Meta Learning for Improved Neural Network Wavefield Solutions

Physics-informed neural networks (PINNs) provide a flexible and effective alternative for estimating seismic wavefield solutions due to their typical mesh-free and unsupervised features. However, their accuracy and training cost restrict their applicability. To address these issues, we propose a novel initialization for PINNs based on meta-learning to enhance their performance. In our framework, we first utilize meta-learning to train a common network initialization for a distribution of medium parameters (i.e., velocity models). This phase employs a unique training data container, comprising a support set and a query set. We use a dual-loop approach, optimizing network parameters through a bidirectional gradient update from the support set to the query set. Following this, we use the meta-trained PINN model as the initial model for a regular PINN training for a new velocity model, where the optimization of the network is jointly constrained by the physical and regularization losses. Numerical results demonstrate that, compared to the vanilla PINN with random initialization, our method achieves a much faster convergence speed, and also obtains a significant improvement in the results accuracy. Meanwhile, we showcase that our method can be integrated with existing optimal techniques to further enhance its performance.