mlsanityData to 14 Oct 2026

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

arXiv 2609.09434 ↗First posted 8 Sep 2026cs.LG cs.CE stat.MLcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 22 of its 56 references that are in the map. First posted on arXiv 8 Sep 2026.

Builds on

22 of 56 references.

References · 22

  1. 2020Weak SINDy For Partial Differential Equationscited by 155
  2. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  3. 2020SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamicscited by 125
  4. 2020Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Datacited by 37
  5. 2020Numerical differentiation of noisy data: A unifying multi-objective optimization frameworkcited by 20
  6. 2023Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamicscited by 20
  7. 2023Weak-Form Latent Space Dynamics Identificationcited by 20
  8. 2020Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated datacited by 13
  9. 2022Online Weak-form Sparse Identification of Partial Differential Equationscited by 13
  10. 2024Physics-informed active learning with simultaneous weak-form latent space dynamics identificationcited by 13
  11. 2023Coarse-Graining Hamiltonian Systems Using WSINDycited by 11
  12. 2024The Weak Form Is Stronger Than You Thinkcited by 11
10 more
  1. 2025A practical identifiability criterion leveraging weak-form parameter estimationcited by 5
  2. 2025Weak Form Scientific Machine Learning: Test Function Construction for System Identificationcited by 5
  3. 2025Learning Physically Interpretable Atmospheric Models from Data with WSINDycited by 4
  4. 2025Bias and Coverage Properties of the WENDy-IRLS Algorithmcited by 3
  5. 2025Weak Form Learning for Mean-Field Partial Differential Equations: an Application to Insect Movementcited by 3
  6. 2024Physics-guided weak-form discovery of reduced-order models for trapped ultracold hydrodynamicscited by 2
  7. 2025WENDy for Nonlinear-in-Parameters ODEscited by 2
  8. 2026Learning effective models from network dynamics data with multiple initial conditions using weak form SINDycited by 2
  9. 2026WSINDy for Model Predictive Control with Applications to Fusion, Drones, and Chaoscited by 1
  10. 2026Robust Moment-Based Estimation via Spectral Gradient Reweightingcited by 1

Built on by

Not cited yet.