.…”

Section: Combining Cost Functionsmentioning

confidence: 99%

“…By design we consider that an increase in the viscosity has to mimic an increase in the density and the wave speed, and vice versa. The same behavior can also be achieved by adding a regularization that opts to optimize the cross product of the gradients, by imposing a penalty on points where the gradients point in different directions-an approach that is described in more detail elsewhere (e.g., Crestel et al 2018).…”

Section: Collinear Gradient Updatesmentioning

confidence: 99%

Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions

Reuber

Simons

2020

Int J Geomath

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We discuss the resolving power of three geophysical imaging and inversion techniques, and their combination, for the reconstruction of material parameters in the Earth’s subsurface. The governing equations are those of Newton and Poisson for gravitational problems, the acoustic wave equation under Hookean elasticity for seismology, and the geodynamics equations of Stokes for incompressible steady-state flow in the mantle. The observables are the gravitational potential, the seismic displacement, and the surface velocity, all measured at the surface. The inversion parameters of interest are the mass density, the acoustic wave speed, and the viscosity. These systems of partial differential equations and their adjoints were implemented in a single Python code using the finite-element library FeNICS. To investigate the shape of the cost functions, we present a grid search in the parameter space for three end-member geological settings: a falling block, a subduction zone, and a mantle plume. The performance of a gradient-based inversion for each single observable separately, and in combination, is presented. We furthermore investigate the performance of a shape-optimizing inverse method, when the material is known, and an inversion that inverts for the material parameters of an anomaly with known shape.

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A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs

Cited by 17 publications

References 36 publications

2022 Review of Data-Driven Plasma Science

2022 Review of Data-Driven Plasma Science

(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods

Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions

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