# KAN 2.0: Kolmogorov-Arnold Networks Meet Science

arXiv: https://arxiv.org/abs/2408.10205 · HTML: https://mlsanity.com/paper/2408.10205/

## Key facts

- Cited by 118 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 101 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Builds on (most cited first, 30 of 72)

- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [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)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [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)
- [LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discovery](https://mlsanity.com/paper/2405.09783/) (2024)
- [DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problems](https://mlsanity.com/paper/2405.19143/) (2024)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [KAN or MLP: A Fairer Comparison](https://mlsanity.com/paper/2407.16674/) (2024)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [TKAN: Temporal Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.07344/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)

## Built on by (most cited first, 30 of 118)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.00278/) (2024)
- [FC-KAN: Function Combinations in Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.01763/) (2024)
- [KANEL'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation](https://mlsanity.com/paper/2512.12850/) (2025)
- [SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2411.06286/) (2024)
- [LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behavior](https://mlsanity.com/paper/2502.17844/) (2025)
- [A Neural Symbolic Model for Space Physics](https://mlsanity.com/paper/2503.07994/) (2025)
- [Sub-Sequential Physics-Informed Learning with State Space Model](https://mlsanity.com/paper/2502.00318/) (2025)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)
- [MedKAN: An Advanced Kolmogorov-Arnold Network for Medical Image Classification](https://mlsanity.com/paper/2502.18416/) (2025)
- [Kolmogorov-Arnold Network Autoencoders](https://mlsanity.com/paper/2410.02077/) (2024)
- [Exploring Kolmogorov-Arnold Networks for Interpretable Time Series Classification](https://mlsanity.com/paper/2411.14904/) (2024)
- [QKAN-LSTM: Quantum-inspired Kolmogorov-Arnold Long Short-term Memory](https://mlsanity.com/paper/2512.05049/) (2025)
- [High precision PINNs in unbounded domains: application to singularity formulation in PDEs](https://mlsanity.com/paper/2506.19243/) (2025)
- [KANO: Kolmogorov-Arnold Neural Operator](https://mlsanity.com/paper/2509.16825/) (2025)
- [Exploring Kolmogorov-Arnold networks for realistic image sharpness assessment](https://mlsanity.com/paper/2409.07762/) (2024)
- [Residual Kolmogorov-Arnold Network for Enhanced Deep Learning](https://mlsanity.com/paper/2410.05500/) (2024)
- [Kolmogorov Arnold Neural Interpolator for Downscaling and Correcting Meteorological Fields from In-Situ Observations](https://mlsanity.com/paper/2501.14404/) (2025)
- [CVKAN: Complex-Valued Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2502.02417/) (2025)
- [KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation](https://mlsanity.com/paper/2505.13315/) (2025)
- [Incorporating Arbitrary Matrix Group Equivariance into KANs](https://mlsanity.com/paper/2410.00435/) (2024)
- [Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics](https://mlsanity.com/paper/2412.04845/) (2024)
- [Exploring Adversarial Transferability between Kolmogorov-arnold Networks](https://mlsanity.com/paper/2503.06276/) (2025)
- [ChemKANs for Combustion Chemistry Modeling and Acceleration](https://mlsanity.com/paper/2504.12580/) (2025)
- [Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement](https://mlsanity.com/paper/2505.18131/) (2025)
- [Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimony](https://mlsanity.com/paper/2506.03302/) (2025)
- [On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimators](https://mlsanity.com/paper/2509.19830/) (2025)

## Abstract (arXiv)

A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.