标题： 随机生成方法用于混沌动力系统的稳定和精确闭合建模 显示英文标题

标题： Stochastic generative methods for stable and accurate closure modeling of chaotic dynamical systems

摘要： 传统的确定性亚网格尺度（SGS）模型通常是耗散的且不稳定的，尤其是在混沌和湍流流动区域。 气候科学和海洋建模领域的持续工作推动了对混沌动力学使用随机SGS模型。 此外，开发底层动力学的随机生成模型是一个迅速扩展的领域。 在本工作中，我们旨在将随机积分应用于混沌动力系统的闭合建模。 此外，我们想探索随机模型对线性化混沌系统可能具有的稳定效果。 我们提出了使用随机微分方程（SDEs）的参数化和生成方法用于闭合建模。 我们推导并实现了基于波动的二次扩散模型，证明了通过将理论模型与生成方法相结合可以提高准确性。 结果在Lorenz-63动力系统上进行了演示。 显示英文摘要

摘要： 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.