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Title: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Abstract

Hejre, we introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. Moreover, the effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [1]
  1. Brown Univ., Providence, RI (United States)
  2. Univ. of Pennsylvania, Philadelphia, PA (United States)
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1595805
Alternate Identifier(s):
OSTI ID: 1635941
Grant/Contract Number:  
SC0019116; N66001-15-2-4055; FA9550-17-1-0013
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 378; Journal Issue: C; Related Information: https://github.com/PredictiveIntelligenceLab/PINNs; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Data-driven scientific computing; Machine learning; Predictive modeling; Runge–Kutta methods; Nonlinear dynamics

Citation Formats

Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. United States: N. p., 2018. Web. doi:10.1016/j.jcp.2018.10.045.
Raissi, Maziar, Perdikaris, Paris, & Karniadakis, George Em. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. United States. https://doi.org/10.1016/j.jcp.2018.10.045
Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em. Sat . "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". United States. https://doi.org/10.1016/j.jcp.2018.10.045. https://www.osti.gov/servlets/purl/1595805.
@article{osti_1595805,
title = {Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
author = {Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em},
abstractNote = {Hejre, we introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. Moreover, the effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.},
doi = {10.1016/j.jcp.2018.10.045},
journal = {Journal of Computational Physics},
number = C,
volume = 378,
place = {United States},
year = {2018},
month = {11}
}

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Cited by: 137 works
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