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

Maziar Raissi, Paris Perdikaris, George E Karniadakis

6/13/2018

Keywords: Fundamentals, Science & Engineering, Supervision by Gradient (PDE)

Venue: Journal of Computational Physics 2019

Bibtex: @article{raissi2019physicsinformed, author = {Maziar Raissi and Paris Perdikaris and George E Karniadakis}, journal = {Journal of Computational Physics}, pages = {686--707}, year = {2019}, publisher = {Elsevier}, title = {Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations}, volume = {378}, entrytype = {article}, id = {raissi2019physicsinformed} }

Abstract

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

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