Applications of physics informed neural operators

Rosofsky, Shawn G.; Al Majed, Hani; Huerta, E. A.

doi:10.1088/2632-2153/acd168

Applications of physics informed neural operators

Journal Article · Thu May 18 00:00:00 EDT 2023 · Machine Learning: Science and Technology

DOI:https://doi.org/10.1088/2632-2153/acd168· OSTI ID:1974276

; Al Majed, Hani;

Abstract

We present a critical analysis of physics-informed neural operators (PINOs) to solve partial differential equations (PDEs) that are ubiquitous in the study and modeling of physics phenomena using carefully curated datasets. Further, we provide a benchmarking suite which can be used to evaluate PINOs in solving such problems. We first demonstrate that our methods reproduce the accuracy and performance of other neural operators published elsewhere in the literature to learn the 1D wave equation and the 1D Burgers equation. Thereafter, we apply our PINOs to learn new types of equations, including the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we show that our approach is also applicable to learn the physics of the 2D linear and nonlinear shallow water equations, which involve three coupled PDEs. We release our artificial intelligence surrogates and scientific software to produce initial data and boundary conditions to study a broad range of physically motivated scenarios. We provide the source code , an interactive website to visualize the predictions of our PINOs, and a tutorial for their use at the Data and Learning Hub for Science .

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1974276

Alternate ID(s):: OSTI ID: 2324774
OSTI ID: 1971925

Journal Information:: Machine Learning: Science and Technology, Journal Name: Machine Learning: Science and Technology Journal Issue: 2 Vol. 4; ISSN 2632-2153

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (26)

