# Data-driven model discovery with Kolmogorov-Arnold networks

arXiv: https://arxiv.org/abs/2409.15167 · HTML: https://mlsanity.com/paper/2409.15167/

## 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 (most cited first, 17 of 17)

- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [Machine learning prediction of critical transition and system collapse](https://mlsanity.com/paper/2012.01545/) (2020)
- [Forecasting Chaotic Systems with Very Low Connectivity Reservoir Computers](https://mlsanity.com/paper/1910.00659/) (2019)
- [Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation](https://mlsanity.com/paper/2406.01034/) (2024)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [Model-free prediction of spatiotemporal dynamical systems with recurrent neural networks: Role of network spectral radius](https://mlsanity.com/paper/1910.04426/) (2019)
- [How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification](https://mlsanity.com/paper/1905.08061/) (2019)
- [Model-free tracking control of complex dynamical trajectories with machine learning](https://mlsanity.com/paper/2309.11470/) (2023)
- [Reconstructing propagation networks with natural diversity and identifying hidden sources](https://mlsanity.com/paper/1407.4451/) (2014)
- [Machine-learning parameter tracking with partial state observation](https://mlsanity.com/paper/2311.09142/) (2023)
- [Digital twins of nonlinear dynamical systems: A perspective](https://mlsanity.com/paper/2309.11461/) (2023)

## Built on by (most cited first, 9 of 9)

- [Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony](https://mlsanity.com/paper/2506.03302/) (2025)
- [Reconstructing dynamics from sparse observations with no training on target system](https://mlsanity.com/paper/2410.21222/) (2024)
- [Softly Symbolifying Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2512.07875/) (2025)
- [Optimized Architectures for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2512.12448/) (2025)
- [A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.18672/) (2026)
- [A KAN-based Interpretable Framework for Process-Informed Prediction of Global Warming Potential](https://mlsanity.com/paper/2411.00426/) (2024)
- [Deficiency of equation-finding approach to data-driven modeling of dynamical systems](https://mlsanity.com/paper/2509.03769/) (2025)
- [YOLO with Kolmogorov-Arnold networks and vision-language foundation models for interpretable object detection with trustworthy multimodal AI in computer vision perception](https://mlsanity.com/paper/2603.23037/) (2026)
- [KANs need curvature: penalties for compositional smoothness](https://mlsanity.com/paper/2605.02190/) (2026)

## 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.