用随机微分方程建模混沌系统，提升稳定性与精度
Stochastic generative methods for stable and accurate closure modeling of chaotic dynamical systems
- 用随机微分方程构建闭合模型，替代传统耗散方法
- 在Lorenz-63系统上验证，生成结果更准确
- 适合研究混沌系统建模的气候与流体科学家
传统确定性亚网格尺度（SGS）模型常具有耗散性和不稳定性，尤其在混沌湍流区域。气候科学和海洋建模的研究需求推动了对混沌动力系统使用随机SGS模型。同时，基于生成模型的底层动力学建模正快速发展。本文旨在将随机积分引入混沌动力系统的闭合建模中，并探索随机模型对线性化混沌系统可能的稳定作用。提出基于随机微分方程（SDE）的参数化与生成式闭合建模方法，推导并实现一种基于波动的二次扩散模型，通过连接理论模型与生成方法，显著提升精度。实验在Lorenz-63系统上完成，验证了该方法的有效性。
原文摘要 · Abstract (English)
Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean 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 stochastic integration toward closure modeling for chaotic dynamical systems. Further, we want to explore the potential stabilizing effect that stochastic models could have on linearized chaotic systems. We propose parametric and generative approaches for closure modeling using stochastic differential equations (SDEs). We derive and implement a quadratic diffusion model based on the fluctuations, demonstrating increased accuracy from bridging theoretical models with generative approaches. Results are demonstrated on the Lorenz-63 dynamical system.
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