张量列弱SINDy：识别高维非线性动力学
Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
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中文总结 AI 辅助
提出TT-WSINDy方法，结合MANDy与WSINDy技术，利用张量列格式在高维空间中高效识别非线性动力学，避免维数灾难。
中文摘要 AI 辅助
近年来，弱形式方法在动力系统的数据驱动发现方面取得了显著进展。然而，在高维设置下，现有技术在计算和内存方面都可能代价高昂。在本工作中，我们引入了TT-WSINDy，该方法结合了非线性动力学多维逼近（MANDy）和弱稀疏非线性动力学识别（WSINDy）方法的技术，并以张量列（TT）格式实现所需计算。我们证明，该方法能够搜索指数增长候选函数空间——执行弱形式变换、回归和稀疏化——而不会遭受维数灾难。
英文摘要
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.
发表机构
- University of Colorado（科罗拉多大学）
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