IAdvancing Physics-Informed Neural Networks for ۱D Wave Equation Velocity Inversion

Physics-informed neural networks (PINNs) offer a promising framework for solving inverse problems involving partial differential equations (PDEs). However, the vanilla PINN often fails in complex cases due to inadequate convergence in training. This work focuses on enhancing PINNs for velocity inversion in the ۱D wave equation, emphasizing variable velocity cases. By leveraging modifications in loss calculation—including a logarithmic LossPDE (Loss term responsible to incorporate physics) and sigmoidal self-adaptive regularization—we demonstrate significant improvements in accuracy and stability. We systematically explore cases involving standing waves, constant velocities, and variable velocities, highlighting the efficacy of our approach. The methodological distinctions between constant and variable velocity settings are elaborated upon, ensuring a robust scientific contribution. Our findings underscore the importance of effective loss-balancing mechanisms and their role in advancing PINN applications in wave mechanics.

کلیدواژه ها:

PHYSICS-INFORMED NEURAL NETWORKS ، WAVE EQUATION ، VELOCITY INVERSION ، LOSS FUNCTION MODIFICATION ، INVERSE PROBLEMS