mlsanityData to 7 Oct 2026

DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization

arXiv 2108.00069 ↗First posted 30 Jul 2021math.DS cs.LG math.OCcited by 19

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Abstract (arXiv)

Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework for identifying governing laws in the form of differential equations from large-scale noisy experimental data sets. DySMHO consists of a novel moving horizon dynamic optimization strategy that sequentially learns the underlying governing equations from a large dictionary of basis functions. The sequential nature of DySMHO allows leveraging statistical arguments for eliminating irrelevant basis functions, avoiding overfitting to recover accurate and parsimonious forms of the governing equations. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws, is robust to high levels of measurement noise and that it can handle challenges such as multiple time scale dynamics.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 17 of its 84 references that are in the map. First posted on arXiv 30 Jul 2021.

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17 of 84 references.

References · 17

  1. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  2. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
  3. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
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5 more
  1. 2018A Unified Framework for Sparse Relaxed Regularized Regression: SR3cited by 36
  2. 2020nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applicationscited by 36
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Citing papers per year: 2022: 1; 2023: 4; 2024: 3; 2025: 8; 2026: 3.

19 papers.

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  1. 2023Generalized Teacher Forcing for Learning Chaotic Dynamicscited by 55
  2. 2024Out-of-Domain Generalization in Dynamical Systems Reconstructioncited by 33
  3. 2023Predicting Ordinary Differential Equations with Transformerscited by 26
  4. 2022Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamicscited by 13
  5. 2024A scalable generative model for dynamical system reconstruction from neuroimaging datacited by 9
  6. 2023Physics-constrained robust learning of open-form partial differential equations from limited and noisy datacited by 8
  7. 2025SyMANTIC: An Efficient Symbolic Regression Method for Interpretable and Parsimonious Model Discovery in Science and Beyondcited by 6
  8. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  9. 2025High-order expansion of Neural Ordinary Differential Equations flowscited by 1
  10. 2023Constrained Equation Learner Networks for Precision-Preserving Extrapolation of Robotic Skillscited by 0
  11. 2024Machine learning for cerebral blood vessels' malformationscited by 0
  12. 2025A Bayesian Approach for Discovering Time- Delayed Differential Equation from Datacited by 0
7 more
  1. 2025Impilict Runge-Kutta based sparse identification of governing equations in biologically motivated systemscited by 0
  2. 2025Staying Alive: Online Neural Network Maintenance and Systemic Driftcited by 0
  3. 2025Structural System Identification via Validation and Adaptationcited by 0
  4. 2025Discovering Interpretable Ordinary Differential Equations from Noisy Datacited by 0
  5. 2026An adjoint method for training data-driven reduced-order modelscited by 0
  6. 2026SOCIA-EVO: Automated Simulator Construction via Dual-Anchored Bi-Level Optimizationcited by 0
  7. 2026Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineeringcited by 0