  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 in which 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 fast 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.
