Physics-informed neural networks (PINNs) use physical principles (wave equations) to improve their predictive capability in detecting the features of seismic waves. However, in practice, PINNs face difficulties in determining an approximate optimization direction, resulting in slower convergence, especially in the early stages of network training. This limitation arises from the utilization of automatic differentiation (AD) in evaluating the derivative terms embedded in the wave equation. We develop a hybrid method that combines finite difference (FD) and AD. In the initial stage, FD is used to evaluate derivative terms in the wave equation. AD is used for the rest of the iterations to refine the accuracy in calculating partial derivatives. This approach yields faster convergence with fewer iterations by mitigating AD’s sensitivity to the random initialization in the early stages of training, thereby enhancing the accuracy of seismic wave simulation.

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