# Artificial neural networks for solving ordinary and partial differential equations

@article{Lagaris1998ArtificialNN, title={Artificial neural networks for solving ordinary and partial differential equations}, author={Isaac E. Lagaris and Aristidis Likas and Dimitrios I. Fotiadis}, journal={IEEE transactions on neural networks}, year={1998}, volume={9 5}, pages={ 987-1000 } }

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… Expand

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