Problem
Research questions and friction points this paper is trying to address.
high-dimensional
weak-form methods
data-driven discovery
dynamical systems
curse of dimensionality
Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
🤖 AI Summary
本文提出TT-WSINDy方法，结合MANDy和WSINDy技术，在高维非线性动力系统识别中采用张量训练格式，有效解决了计算和内存成本高的问题。
📝 Abstract
In recent years, weak-form methods have made significant advances in data-driven discovery of dynamical systems. However, in high-dimensional settings, current techniques can prove expensive in both computation and memory. In this work, we introduce TT-WSINDy, which combines techniques of the Multidimensional Approximation of Nonlinear Dynamics (MANDy) and Weak Sparse Identification of Nonlinear Dynamics (WSINDy) methods, implementing requisite computations in the tensor-train (TT) format. We demonstrate that this method is able to search an exponentially-growing space of candidate functions -- performing weak-form transformation, regression, and sparsification -- without suffering from the curse of dimensionality.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Tensor-Train
Weak-form
High-dimensional
Sparsification
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