B03 Robust data-driven coarse-graining for surrogate modeling

Determining effective low-dimensional reduced order models from observations of a system with widely separated scales can be severely ill-posed. In this project, we will develop and analyze novel parametric as well as non-parametric methodologies with provable stability and robustness guarantees. The mathematical foundation of these approaches will be based on connecting techniques of the theory of homogenization for singularly perturbed stochastic dynamical systems, regularization techniques for inverse problems, and Bayesian learning methodologies.