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Abstract <p>The study implements and analyzes a method of using physics-informed neural networks (PINNs) to solve the Maxwell–Cattaneo problem for a rod with zero boundary conditions and a given initial temperature distribution. A multilayer neural network is used as an approximation of the solution. The network is trained using the Adam method. For verification, the results are compared with the analytical solution. The resulting exact match of the temperature field profiles confirms that physics-informed neural networks are capable of correctly reproducing both the exponential attenuation and the oscillatory nature of the wave component.</p>

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Modeling Thermal Conductivity in a Rod Based on the Maxwell–Cattaneo Equation Using Deep Machine Learning

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Ya. A. Vakhterova,
  • E. L. Kuznetsova,
  • Phan Tung Son

摘要

Abstract

The study implements and analyzes a method of using physics-informed neural networks (PINNs) to solve the Maxwell–Cattaneo problem for a rod with zero boundary conditions and a given initial temperature distribution. A multilayer neural network is used as an approximation of the solution. The network is trained using the Adam method. For verification, the results are compared with the analytical solution. The resulting exact match of the temperature field profiles confirms that physics-informed neural networks are capable of correctly reproducing both the exponential attenuation and the oscillatory nature of the wave component.