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

NEUROCOMPUTING

卷:155

Article

Rudd, Keith¹  Ferrari, Silvia¹ 

[1] Duke Univ, Dept Mech Engn & Mat Sci, Lab Intelligent Syst & Controls, Durham, NC 27706 USA

关键词: Neural networks;    Initial-boundary value problem;    Galerkin methods;    Spectral methods;    Partial differential equations;    Irregular domains;   

DOI  :  10.1016/j.neucom.2014.11.058

来源: Elsevier

【 摘 要 】

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. (C) 2014 The Authors. Published by Elsevier B.V.

【 授权许可】

Free