mlsanityData to 7 Oct 2026

Physics-informed AI and ML-based sparse system identification algorithm for discovery of PDE's representing nonlinear dynamic systems

arXiv 2410.10023 ↗First posted 13 Oct 2024physics.comp-ph cs.LGcited by 3

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Abstract (arXiv)

Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true and false functions difficult, which limits the choice of functions. In this study, an equation discovery method has been proposed to tackle these problems. The key elements include a) use of B-splines for data fitting to get analytical derivatives superior to numerical derivatives, b) sequentially regularized derivatives for denoising (SRDD) algorithm, highly effective in removing noise from signal without system information loss, c) uncorrelated component analysis (UCA) algorithm that identifies and eliminates highly correlated functions while retaining the true functions, and d) physics-informed spline fitting (PISF) where the spline fitting is updated gradually while satisfying the governing equation with a dictionary of candidate functions to converge to the correct equation sequentially. The complete framework is built on a unified deep-learning architecture that eases the optimization process. The proposed method is demonstrated to discover various differential equations at various noise levels, including three-dimensional, fourth-order, and stiff equations. The parameter estimation converges accurately to the true values with a small coefficient of variation, suggesting robustness to the noise.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 14 of its 38 references that are in the map. First posted on arXiv 13 Oct 2024.

Builds on

14 of 38 references.

References · 14

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2017PDE-Net: Learning PDEs from Datacited by 304
  3. 2017Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equationscited by 208
  4. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 208
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  8. 2022Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learningcited by 24
  9. 2020Sparse Identification of Nonlinear Dynamical Systems via Reweighted ℓ1-regularized Least Squarescited by 21
  10. 2021Robust discovery of partial differential equations in complex situationscited by 21
  11. 2018Nonlinear System Identification of Soft Robot Dynamics Using Koopman Operator Theorycited by 7
  12. 2021A Hybrid Science-Guided Machine Learning Approach for Modeling and Optimizing Chemical Processescited by 7
2 more
  1. 2021Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equationscited by 3
  2. 2021Data-Driven Theory-guided Learning of Partial Differential Equations using SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE)cited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamicscited by 4
  2. 2024KAN/MultKAN with Physics-Informed Spline fitting (KAN-PISF) for ordinary/partial differential equation discovery of nonlinear dynamic systemscited by 1
  3. 2026Symbolic Graph Networks for Robust PDE Discovery from Noisy Sparse Datacited by 0