Computational Mathematics and Scientific Computing Seminar
Dynamic Coupling of Full and Reduced Models via Randomized Online Basis Updates
Speaker: Benjamin Peherstorfer, Courant
Location: Warren Weaver Hall 1302
Date: Oct. 26, 2018, 10 a.m.
Traditional model reduction approaches typically fail for convection-dominated problems because the manifolds induced by the solutions of the full models contain high-dimensional features. We exploit that the manifolds are low dimensional in a local sense, so that they can be well-approximated locally with low-dimensional (reduced) spaces. We iteratively learn and adapt reduced spaces from randomly sampled data of the full models to locally approximate the solution manifolds. Furthermore, we discuss deterministic sampling strategies for basis adaptation that take structure of the reduced spaces into account to guide the sampling. Numerical experiments to predict pressure waves in combustion dynamics demonstrate that our approach achieves significant speedups in contrast to classical, static reduced models, which can be even more expensive to evaluate than the full models.