Multiple-Input Fourier Neural Operator (MIFNO) for source-dependent 3D
  elastodynamics
Fanny Lehmann Filippo Gatti Didier Clouteau
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 30000 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 80% of the predictions have an excellent phase GOF. The
fluctuations amplitudes are good for 87% of the predictions. The envelope score
is hindered by the small-scale fluctuations that are challenging to capture due
to 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 improves the
accuracy with limited additional costs, since GOF scores improved by more than
1 GOF unit with only 500 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.