Colloque - Evie Nielen : Efficient Greedy Sampling for Model Order Reduction

Yvon Maday Chaire Informatique et sciences numériques Collège de France Année 2025-2026 Colloque : Aspects mathématiques et appliqués des méthodes de réduction de complexité - Evie Nielen : Efficient Greedy Sampling for Model Order Reduction Evie Nielen Doctoral Candidate, Mathematics and Computer Science, Computational Science, University of Technology Eindhoven, Netherlands Résumé This talk presents the Polytope Division Method (PDM), a greedy algorithm for solving high-dimensional configuration optimization problems—such as those arising in model reduction and optimal experimental design—where one seeks an optimal sampling of parameter spaces. Classical approaches like standard greedy sampling rely on fixed training sets and quickly suffer from the curse of dimensionality. PDM replaces global sampling with an adaptive, geometry-driven strategy based on recursive polytope subdivision. At each step, the method evaluates the objective only at samples in dynamically refined regions. This yields a sampling complexity that scales linearly with dimension, avoiding exponential growth. The approach requires no a priori choice of training set size and focuses computational effort where it matters most. Applications to reduced basis methods and empirical interpolation demonstrate strong performance gains. Numerical results show that PDM achieves comparable accuracy to classical methods at significantly lower offline reduced cost.