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This study presents a novel approach for solving Partial Differential Equations (PDEs) using Kolmogorov-Arnold Networks (KAN). By integrating physics-informed loss functions and leveraging the structured KAN architecture, our method significantly enhances both accuracy and computational efficiency. Experimental results demonstrate that KAN models achieve up to 40% better mean squared error (MSE) compared to traditional Multi-Layer Perceptrons (MLP) when applied to Poisson, Heat, and Wave equations. The KAN models achieved an MSE of 0.0001 for the Poisson equation, compared to 0.0002 for MLP, showcasing their superior performance. Additionally, the training times for KAN models were comparable to MLP models, highlighting the computational efficiency of our approach. This research underscores the potential of KANs for solving complex PDEs, offering a robust and efficient alternative to existing methods.

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KAN-PDEs: A Novel Approach to Solving Partial Differential Equations Using Kolmogorov-Arnold Networks—Enhanced Accuracy and Efficiency

  • 会议论文

  • 发表日期：

    2025年

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  • Sanghyun Yeo,
  • Phuong Anh Nguyen,
  • Anh Ngoc Le,
  • Satyam Mishra

摘要

This study presents a novel approach for solving Partial Differential Equations (PDEs) using Kolmogorov-Arnold Networks (KAN). By integrating physics-informed loss functions and leveraging the structured KAN architecture, our method significantly enhances both accuracy and computational efficiency. Experimental results demonstrate that KAN models achieve up to 40% better mean squared error (MSE) compared to traditional Multi-Layer Perceptrons (MLP) when applied to Poisson, Heat, and Wave equations. The KAN models achieved an MSE of 0.0001 for the Poisson equation, compared to 0.0002 for MLP, showcasing their superior performance. Additionally, the training times for KAN models were comparable to MLP models, highlighting the computational efficiency of our approach. This research underscores the potential of KANs for solving complex PDEs, offering a robust and efficient alternative to existing methods.