Predicting near optimal interpolation points for parametric model order reduction using regression models

Abstract

The design of vibro-acoustic systems, such as vehicle interiors, regarding optimal vibrational or sound radiation properties requires the solution of many numerical models under varying parameters, as often material or geometric uncertainties have to be considered. Vibro-acoustic systems are typically large and numerically expensive to solve, so it is desirable to use an efficient parametrized surrogate model for optimization tasks. High quality reduced models of non-parametric systems can be computed by projection, given a set of optimal expansion points. However, finding a set of optimal expansion points can be computationally expensive and each set is valid for a specific parameter realization only. The method presented in this contribution learns the map between a model's parameter realizations and the corresponding sets of expansion points using data-driven methods. Queried with an unknown set of parameters, the learned model returns a set of expansion points which are used to compute the corresponding reduced model efficiently. Numerical experiments on two vibro-acoustic models of different complexity are performed and three data driven regression methods are evaluated: multivariate polynomial regression, k-nearest neighbors, and support vector regression. Especially k-nearest neighbors regression yields accurate results for different types of physical models while being computationally inexpensive to fit.