Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
cs.LG, cs.CE, stat.ML
Submitted: 2026-09-08
Updated: 2026-10-01
Comments: 34 pages, 8 figures
Code: https://github.com/whouser2001/TT-WSINDy
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: In recent years, weak-form methods have made significant advances in data-driven discovery of dynamical systems.
Terminology
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.
Sources
- Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)
- PDE Identification Using Noise Adaptive Differentiation in Strong Form (S-IDENT)
- Physics-informed active learning with simultaneous weak-form latent space dynamics identification
- WSINDy for Model Predictive Control with Applications to Fusion, Drones, and Chaos
- Learning interpretable closures for thermal radiation transport in optically-thin media using WSINDy
- Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy
- Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data
- Robust Moment-Based Estimation via Spectral Gradient Reweighting
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