Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis
11/28/2017
cs.AIcs.LGmath.AP

Official code: maziarraissi/PINNs (6,034 stars, MIT, last commit 2026-02-11).

Abstract

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second part of our two-part treatise, we focus on the problem of data-driven discovery of partial differential equations. Depending on whether the available data is scattered in space-time or arranged in fixed temporal snapshots, we introduce two main classes of algorithms, namely continuous time and discrete time models. The effectiveness of our approach is demonstrated using a wide range of benchmark problems in mathematical physics, including conservation laws, incompressible fluid flow, and the propagation of nonlinear shallow-water waves.

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Physics Informed Deep Learning: Data-driven Solutions and Discovery of Nonlinear Partial Differential Equations

6,0341,603Python, Wolfram LanguageJan 21, 20188 months agoMIT

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Cite this paper

@article{raissi2017physics,
  title  = {Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations},
  author = {Maziar Raissi and Paris Perdikaris and George Em Karniadakis},
  year   = {2017},
  eprint = {1711.10566},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1711.10566}
}

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