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Raissi, M.; Perdikaris, P.; Karniadakis, G. E. Journal of Computational Physics, Vol. 378 https://doi.org/10.1016/j.jcp.2018.10.045	journal	February 2019
Large-Scale Condensed Matter DFT Simulations: Performance and Capabilities of the CRYSTAL Code Erba, A.; Baima, J.; Bush, I. Journal of Chemical Theory and Computation, Vol. 13, Issue 10 https://doi.org/10.1021/acs.jctc.7b00687	journal	September 2017
Accelerated, scalable and reproducible AI-driven gravitational wave detection Huerta, E. A.; Khan, Asad; Huang, Xiaobo Nature Astronomy, Vol. 5, Issue 10 https://doi.org/10.1038/s41550-021-01405-0	journal	July 2021
A FAIR and AI-ready Higgs boson decay dataset Chen, Yifan; Huerta, E. A.; Duarte, Javier Scientific Data, Vol. 9, Issue 1 https://doi.org/10.1038/s41597-021-01109-0	journal	February 2022
FAIR principles for AI models with a practical application for accelerated high energy diffraction microscopy Ravi, Nikil; Chaturvedi, Pranshu; Huerta, E. A. Scientific Data, Vol. 9, Issue 1 https://doi.org/10.1038/s41597-022-01712-9	journal	November 2022
Enabling real-time multi-messenger astrophysics discoveries with deep learning Huerta, E. A.; Allen, Gabrielle; Andreoni, Igor Nature Reviews Physics, Vol. 1, Issue 10 https://doi.org/10.1038/s42254-019-0097-4	journal	October 2019
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators Lu, Lu; Jin, Pengzhan; Pang, Guofei Nature Machine Intelligence, Vol. 3, Issue 3 https://doi.org/10.1038/s42256-021-00302-5	journal	March 2021
The FAIR Guiding Principles for scientific data management and stewardship Wilkinson, Mark D.; Dumontier, Michel; Aalbersberg, IJsbrand Jan Scientific Data, Vol. 3, Issue 1 https://doi.org/10.1038/sdata.2016.18	journal	March 2016
Enhancing gravitational-wave science with machine learning Cuoco, Elena; Powell, Jade; Cavaglià, Marco Machine Learning: Science and Technology, Vol. 2, Issue 1 https://doi.org/10.1088/2632-2153/abb93a	journal	December 2020
Artificial neural network subgrid models of 2D compressible magnetohydrodynamic turbulence Rosofsky, Shawn G.; Huerta, E. A. Physical Review D, Vol. 101, Issue 8 https://doi.org/10.1103/PhysRevD.101.084024	journal	April 2020
Interpretable AI forecasting for numerical relativity waveforms of quasicircular, spinning, nonprecessing binary black hole mergers Khan, Asad; Huerta, E. A.; Zheng, Huihuo Physical Review D, Vol. 105, Issue 2 https://doi.org/10.1103/PhysRevD.105.024024	journal	January 2022
Accelerating parameter inference with graphics processing units Wysocki, D.; O’Shaughnessy, R.; Lange, Jacob Physical Review D, Vol. 99, Issue 8 https://doi.org/10.1103/PhysRevD.99.084026	journal	April 2019
BAMBI: blind accelerated multimodal Bayesian inference: BAMBI Graff, Philip; Feroz, Farhan; Hobson, Michael P. Monthly Notices of the Royal Astronomical Society https://doi.org/10.1111/j.1365-2966.2011.20288.x	journal	January 2012
Self-driving laboratory for accelerated discovery of thin-film materials MacLeod, B. P.; Parlane, F. G. L.; Morrissey, T. D. Science Advances, Vol. 6, Issue 20 https://doi.org/10.1126/sciadv.aaz8867	journal	May 2020
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets Wang, Sifan; Wang, Hanwen; Perdikaris, Paris Science Advances, Vol. 7, Issue 40 https://doi.org/10.1126/sciadv.abi8605	journal	October 2021
fPINNs: Fractional Physics-Informed Neural Networks Pang, Guofei; Lu, Lu; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 41, Issue 4 https://doi.org/10.1137/18M1229845	journal	January 2019
DeepXDE: A Deep Learning Library for Solving Differential Equations Lu, Lu; Meng, Xuhui; Mao, Zhiping SIAM Review, Vol. 63, Issue 1 https://doi.org/10.1137/19M1274067	journal	January 2021
Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control Ainsworth, Mark; Dong, Justin SIAM Journal on Scientific Computing, Vol. 43, Issue 4 https://doi.org/10.1137/20M1366587	journal	January 2021
Weather Forecasting Using GPU-Based Large-Eddy Simulations Schalkwijk, Jerôme; Jonker, Harmen J. J.; Siebesma, A. Pier Bulletin of the American Meteorological Society, Vol. 96, Issue 5 https://doi.org/10.1175/BAMS-D-14-00114.1	journal	May 2015
Big data and extreme-scale computing: Pathways to Convergence-Toward a shaping strategy for a future software and data ecosystem for scientific inquiry Asch, M.; Moore, T.; Badia, R. The International Journal of High Performance Computing Applications, Vol. 32, Issue 4 https://doi.org/10.1177/1094342018778123	journal	July 2018
Convergence of artificial intelligence and high performance computing on NSF-supported cyberinfrastructure Huerta, E. A.; Khan, Asad; Davis, Edward Journal of Big Data, Vol. 7, Issue 1 https://doi.org/10.1186/s40537-020-00361-2	journal	October 2020
A data ecosystem to support machine learning in materials science Blaiszik, Ben; Ward, Logan; Schwarting, Marcus MRS Communications, Vol. 9, Issue 4 https://doi.org/10.1557/mrc.2019.118	journal	October 2019
Inference-Optimized AI and High Performance Computing for Gravitational Wave Detection at Scale Chaturvedi, Pranshu; Khan, Asad; Tian, Minyang Frontiers in Artificial Intelligence, Vol. 5 https://doi.org/10.3389/frai.2022.828672	journal	February 2022
A Brief Overview of Black Hole-Neutron Star Mergers Foucart, Francois Frontiers in Astronomy and Space Sciences, Vol. 7 https://doi.org/10.3389/fspas.2020.00046	journal	July 2020
Machine Learning Interpretability: A Survey on Methods and Metrics Carvalho, Diogo V.; Pereira, Eduardo M.; Cardoso, Jaime S. Electronics, Vol. 8, Issue 8 https://doi.org/10.3390/electronics8080832	journal	July 2019
Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model Radice, David Symmetry, Vol. 12, Issue 8 https://doi.org/10.3390/sym12081249	journal	July 2020

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