Accelerating wave simulations with neural dispersion correctors

We present a Fourier neural operator network, designed to correct dispersion errors in numerical wave simulations. The neural dispersion corrector enables the replacement of a computationally expensive high-accuracy simulation by a less expensive low-accuracy simulation. In contrast to neural network surrogates that fully replace a wave equation, the neural dispersion corrector has only a weak dependence on the distribution of model parameters, such as wave speeds. Consequently, the network can be trained with a significantly smaller dataset, while still generalising to unseen input parameters. Following a description of the network architecture and training, we provide examples for the 3-D elastic wave equation. After training with merely 1$\,$000 examples on one GPU, the neural corrector achieves a speed-up of 16$\times$ compared to a reference spectral-element simulation and a generalisation to a broad range of strongly heterogeneous wave speed distributions.