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<p>This study investigates the application of adaptive physics-informed neural networks (PINNs) to solve two-dimensional time-domain Maxwell’s equations in their differential form. The system is reformulated as hyperbolic-type equations governing the electric and magnetic field components. A fully connected neural network is constructed to approximate the solution while enforcing boundary and initial conditions. To improve convergence, a hybrid optimization strategy combining the Adam and L-BFGS algorithms is employed. The effects of key architectural choices, including the number of hidden layers, neurons, and activation functions, were systematically examined. A benchmark problem with known analytical solutions is used to evaluate accuracy, and errors are compared with a reference finite-difference time-domain solver. The results confirm that the adaptive PINNs provide an accurate and computationally efficient alternative for solving 2D Maxwell’s equations, with strong potential for extension to frequency-domain and three-dimensional problems.</p>

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Adaptive physics informed neural networks framework for accurate and mesh free solution of two dimensional time domain maxwell equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • Abdenie Tukie Tufa,
  • Tamirat Temesgen Dufera,
  • Mitiku Daba Firdi,
  • Alemayehu Tamirie Deresse

摘要

This study investigates the application of adaptive physics-informed neural networks (PINNs) to solve two-dimensional time-domain Maxwell’s equations in their differential form. The system is reformulated as hyperbolic-type equations governing the electric and magnetic field components. A fully connected neural network is constructed to approximate the solution while enforcing boundary and initial conditions. To improve convergence, a hybrid optimization strategy combining the Adam and L-BFGS algorithms is employed. The effects of key architectural choices, including the number of hidden layers, neurons, and activation functions, were systematically examined. A benchmark problem with known analytical solutions is used to evaluate accuracy, and errors are compared with a reference finite-difference time-domain solver. The results confirm that the adaptive PINNs provide an accurate and computationally efficient alternative for solving 2D Maxwell’s equations, with strong potential for extension to frequency-domain and three-dimensional problems.