Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
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.
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BibTeX
@misc{houser2026tensortrain,
title = {{Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics}},
author = {Will Houser and Vanja Dukic and David M. Bortz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.09434},
eprint = {2609.09434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09434},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
AU - Will Houser
AU - Vanja Dukic
AU - David M. Bortz
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.09434
UR - https://arxiv.org/abs/2609.09434
AB - 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.
ER -