Physically constrained neural network models for simulation

Abstract

We present a method for combining measurements of a system and mathematical descriptions of its behavior. The approach is the opposite of data assimilation, where data is used in order to correct the results of a model based on differential equations. Here, differential equations are used in order to correct interpolation results. The method may be interpreted as a regularization technique, able to handle the ill-posed character of a neural network regression problem. Significant examples illustrate the numerical behavior and show that the method proposed is effective to calculate. © 2007 Springer.