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Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
arXiv:2609.09434v1 Announce Type: new Abstract: In recent years, weak-form methods have made significant advances in data-driven discovery of dynamical systems. However, in high-dimensional settings,
arXiv:2609.09434v1 Announce Type: new 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.
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Source: arXiv cs.LG | 2026-09-10