Parametric Reduced Order Models Using Adaptive Sampling and Interpolation

Abstract Over the past decade, a number of approaches have been put forth to improve the accuracy of projection-based reduced order models over parameter ranges. These can be classified as either i.) building a global basis that is suitable for a large parameter set by applying sampling strategies, ii.) identifying parameter dependent coefficient functions in the reduced order model, or iii.) changing the basis as parameters change. We propose a strategy that combines sampling with basis interpolation. We apply sampling strategies that identify suitable parameter values from which associated basis functions are interpolated at any parameter value in a region. While our approach has practical limits to roughly a handful of parameters, it has the advantage of achieving a desired level of accuracy in parametric reduced-order models of relatively small size. We present this method using a proper orthogonal decomposition model of a nonlinear partial differential equation with variable coefficients and initial conditions.