Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator
This work addresses the need for more generalizable closure models in fields like climate science and fluid dynamics, though it appears incremental as it builds on existing generative machine learning techniques.
The authors tackled the problem of simulating complex multiscale dynamical systems like turbulence by developing a data-driven stochastic closure model using conditional diffusion models and neural operators, which provides a systematic approach for constructing such models with continuous spatiotemporal fields.
Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system, for which direct numerical simulation that resolves all scales is often too expensive. For those systems without a clear scale separation, deterministic and local closure models often lack enough generalization capability, which limits their performance in many real-world applications. In this work, we propose a data-driven modeling framework for constructing stochastic and non-local closure models via conditional diffusion model and neural operator. Specifically, the Fourier neural operator is incorporated into a score-based diffusion model, which serves as a data-driven stochastic closure model for complex dynamical systems governed by partial differential equations (PDEs). We also demonstrate how accelerated sampling methods can improve the efficiency of the data-driven stochastic closure model. The results show that the proposed methodology provides a systematic approach via generative machine learning techniques to construct data-driven stochastic closure models for multiscale dynamical systems with continuous spatiotemporal fields.