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A joint optimization approach to identifying sparse dynamics using least squares kernel collocation

arXiv 2511.18555 ↗First posted 23 Nov 2025stat.ME cs.LG math.DScited by 0

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Abstract (arXiv)

We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery strategies for the ODE over a function library combined with techniques from reproducing kernel Hilbert space (RKHS) theory for estimating the state and discretizing the ODE. Our numerical experiments reveal that the proposed strategy leads to significant gains in terms of accuracy, sample efficiency, and robustness to noise, both in terms of learning the equation and estimating the unknown states. This work demonstrates capabilities well beyond existing and widely used algorithms while extending the modeling flexibility of other recent developments in equation discovery.

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References · 40

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  3. 2022On Neural Differential Equationscited by 268
  4. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 235
  5. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
  6. 2020Physics-informed learning of governing equations from scarce datacited by 167
  7. 2020Weak SINDy For Partial Differential Equationscited by 155
  8. 2021Equinox: neural networks in JAX via callable PyTrees and filtered transformationscited by 148
  9. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 137
  10. 2021Solving and Learning Nonlinear PDEs with Gaussian Processescited by 129
  11. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 89
  12. 2022Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoderscited by 58
28 more
  1. 2019A unified sparse optimization framework to learn parsimonious physics-informed models from datacited by 49
  2. 2020Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Datacited by 37
  3. 2018A Unified Framework for Sparse Relaxed Regularized Regression: SR3cited by 36
  4. 2022Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimizationcited by 29
  5. 2021Computational Graph Completioncited by 28
  6. 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
  7. 2020Learning dynamical systems from data: a simple cross-validation perspectivecited by 23
  8. 2020Numerical differentiation of noisy data: A unifying multi-objective optimization frameworkcited by 20
  9. 2021Physics-informed Spline Learning for Nonlinear Dynamics Discoverycited by 18
  10. 2019On the smoothness of nonlinear system identificationcited by 17
  11. 2020Bayesian differential programming for robust systems identification under uncertaintycited by 16
  12. 2023Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discoverycited by 15
  13. 2024Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy datacited by 15
  14. 2022Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertaintycited by 13
  15. 2016Generalized Kalman Smoothing: Modeling and Algorithmscited by 10
  16. 2022Simultaneous Identification and Denoising of Dynamical Systemscited by 10
  17. 2015A penalty method for PDE-constrained optimization in inverse problemscited by 9
  18. 2024Toward Efficient Kernel-Based Solvers for Nonlinear PDEscited by 7
  19. 2025Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysiscited by 7
  20. 2018Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusioncited by 6
  21. 2024Statistical Mechanics of Dynamical System Identificationcited by 5
  22. 2022Learning nonparametric ordinary differential equations from noisy datacited by 4
  23. 2023A Levenberg-Marquardt Method for Nonsmooth Regularized Least Squarescited by 4
  24. 2016Efficient quadratic penalization through the partial minimization techniquecited by 3
  25. 2022A Bayesian Approach for Spatio-Temporal Data-Driven Dynamic Equation Discoverycited by 3
  26. 2024An Analysis of Constraint-Relaxation in PDE-Based Inverse Problemscited by 2
  27. 2021Theoretical Advances in Current Estimation and Navigation from a Glider-Based Acoustic Doppler Current Profiler (ADCP)cited by 1
  28. 2025Overcoming error-in-variable problem in data-driven model discovery by orthogonal distance regressioncited by 1

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