Scalable algorithms for physics-informed neural and graph networks

Shukla, Khemraj; Xu, Mengjia; Trask, Nathaniel; Karniadakis, George E.

doi:10.1017/dce.2022.24

Title: Scalable algorithms for physics-informed neural and graph networks

Journal Article · Wed Jun 29 00:00:00 EDT 2022 · Data-Centric Engineering

DOI:https://doi.org/10.1017/dce.2022.24· OSTI ID:1872036

Shukla, Khemraj ^[1]; Xu, Mengjia ^[2]; Trask, Nathaniel ^[3];

^[1]

Brown University, Providence, RI (United States)
Brown University, Providence, RI (United States); Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space–time domain. Such PIML integrates multimodality and multifidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs). We present representative examples for both forward and inverse problems and discuss what advances are needed to scale up PINNs, PIGNs and more broadly GNNs for large-scale engineering problems.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: NA0003525; SC0019453; FA9550-20-1-0358

OSTI ID:: 1872036

Report Number(s):: SAND2022-6955J; 706667

Journal Information:: Data-Centric Engineering, Vol. 3; ISSN 2632-6736

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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