Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Wang, Sifan; Wang, Hanwen; Perdikaris, Paris

doi:10.1126/sciadv.abi8605

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Journal Article · Wed Sep 29 00:00:00 EDT 2021 · Science Advances

DOI:https://doi.org/10.1126/sciadv.abi8605· OSTI ID:1904189

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University of Pennsylvania, Philadelphia, PA (United States); OSTI
University of Pennsylvania, Philadelphia, PA (United States)
Univ. of Pennsylvania, Philadelphia, PA (United States)

Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

View Accepted Manuscript (DOE)

Research Organization:: University of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: US Air Force Office of Scientific Research (AFOSR); USDOE Advanced Research Projects Agency - Energy (ARPA-E); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AR0001201; SC0019116

OSTI ID:: 1904189

Alternate ID(s):: OSTI ID: 2339533

Journal Information:: Science Advances, Journal Name: Science Advances Journal Issue: 40 Vol. 7; ISSN 2375-2548

Publisher:: AAASCopyright Statement

Country of Publication:: United States

Language:: English

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