Adaptive solution of differential equations for the regularization of artificial neural networks

The authors propose using artificial neural networks to model the solution of the two-dimensional Euler equation which models inviscid and compressible fluid flow. The code thus created should not only have the same accuracy as a more conventional computer code, but should still retain the ability of an ANN to modify itself when exposed to experimental data, thus yielding software that could be specialized with experimental results. To accomplish these objectives, the method of optimal incremental function approximation has been developed for the adaptive solution of differential equations using ANN architecture. Two major attractive features of this approach are that: (1) the developed method is flexible enough to use any of the popular transfer functions and (2) the developed method requires minimal user interaction. The latter is especially advantageous when dealing with complicated physical or computational domains. Numerical results are presented and compared to conventional methods. The accuracy is considered satisfactory.