Artificial Neural Networks for Solving Ordinary and Partial Differential Equations  

Oleh:

Lagaris, I. E. ; Fotiadis, D. I. ; Likas, A.

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: IEEE Transactions on Neural Networks vol. 9 no. 5 (1998), page 987-1000.
Topik: EQUATIONS; artificial; neural networks; ordinary; partial differential; equations

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: II36.3 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

Lihat Detail Induk

Isi artikel

We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the initial / boundary conditions and contains no adjustable parameters. The second part is constructed so as not to affect the initial / boundary conditions. This part involves a feedforward neural network containing adjustable parameters (the weights). Hence by construction the initial / boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ordinary differential equations (ODE), to systems of coupled ODE and also to partial differential equations (PDE). In this article, we illustrate the method by solving a variety of model problems and present comparisons with solutions obtained using the Galerkin finite element method for several cases of partial differential equations. With the advent of neuroprocessors and digital signal processors the method becomes particularly interesting due to the expected essential gains in the execution speed.

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