Physics Informed Machine Learning For Time Domain Electromagnetic Simulation



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Neural Networks have been widely used in all fields of research and have achieved great success. The Physics Informed Neural Network (PINN) is an important and relatively new attempt among deep neural network applications. PINN is built upon a differentiable programming platform and aims at solving differential equations. PINN provides an alternative way to solve physics problems apart from conventional numerical methods like Finite-Difference Time-Domain (FDTD) method or Finite Element Analysis (FEA), and turns the solving of equations to an optimization process. In this thesis paper, I follow the work of Pan Zhang and test PINNs on several time-domain electromagnetic simulation examples. I concentrate on a simple 1D electromagnetic cavity model with isotropic and homogeneous media without current sources. During the experiment, I extend the training time range to investigate the PINN performance on large time-scale problems. We do find that PINN is less likely to converge to an expected physical solution when the time scale gets larger and finally fails to produce any meaningful results, which is known as the “Spectral Bias”. To further understand this problem, we firstly define a parameter “Threshold Period Number” (TPN) and tune the PINN parameters to see how these values influence the TPN. Then we change and improve the PINN structure, trying to avoid the failure for the large time-scale problem. We also visualize the PINN training process to help us analyze the problem. Although we still can not totally solve the spectral bias, we find out some effective methods to practically increase TPN and get better results within certain large time scales.



Machine learning, Physics Informed Neural Network, PINN, Maxwell Equation, Spectral Bias, Threshold Period Number