Special CMX Seminar

Developing reliable reduced-order models for multiscale systems requires representing the influence of unresolved variables on both the stationary statistics and temporal behavior of the resolved dynamics. This is the central challenge of building stochastic closures. Standard a priori Markovian closures often fail to preserve these properties, while non-Markovian and a posteriori approaches can be computationally expensive, requiring explicit memory representations, repeated model integrations, or differentiation through numerical solvers. In this talk, I will present a new direction that leverages recent breakthroughs in score-based generative modeling to construct a priori Markovian stochastic closures designed to reproduce selected statistical and dynamical observables. I will illustrate the framework through applications to a diverse range of systems, from coarse-grained stochastic partial differential equations and nonlinear chaotic dynamics to geophysical systems.