Scholarlink

<p>This paper introduces RBF-fPINN, a cutting-edge fractional Physics-Informed Neural Network (fPINN) that leverages radial basis functions (RBF) neural networks to significantly enhance solution accuracy. Unlike traditional fPINNs, the RBF-fPINN features a single hidden layer and employs RBFs as its activation functions. We evaluate Gaussian, inverse quadratic, and inverse multiquadric radial basis functions to identify the most effective radial basis function for solving fractional partial differential equations (PDEs). These problems, driven by fractional derivatives, capture non-local dynamics and anomalous transport processes in various engineering fields. Traditional numerical methods often struggle with these problems, particularly in high-dimensional or complex domains. The novel RBF-fPINN framework is validated through numerical experiments even with typical solutions on complex and irregular 2D and 3D domains, demonstrating its potential for enhancing the application of neural networks in complex fractional models, especially in mobile-immobile (MIM) equations.</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

RBF-fPINNs: radial basis function-enhanced fractional physics-informed neural networks

  • 期刊论文

  • 发表日期：

    2026年2月8日

查看全文
  • Maryam Mohammadi,
  • Reza Mokhtari,
  • Mohadese Ramezani

摘要

This paper introduces RBF-fPINN, a cutting-edge fractional Physics-Informed Neural Network (fPINN) that leverages radial basis functions (RBF) neural networks to significantly enhance solution accuracy. Unlike traditional fPINNs, the RBF-fPINN features a single hidden layer and employs RBFs as its activation functions. We evaluate Gaussian, inverse quadratic, and inverse multiquadric radial basis functions to identify the most effective radial basis function for solving fractional partial differential equations (PDEs). These problems, driven by fractional derivatives, capture non-local dynamics and anomalous transport processes in various engineering fields. Traditional numerical methods often struggle with these problems, particularly in high-dimensional or complex domains. The novel RBF-fPINN framework is validated through numerical experiments even with typical solutions on complex and irregular 2D and 3D domains, demonstrating its potential for enhancing the application of neural networks in complex fractional models, especially in mobile-immobile (MIM) equations.