Tensor-Train Weak SINDy: Identifying High-Dimensional Nonlinear Dynamics
TT-WSINDy combines MANDy and WSINDy methods to discover high-dimensional nonlinear dynamical systems from data The tensor-train (TT) format enables computations without suffering from the curse of dimensionality The method performs weak-form transformation, regression, and sparsification over an exponentially-growing candidate function space Addresses computational and memory bottlenecks that plague existing weak-form methods in high-dimensional settings Submitted to arXiv on September 8, 2026 b
Analysis
TL;DR
- TT-WSINDy combines MANDy and WSINDy methods to discover high-dimensional nonlinear dynamical systems from data
- The tensor-train (TT) format enables computations without suffering from the curse of dimensionality
- The method performs weak-form transformation, regression, and sparsification over an exponentially-growing candidate function space
- Addresses computational and memory bottlenecks that plague existing weak-form methods in high-dimensional settings
- Submitted to arXiv on September 8, 2026 by Will Houser, Vanja Dukic, and David M. Bortz
Why It Matters
This work bridges a critical gap in data-driven scientific discovery: enabling the identification of nonlinear dynamics in high-dimensional systems that were previously computationally intractable. For AI practitioners and computational scientists working with complex dynamical systems—such as fluid dynamics, climate modeling, or biological networks—TT-WSINDy offers a scalable pathway to extract interpretable governing equations directly from observational data.
Technical Details
- Methodological synthesis: TT-WSINDy merges the Multidimensional Approximation of Nonlinear Dynamics (MANDy) framework with Weak Sparse Identification of Nonlinear Dynamics (WSINDy), leveraging the tensor-train decomposition to represent high-dimensional candidate function libraries compactly.
- Tensor-train format: The core innovation lies in implementing weak-form transformations, regression, and sparsification operations within the TT format, which compresses exponentially large tensors into a sequence of low-rank core tensors, circumventing the curse of dimensionality.
- Three-stage pipeline: The method executes (1) weak-form transformation of candidate functions against trajectory data, (2) regression to fit coefficients, and (3) sparsification (e.g., via sequential thresholding) to identify the governing terms.
- Applicable domains: The work targets problems in computational engineering, finance, and science where high-dimensional nonlinear dynamics need to be discovered from data, as reflected in its ACM and MSC classification codes.
Industry Insight
- The tensor-train approach could become a standard tool for scientific machine learning pipelines, particularly in physics-informed AI applications where interpretability of discovered equations is valued alongside predictive accuracy.
- As high-dimensional dynamical systems become increasingly relevant in climate science, materials discovery, and systems biology, methods like TT-WSINDy that scale beyond low-dimensional toy problems will see growing adoption in both academia and industry R&D.
- Practitioners should monitor the evolution of tensor-decomposition-based methods as a promising alternative to purely neural approaches for interpretable system identification, especially when data is limited but dimensional complexity is high.
Disclaimer: The above content is generated by AI and is for reference only.