کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6866007 679603 2015 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A constrained integration (CINT) approach to solving partial differential equations using artificial neural networks
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
A constrained integration (CINT) approach to solving partial differential equations using artificial neural networks
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Neurocomputing - Volume 155, 1 May 2015, Pages 277-285
نویسندگان
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