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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