A constrained integration (CINT) approach to solving partial differential equations using artificial neural networks

Journal Article (Journal Article)

This paper presents a novel constrained integration (CINT) method for solving initial boundary value partial differential equations (PDEs). The CINT method combines classical Galerkin methods with a constrained backpropogation training approach to obtain an artificial neural network representation of the PDE solution that approximately satisfies the boundary conditions at every integration step. The advantage of CINT over existing methods is that it is readily applicable to solving PDEs on irregular domains, and requires no special modification for domains with complex geometries. Furthermore, the CINT method provides a semi-analytical solution that is infinitely differentiable. In this paper the CINT method is demonstrated on two hyperbolic and one parabolic initial boundary value problems with a known analytical solutions that can be used for performance comparison. The numerical results show that, when compared to the most efficient finite element methods, the CINT method achieves significant improvements both in terms of computational time and accuracy.

Full Text

Duke Authors

Cited Authors

  • Rudd, K; Ferrari, S

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 155 /

Start / End Page

  • 277 - 285

Electronic International Standard Serial Number (EISSN)

  • 1872-8286

International Standard Serial Number (ISSN)

  • 0925-2312

Digital Object Identifier (DOI)

  • 10.1016/j.neucom.2014.11.058

Citation Source

  • Scopus