Scholarlink

<p>Many physical systems are often modeled using partial differential equations (PDEs), which are notoriously challenging to solve analytically or numerically. Deep learning-based approaches have recently gained prominence in solving PDEs, but achieving high accuracy remains a significant challenge. In this work, we propose a new approach to learning PDE solutions by integrating the Kolmogorov-Arnold Neural Network (KAN) with a method based on the Lie symmetry group. We demonstrate that our approach achieves superior performance through comparative analysis with two baseline methods. Our analysis shows that both the KAN and domain decomposition methods are crucial for improving accuracy. The error of the learned solution decreases compared to the baseline algorithms.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Learning Solutions of PDEs with Symmetry and Kolmogorov-Arnold Neural Network

  • 期刊论文

  • 发表日期：

    2026年4月10日

查看全文
  • Minhyuk Yoon,
  • Inkyu Jang,
  • H. Jin Kim

摘要

Many physical systems are often modeled using partial differential equations (PDEs), which are notoriously challenging to solve analytically or numerically. Deep learning-based approaches have recently gained prominence in solving PDEs, but achieving high accuracy remains a significant challenge. In this work, we propose a new approach to learning PDE solutions by integrating the Kolmogorov-Arnold Neural Network (KAN) with a method based on the Lie symmetry group. We demonstrate that our approach achieves superior performance through comparative analysis with two baseline methods. Our analysis shows that both the KAN and domain decomposition methods are crucial for improving accuracy. The error of the learned solution decreases compared to the baseline algorithms.