This paper presents an adaptive collocation point strategy aimed at improving both the learning capacity and computational efficiency of Physics-Informed Neural Networks (PINNs). The proposed method determines the selection probabilities of collocation points based on both the loss function residuals and the distribution of its gradients. To prevent convergence to local optima, the strategy involves resampling after several iterations. By concentrating collocation points in regions characterized by higher residuals or substantial gradient variations, the method optimizes the point distribution, thereby improving accuracy with fewer collocation points. Furthermore, a weight adjustment mechanism is introduced, which assigns higher weights to points with larger residuals. This enables the PINN to prioritize regions with higher losses, enhancing its ability to learn complex patterns. Experimental results on seismic wave propagation demonstrate that the proposed method significantly improves both solution accuracy and computational efficiency while reducing the number of collocation points and required iterations.

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Solving Seismic Wave Propagation Using an Adaptive Collocation Point-Based Physics-Informed Neural Network

  • Yanan Guo,
  • Xiaoqun Cao,
  • Mengge Zhou

摘要

This paper presents an adaptive collocation point strategy aimed at improving both the learning capacity and computational efficiency of Physics-Informed Neural Networks (PINNs). The proposed method determines the selection probabilities of collocation points based on both the loss function residuals and the distribution of its gradients. To prevent convergence to local optima, the strategy involves resampling after several iterations. By concentrating collocation points in regions characterized by higher residuals or substantial gradient variations, the method optimizes the point distribution, thereby improving accuracy with fewer collocation points. Furthermore, a weight adjustment mechanism is introduced, which assigns higher weights to points with larger residuals. This enables the PINN to prioritize regions with higher losses, enhancing its ability to learn complex patterns. Experimental results on seismic wave propagation demonstrate that the proposed method significantly improves both solution accuracy and computational efficiency while reducing the number of collocation points and required iterations.