Feedforward neural nets as discretization schemes for ODEs and DAEs
Because of their neurophysical origin neural nets can be studied for classification tasks, approximation properties or iterative algorithms. They can be interpreted as a distributed or massively parallel computer, where each unit accumulates a scalar product and computes a one-dimensional nonlinear activation function. A supervised learning strategy defines a nonlinear least squares problem, which is solved by gradient techniques such as backpropagation. Interpreting the weights in a net as state variable feedforward neural nets can be designed as numerical discretization schemes for ordinary differential equations (ODEs) and differential-algebraic equations (DAEs). The net architecture for the implicit Euler scheme is presented here and some experiments are given. The net approach is of interest for the overdetermined index-3 approach of DAEs from multibody system dynamics. More generally, these nets determine a parallel shooting-type algorithm.
scientific article; zbMATH DE number 1084093