Model order reduction of multiscale models using kernel methods

This work investigates the possibilities of model order reduction of multiscale systems using kernel methods. 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 inand output of the microscale model. As learning methods we propose both support vector machines and a vectorial kernel greedy algorithm. We demonstrate the applicability of our approach using two multiscale models. 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.

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