  We investigate the use of Physics-Informed Neural Networks (PINNs) for
solving the wave equation. Whilst PINNs have been successfully applied across
many physical systems, the wave equation presents unique challenges due to the
multi-scale, propagating and oscillatory nature of its solutions, and it is
unclear how well they perform in this setting. We use a deep neural network to
learn solutions of the wave equation, using the wave equation and a boundary
condition as direct constraints in the loss function when training the network.
We test the approach by solving the 2D acoustic wave equation for
spatially-varying velocity models of increasing complexity, including
homogeneous, layered and Earth-realistic models, and find the network is able
to accurately simulate the wavefield across these cases. By using the physics
constraint in the loss function the network is able to solve for the wavefield
far outside of its boundary training data, offering a way to reduce the
generalisation issues of existing deep learning approaches. We extend the
approach for the Earth-realistic case by conditioning the network on the source
location and find that it is able to generalise over this initial condition,
removing the need to retrain the network for each solution. In contrast to
traditional numerical simulation this approach is very efficient when computing
arbitrary space-time points in the wavefield, as once trained the network
carries out inference in a single step without needing to compute the entire
wavefield. We discuss the potential applications, limitations and further
research directions of this work.
