Long-time integration of parametric evolution equations with physics-informed DeepONets

Wang, Sifan; Perdikaris, Paris

doi:10.1016/j.jcp.2022.111855

Long-time integration of parametric evolution equations with physics-informed DeepONets

Journal Article · Mon Dec 19 00:00:00 EST 2022 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2022.111855· OSTI ID:2339532

Wang, Sifan ^[1]; ^[2]

University of Pennsylvania, Philadelphia, PA (United States); University of Pennsylvania
University of Pennsylvania, Philadelphia, PA (United States)

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to introduce new effective ways of simulating such equations, however existing approaches are not able to reliably return stable and accurate predictions across long temporal horizons. We aim to address this challenge by introducing an effective framework for learning evolution operators that map random initial conditions to associated ODE/PDE solutions within a short time interval. Such operators can be parametrized by deep neural networks that are trained in an entirely self-supervised manner without requiring one to generate any paired input-output observations. Global long-time predictions across a range of initial conditions can be then obtained by iteratively evaluating the trained model using each prediction as the initial condition for the next evaluation step. Here, this introduces a new approach to temporal domain decomposition that is shown to be effective in performing accurate long-time simulations for a wide range of parametric ODE and PDE systems, from wave propagation, to reaction-diffusion dynamics and stiff chemical kinetics, introducing a new way of rapidly emulating non-equilibrium processes in science and engineering.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: Air Force Office of 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:: 2339532

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 475; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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