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  • Featured in Physics
  • Open Access

Kolmogorov-Arnold Networks Meet Science

Ziming Liu* and Max Tegmark

Pingchuan Ma and Wojciech Matusik

Yixuan Wang

  • *Contact author: zmliu@mit.edu
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Phys. Rev. X 15, 041051 – Published 17 December, 2025

DOI: https://doi.org/10.1103/4t7t-v19l

Abstract

A major challenge of AI plus science lies in its 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 pykan: (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) into 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.

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Physics Subject Headings (PhySH)

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Advancing Physical Understanding with Interpretable Machine Learning

Published 17 December, 2025

A new artificial neural-network architecture opens a window into the workings of a tool previously regarded as a black box.

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Popular Summary

Deep neural networks often achieve excellent predictive performance but struggle with interpretability, making it difficult to use them for generating scientific insights. In this study, we introduce Kolmogorov-Arnold networks (KANs), a new class of neural networks designed to bridge the gap between prediction and explanation. Unlike conventional networks, KANs possess a built-in duality with symbolic formulas, allowing them to both uncover new scientific knowledge and integrate existing theories with ease.

To demonstrate this capability, we apply KANs to a range of physics problems where both data-driven and model-driven approaches are important. By embedding scientific principles directly into the network’s architecture, KANs retain the interpretability of theoretical models while maintaining the expressive power of deep learning. This unique integration enables us to both validate established physical laws and explore potential new ones in ways that were previously out of reach with standard neural networks.

KANs represent a step toward more transparent and scientifically useful machine learning. By combining interpretability with predictive strength, they offer a pathway to transform how we use AI in scientific research. Looking ahead, this framework could accelerate discoveries in physics and beyond, especially in areas where theory and data must be reconciled.

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Phys. Rev. X 15, 041051– Published 17 December, 2025
  • Received 1 December 2024
  • Accepted 30 September 2025
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