  With the recent rise of neural operators, scientific machine learning offers
new solutions to quantify uncertainties associated with high-fidelity numerical
simulations. Traditional neural networks, such as Convolutional Neural Networks
(CNN) or Physics-Informed Neural Networks (PINN), are restricted to the
prediction of solutions in a predefined configuration. With neural operators,
one can learn the general solution of Partial Differential Equations, such as
the elastic wave equation, with varying parameters. There have been very few
applications of neural operators in seismology. All of them were limited to
two-dimensional settings, although the importance of three-dimensional (3D)
effects is well known.
  In this work, we apply the Fourier Neural Operator (FNO) to predict ground
motion time series from a 3D geological description. We used a high-fidelity
simulation code, SEM3D, to build an extensive database of ground motions
generated by 30,000 different geologies. With this database, we show that the
FNO can produce accurate ground motion even when the underlying geology
exhibits large heterogeneities. Intensity measures at moderate and large
periods are especially well reproduced.
  We present the first seismological application of Fourier Neural Operators in
3D. Thanks to the generalizability of our database, we believe that our model
can be used to assess the influence of geological features such as sedimentary
basins on ground motion, which is paramount to evaluating site effects.
