mlsanityData to 13 Oct 2026

SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks

arXiv 2603.18548 ↗First posted 19 Mar 2026cs.LGcited by 2

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Abstract (arXiv)

Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse identification of nonlinear dynamics (SINDy) is a complementary approach that allows for learning sparse equations for dynamical systems from data; however, learned equations are limited by the library. In this work, we present SINDy-KANs, which simultaneously train a KAN and a SINDy-like representation to increase interpretability of KAN representations with SINDy applied at the level of each activation function, while maintaining the function compositions possible through deep KANs. We apply our method to a number of symbolic regression tasks, including dynamical systems, to show accurate equation discovery across a range of systems.

Key facts. Cited by 2 papers in the map (data through 13 Oct 2026). Builds on 38 of its 66 references that are in the map. First posted on arXiv 19 Mar 2026.

Builds on

38 of 66 references.

References · 38

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,093
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 641
  3. 2020Weak SINDy For Partial Differential Equationscited by 154
  4. 2017Sparse identification of nonlinear dynamics for model predictive control in the low-data limitcited by 140
  5. 2021Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and controlcited by 135
  6. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 116
  7. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  8. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  9. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 97
  10. 2021PySINDy: A comprehensive Python package for robust sparse system identificationcited by 88
  11. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 82
  12. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
26 more
  1. 2023Residual-based attention in physics-informed neural networkscited by 72
  2. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  3. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 66
  4. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 52
  5. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 48
  6. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 46
  7. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
  8. 2021Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approachcited by 36
  9. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  10. 2024Kolmogorov-Arnold Graph Neural Networkscited by 31
  11. 2024SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learningcited by 26
  12. 2024Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networkscited by 23
  13. 2025A Practitioner's Guide to Kolmogorov-Arnold Networkscited by 16
  14. 2024Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networkscited by 15
  15. 2024Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometriescited by 12
  16. 2025LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behaviorcited by 12
  17. 2024ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identificationcited by 11
  18. 2025Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Studycited by 10
  19. 2024Exploring Kolmogorov-Arnold Networks for Interpretable Time Series Classificationcited by 8
  20. 2025Scientific Machine Learning with Kolmogorov-Arnold Networkscited by 6
  21. 2025Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimonycited by 4
  22. 2025Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networkscited by 3
  23. 2025Automatic Grid Updates for Kolmogorov-Arnold Networks using Layer Histogramscited by 3
  24. 2025KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Frameworkcited by 2
  25. 2025Softly Symbolifying Kolmogorov-Arnold Networkscited by 2
  26. 2025Interpretable Machine Learning for Reservoir Water Temperatures in the U.S. Red River Basin of the Southcited by 1

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Making Gaussian Kolmogorov-Arnold Networks Reliable and Accuratecited by 3
  2. 2026Partition-of-Unity Gaussian Kolmogorov-Arnold Networkscited by 1