Correction of Model Reduction Errors in Simulations

Abstract

In simulations of complex physical phenomena, model reductions are often required to decrease the computation time of the simulation model to a feasible level. Model reduction is often obtained by using a reduced model, which may be based on a reduced numerical approximation and simplifications of the underlying accurate model. The use of a reduced model, however, induces errors to the simulation results. In this paper, we describe and evaluate a novel approach for the correction of the approximation errors in reduced simulation models. The key idea is to model the approximation error between the accurate and reduced simulation model as an additive noise term to the reduced model and construct a low-cost predictor model for the approximation error based on statistical learning. In this paper, the approximation error approach is evaluated with the following problems: correction of spatial and temporal discretization errors in a time-varying heat equation--based evolution model, correction of spatial discre...