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

arXiv: https://arxiv.org/abs/2603.18548 · HTML: https://mlsanity.com/paper/2603.18548/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 66 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Residual-based attention in physics-informed neural networks](https://mlsanity.com/paper/2307.00379/) (2023)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.11045/) (2024)
- [GKAN: Graph Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.06470/) (2024)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.17611/) (2024)
- [Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach](https://mlsanity.com/paper/2105.04869/) (2021)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [Kolmogorov-Arnold Graph Neural Networks](https://mlsanity.com/paper/2406.18354/) (2024)
- [SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning](https://mlsanity.com/paper/2403.09110/) (2024)
- [Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07488/) (2024)
- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.15727/) (2024)
- [Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries](https://mlsanity.com/paper/2408.02950/) (2024)
- [LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behavior](https://mlsanity.com/paper/2502.17844/) (2025)
- [ADAM-SINDy: An Efficient Optimization Framework for Parameterized Nonlinear Dynamical System Identification](https://mlsanity.com/paper/2410.16528/) (2024)
- [Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study](https://mlsanity.com/paper/2509.03417/) (2025)

## Built on by (most cited first, 3 of 3)

- [Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate](https://mlsanity.com/paper/2604.21174/) (2026)
- [Partition-of-Unity Gaussian Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2604.23599/) (2026)
- [Low-Rank Kolmogorov-Arnold Generator Flows for Interpretable Operator Learning](https://mlsanity.com/paper/2610.13028/) (2026)

## 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.