Generative modeling for closure and linearized stability of chaotic dynamical systems

Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in earth system modeling motivates the use of stochastic SGS models for chaotic dynamics. Further, developing stochastic generative models of underlying dynamics is a rapidly expanding field. In this work, we aim to incorporate diffusion modeling toward closure modeling for chaotic dynamical systems. We also want to explore the potential stabilizing effect that these models could have on linearized chaotic systems.