Neural Operator for Modeling Dynamical Systems with Trajectories and Statistics Matching

Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and Earth’s climate, for which direct numerical simulation that resolves all scales is often too expensive. In recent years, neural operator and neural ODE provide spatially and temporally continuous frameworks that are independent of discretization for learning an unknown dynamical system. In this talk, we present a data-driven modeling framework for constructing continuous closure models that can efficiently match both short-term trajectories and long-term statistics for complex dynamical systems, leading to more predictive and stable data-driven closure models. Specifically, neural operator with a hybrid learning method will be demonstrated by a few canonical examples. We also show how different types of regularization can be imposed to improve the performance of the learned closure models. The results show that the proposed methodology provides an efficient and robust framework for constructing generalizable data-driven closure models for dynamical systems.