Self-learning multi-head weight and enhanced physics-informed residual connection neural networks

In recent years, physics-informed neural networks (PINNs) that can simultaneously utilize data and mathematical physical models have shown great potential in numerical computation. However, PINNs often struggle to provide accurate predictions in scenarios with drastic changes. To address this, we have designed a multi-head adaptive weighted structure that aims to make the network focus its attention on areas that are difficult to predict. Additionally, to prevent the network from learning erroneous information in cases where the dataset is noisy or has other issues, we have used enhanced physical information as a regularization term to constrain the network. However, complex network structures can make it difficult for optimizers to work effectively. To ensure that the network can be optimized smoothly, we have used ResNet blocks. We conducted numerical experiments using noisy forward and inverse problems, which resulted in significantly improved prediction accuracy. Furthermore, we used ablation study to verify the role of each component.