mlsanityData to 14 Oct 2026

Data-driven model discovery with Kolmogorov-Arnold networks

arXiv 2409.15167 ↗First posted 23 Sep 2024cs.LG math.DS nlin.CDcited by 9

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Abstract (arXiv)

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 17 of its 107 references that are in the map. First posted on arXiv 23 Sep 2024.

Builds on

17 of 107 references.

References · 17

  1. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 554
  2. 2021Next Generation Reservoir Computingcited by 160
  3. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 128
  4. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 122
  5. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 64
  6. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 62
  7. 2020Machine learning prediction of critical transition and system collapsecited by 54
  8. 2019Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computerscited by 43
  9. 2024Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformationcited by 42
  10. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 35
  11. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  12. 2019Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radiuscited by 34
5 more
  1. 2019How Entropic Regression Beats the Outliers Problem in Nonlinear System Identificationcited by 14
  2. 2023Model-free tracking control of complex dynamical trajectories with machine learningcited by 13
  3. 2014Reconstructing propagation networks with natural diversity and identifying hidden sourcescited by 5
  4. 2023Machine-learning parameter tracking with partial state observationcited by 4
  5. 2023Digital twins of nonlinear dynamical systems: A perspectivecited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 4; 2026: 3.

9 papers.

  1. 2025Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimonycited by 4
  2. 2024Reconstructing dynamics from sparse observations with no training on target systemcited by 2
  3. 2025Softly Symbolifying Kolmogorov-Arnold Networkscited by 2
  4. 2025Optimized Architectures for Kolmogorov-Arnold Networkscited by 1
  5. 2026A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networkscited by 1
  6. 2024A KAN-based Interpretable Framework for Process-Informed Prediction of Global Warming Potentialcited by 0
  7. 2025Deficiency of equation-finding approach to data-driven modeling of dynamical systemscited by 0
  8. 2026YOLO with Kolmogorov-Arnold networks and vision-language foundation models for interpretable object detection with trustworthy multimodal AI in computer vision perceptioncited by 0
  9. 2026KANs need curvature: penalties for compositional smoothnesscited by 0