从观测数据学习随机多尺度模型，提升复杂系统模拟精度。
Learning Stochastic Multiscale Models
- 用粗网格宏观状态+微观隐变量建模未解析动力学
- 相比直接模拟和简化模型，预测误差显著更低
- 无需模拟器，适合缺乏物理方程的复杂系统研究
物理科学中存在大量需处理宽范围时空尺度的动力系统，直接数值模拟因需在最细尺度离散化，导致状态空间维数极高。本文提出一种从观测数据直接学习随机多尺度模型的方法，该模型以随机微分方程形式表达。借鉴物理多尺度建模思想，在粗网格上定义宏观状态，并引入微观隐状态显式建模未解析动力学。采用无需模拟器的变分推断方法学习模型参数，使用专家乘积似然函数强制实现尺度分离。详细数值实验表明，所学多尺度模型在等效分辨率下，相比欠解析直接模拟和闭包型模型，以及降阶建模方法，均展现出更优的预测准确性。
原文摘要 · Abstract (English)
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at the finest relevant scales, leading to a high-dimensional state space. In this work, we propose an approach to learn stochastic multiscale models in the form of stochastic differential equations directly from observational data. Drawing inspiration from physics-based multiscale modeling approaches, we resolve the macroscale state on a coarse mesh while introducing a microscale latent state to explicitly model unresolved dynamics. We learn the parameters of the multiscale model using a simulator-free amortized variational inference method with a Product of Experts likelihood that enforces scale separation. We present detailed numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy compared to under-resolved direct numerical simulation and closure-type models at equivalent resolution, as well as reduced-order modeling approaches.
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