Surrogate modeling of multiscale models using kernel methods

Abstract

This work investigates the possibilities of acceleration and approximation of multiscale systems using kernel methods. The key element is to learn the interface between the different scales using a fast surrogate for the microscale model, which is given by multivariate kernel expansions. The expansions are computed using statistically representative samples of in- and output of the microscale model. As learning methods we apply both support vector machines and a vectorial kernel greedy algorithm. We demonstrate the applicability of the resulting surrogate models using two multiscale models from different engineering disciplines. First, we consider a human spine model coupling a macroscale multibody system with a microscale intervertebral spine disc model, and second, a model for simulation of saturation overshoots in porous media involving nonclassical shock waves.