Artificial neural networks, incremental approximation, basis functions, meshless solution adaptivity, optimization, direct search methods, parallel processing, computational fluid dynamics. It is proposed to extend this capability further by attempting to use ANNs to model the solution of the two-dimensional compressible Euler equations. 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. The latter is especially advantagous when dealing with complicated physical or computational domains.
Computational efficiency is increased by using augmented radial bases and concurrent computing.
Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems, ensuring that the problem is well-posed. Numerical results and convergence rates are reported for steady-state problems, including the nonlinear compressible Euler equations. This work was supported under NASA Graduate Fellowship number NGT-70353.