arXiv：cs.LG（机器学习，全量分类）· Will Houser, Vanja Dukic, David M. Bortz·· 15 小时前AI 评分34
Tensor-Train Weak SINDy：识别高维非线性动力学
Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
AI 导读
研究者提出 TT-WSINDy，将弱形式稀疏辨识（WSINDy）与张量列（TT）表示结合，在 TT 格式下完成弱形式变换、回归与稀疏化，解决了高维系统中候选函数库随状态维度指数增长的问题。该方法证明 TT 形式可还原对应的 WSINDy 回归问题，并给出张量列稀疏化过程的多项式时间与内存复杂度上界。数值实验显示其在高维系统下对测量噪声具有鲁棒性并节省计算开销。
正文
Abstract:Weak Sparse Identification of Nonlinear Dynamics (WSINDy) provides a noise-robust approach for learning dynamical systems from data without requiring numerical differentiation. However, for high-dimensional systems, tensor-product libraries of candidate functions grow exponentially with the state dimension, making standard WSINDy expensive in both computation and memory. The Multidimensional Approximation of Nonlinear Dynamics (MANDy) addresses this scaling through a tensor-train (TT) representation of the candidate library, but does not provide a mechanism for sparse model selection. Here, we combine these approaches to develop TT-WSINDy, which performs the weak-form transformation, regression, and sparsification in TT format. We show that the TT formulation recovers the corresponding WSINDy regression problem and derive polynomial time and memory complexity bounds for the tensor-train sparsification procedure. Numerical experiments demonstrate robustness to measurement noise and computational savings for high-dimensional systems.
| Comments: | 34 pages, 8 figures |
| Subjects: | Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Machine Learning (stat.ML) |
| MSC classes: | 65F55, 15A69, 93B30, 65L09 |
| ACM classes: | G.1.3 |
| Cite as: | arXiv:2609.09434 [cs.LG] |
| (or arXiv:2609.09434v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.09434 arXiv-issued DOI via DataCite |
Submission history
From: William Houser [view email]
[v1]
Tue, 8 Sep 2026 20:35:25 UTC (1,812 KB)
[v2]
Thu, 1 Oct 2026 17:31:53 UTC (1,812 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org