PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

Zichao Long, Yiping Lu, Bin Dong

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven discovery of PDEs. In this paper, we propose a new deep neural network, called PDE-Net 2.0, to discover (time-dependent) PDEs from observed dynamic data with minor prior knowledge on the underlying mechanism that drives the dynamics. The design of PDE-Net 2.0 is based on our earlier work [1] where the original version of PDE-Net was proposed. PDE-Net 2.0 is a combination of numerical approximation of differential operators by convolutions and a symbolic multi-layer neural network for model recovery. Comparing with existing approaches, PDE-Net 2.0 has the most flexibility and expressive power by learning both differential operators and the nonlinear response function of the underlying PDE model. Numerical experiments show that the PDE-Net 2.0 has the potential to uncover the hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment.

Original languageEnglish (US)
Article number108925
JournalJournal of Computational Physics
Volume399
DOIs
StatePublished - Dec 15 2019
Externally publishedYes

Fingerprint

Numerics
partial differential equations
learning
Partial differential equations
Partial differential equation
differential operators
Mathematical operators
Differential operator
Learning
Multilayer Neural Network
Nonlinear Response
Expressive Power
Multilayer neural networks
Response Function
Numerical Approximation
Convolution
Prior Knowledge
Data-driven
convolution integrals
Dynamical Behavior

Keywords

  • Convolutional neural network
  • Dynamic system
  • Partial differential equations
  • Symbolic neural network

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

PDE-Net 2.0 : Learning PDEs from data with a numeric-symbolic hybrid deep network. / Long, Zichao; Lu, Yiping; Dong, Bin.

In: Journal of Computational Physics, Vol. 399, 108925, 15.12.2019.

Research output: Contribution to journalArticle

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