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In this paper the wave equation describing a scalar field propagation in the space-time of Schwarzschild black hole with a horizon \( r = 2M \) is studied. We shall find first the analytical solutions of this problem. Then we shall apply physics informed neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. Moreover, we shall introduce physics informed cellular neural networks in order to obtain the solutions in a fast way and in real time. Numerical simulations will illustrate the theoretical results proved in the paper.

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Physics Informed Neural Networks for Solving Nonstandard Initial-Boundary Value Problem for Second Order Hyperbolic Equation

  • 会议论文

  • 发表日期：

    2025年

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  • Petar Popivanov,
  • Angela Slavova,
  • Stoycho Yazadzhiev

摘要

In this paper the wave equation describing a scalar field propagation in the space-time of Schwarzschild black hole with a horizon \( r = 2M \) is studied. We shall find first the analytical solutions of this problem. Then we shall apply physics informed neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. Moreover, we shall introduce physics informed cellular neural networks in order to obtain the solutions in a fast way and in real time. Numerical simulations will illustrate the theoretical results proved in the paper.