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.

本研究解决了在没有明显尺度分离的复杂多尺度动态系统中，传统确定性闭合模型泛化能力不足的问题。提出了一种数据驱动的建模框架，采用条件扩散模型和神经算子构建随机非局部闭合模型，显著提高了模型的效率和适用性。结果表明，该方法能够有效构建用于多尺度动态系统的随机闭合模型，具有广泛的应用潜力。

基于条件扩散模型和神经算子的 数据驱动随机闭合建模

基于条件扩散模型和神经算子的数据驱动随机闭合建模