Multilayer feedforward networks are universal approximators
Neural Networks
Neural algorithm for solving differential equations
Journal of Computational Physics
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
Neural Network Method for Solving Partial Differential Equations
Neural Processing Letters
Novel determination of differential-equation solutions: universal approximation method
Journal of Computational and Applied Mathematics
An artificial neural network method for solving boundary value problems - With arbitrary irregular boundary conditions
A comparative study of transformation functions for nonrigid image registration
IEEE Transactions on Image Processing
Artificial neural networks for solving ordinary and partial differential equations
IEEE Transactions on Neural Networks
Neural-network methods for boundary value problems with irregular boundaries
IEEE Transactions on Neural Networks
Comparison of artificial neural network architecture in solving ordinary differential equations
Advances in Artificial Neural Systems
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A method for solving boundary value problems (BVPs) is introduced using artificial neural networks (ANNs) for irregular domain boundaries with mixed Dirichlet/Neumann boundary conditions (BCs). The approximate ANN solution automatically satisfies BCs at all stages of training, including before training commences. This method is simpler than other ANN methods for solving BVPs due to its unconstrained nature and because automatic satisfaction of Dirichlet BCs provides a good starting approximate solution for significant portions of the domain. Automatic satisfaction of BCs is accomplished by the introduction of an innovative length factor. Several examples of BVP solution are presented for both linear and nonlinear differential equations in two and three dimensions. Error norms in the approximate solution on the order of 10-4 to 10-5 are reported for all example problems.