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Title: Physics-informed machine learning

Abstract

Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Furthermore, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3];  [4];  [4]; ORCiD logo [1]
+ Show Author Affiliations
  1. Brown University, Providence, RI (United States)
  2. Johns Hopkins University, Baltimore, MD (United States)
  3. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
  4. University of Pennsylvania, Philadelphia, PA (United States)
Publication Date:
Research Org.:
Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE Advanced Research Projects Agency - Energy (ARPA-E); US Air Force Office of Scientific Research (AFOSR)
OSTI Identifier:
2282016
Grant/Contract Number:  
SC0019453; FA9550-20-1-0060; 1256545; FA9550-20-1-0358
Resource Type:
Accepted Manuscript
Journal Name:
Nature Reviews Physics
Additional Journal Information:
Journal Volume: 3; Journal Issue: 6; Journal ID: ISSN 2522-5820
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Applied mathematics; Computational science

Citation Formats

Karniadakis, George Em, Kevrekidis, Ioannis G., Lu, Lu, Perdikaris, Paris, Wang, Sifan, and Yang, Liu. Physics-informed machine learning. United States: N. p., 2021. Web. doi:10.1038/s42254-021-00314-5.
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Karniadakis, George Em, Kevrekidis, Ioannis G., Lu, Lu, Perdikaris, Paris, Wang, Sifan, & Yang, Liu. Physics-informed machine learning. United States. https://doi.org/10.1038/s42254-021-00314-5
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Karniadakis, George Em, Kevrekidis, Ioannis G., Lu, Lu, Perdikaris, Paris, Wang, Sifan, and Yang, Liu. Mon . "Physics-informed machine learning". United States. https://doi.org/10.1038/s42254-021-00314-5. https://www.osti.gov/servlets/purl/2282016.
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@article{osti_2282016,
title = {Physics-informed machine learning},
author = {Karniadakis, George Em and Kevrekidis, Ioannis G. and Lu, Lu and Perdikaris, Paris and Wang, Sifan and Yang, Liu},
abstractNote = {Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Furthermore, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.},
doi = {10.1038/s42254-021-00314-5},
journal = {Nature Reviews Physics},
number = 6,
volume = 3,
place = {United States},
year = {Mon May 24 00:00:00 EDT 2021},
month = {Mon May 24 00:00:00 EDT 2021}
}
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https://doi.org/10.1038/s42254-021-00314-5
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