Multiple-input Fourier Neural Operator (MIFNO) for source-dependent 3D elastodynamics

Numerical simulations are essential tools to evaluate the solution of the wave equation in complex settings, such as three-dimensional (3D) domains with heterogeneous properties. However, their application is limited by high computational costs and existing surrogate models lack the flexibility of numerical solvers.

This work introduces the Multiple-Input Fourier Neural Operator (MIFNO) to deal with structured 3D fields representing material properties as well as vectors describing the source characteristics. The MIFNO is applied to the problem of elastic wave propagation in the Earth's crust. It is trained on the HEMEW^S-3D database containing

earthquake simulations in different heterogeneous domains with random source positions and orientations. Outputs are time- and space-dependent surface wavefields.

The MIFNO predictions are assessed as good to excellent based on Goodness-Of-Fit (GOF) criteria. Wave arrival times and wave fronts propagation are very accurate since

of the predictions have an excellent phase GOF (larger than

). The fluctuations amplitudes are good for

of the predictions (envelope GOF larger than

) and excellent for

. The envelope score is hindered by the small-scale fluctuations that are challenging to capture due to the spectral bias inherent to neural networks and the complex physical phenomena associated with high-frequency features. Nevertheless, the MIFNO can generalize to sources located outside the training domain and it shows good generalization ability to a real complex overthrust geology. When focusing on a region of interest, transfer learning is an efficient approach to improve the accuracy with limited additional costs, since GOF scores improved by more than 1 GOF unit with only

additional specific samples.

The MIFNO is the first surrogate model offering the flexibility of an earthquake simulator with varying sources and material properties. Its good accuracy and massive speed-up offer new perspectives to replace numerical simulations in many-query problems.