arXiv：cs.LG· Evan Habbershaw, John Harlim, Senwei Liang·· 3 小时前AI 评分29
用核岭回归学习动力系统的闭合模型
Learning Closure of Dynamical Systems with Kernel Ridge Regression
AI 导读
研究者提出基于核岭回归（KRR）的闭合建模框架，用于识别动力系统中缺失的分量，覆盖 ODE/PDE 的差分方程闭合与动理学方程矩闭合两类问题。在 Lorenz-63 和 Kuramoto-Sivashinsky 方程上，该方法实现准确的长时程预测，并显著优于基于 LSTM 的闭合模型。
正文
Abstract:We develop a closure modeling framework for identifying missing components of dynamical systems using Kernel Ridge Regression (KRR). The framework addresses two classes of closure problems: difference-equation closures arising in ODE and PDE settings, and algebraic closures arising from moment closure in kinetic equations. For the first class, we derive an error bound in an ODE setting that quantifies contributions from time integration, approximation of unresolved scales, and interpolation required to couple unresolved-scale effects to the resolved solver. Numerical experiments on the Lorenz-63 system and the Kuramoto-Sivashinsky equation demonstrate accurate long-horizon predictions and substantial improvements over an LSTM-based closure model. For the second class, we consider moment closure for a one-dimensional kinetic equation by modeling discrepancies between kinetic and macroscopic fluxes as a function of the resolved macroscopic variables. We compare global KRR models based on PCA coordinates with spatially local models. While the global model performs well for unimodal initial conditions, its accuracy deteriorates for bimodal initial conditions. Spatially local models with appropriate modeling inputs improve robustness and achieve higher predictive accuracy.
| Comments: | 31 pages, 8 figures |
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG); Dynamical Systems (math.DS) |
| MSC classes: | 37M05 (Primary), 62J07, 68T05 |
| Cite as: | arXiv:2610.02564 [math.NA] |
| (or arXiv:2610.02564v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02564 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Evan Habbershaw [view email]
[v1]
Thu, 1 Oct 2026 22:57:05 UTC (1,034 KB)
来源：arXiv：cs.LG · arxiv.org