Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics

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.

Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Machine Learning (stat.ML)

arXiv:2609.09434 [cs.LG]

(or arXiv:2609.09434v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.09434 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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