Fourier Neural Operator Surrogate Model to Predict 3D Seismic Waves Propagation

Abstract

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.

Figures (7)

• Figure 1: Architecture of our UNO. The input (3D geology $a$) is uplifted by the sub-network $P$, then transformed trough 8 Fourier layers $F_1, \cdots, F_8$. Finally, three sub-networks $Q_E$, $Q_N$, and $Q_Z$ project the components of the velocity $u_E$, $u_N$, $u_Z$. The detail of the sixth Fourier block is shown in the right corner (image reproduced from liFourierNeuralOperator2021). Dotted lines show the skip connections with a concatenation of inputs.
• Figure 2: Evolution of the training loss (line) and the validation loss (dashed line) as a function of epochs. The loss is summed over the three components.
• Figure 3: For 1000 elements of the training dataset (blue) and validation dataset (orange), distribution of the Mean Absolute Error (MAE) between the neural operator prediction and the ground truth. Each subpanel shows one velocity component (E-W: East-West), (N-S: North-South), (Z: vertical).
• Figure 4: Comparison of simulations (considered as ground truth) and neural operator predictions for one geology in the validation dataset.
• Figure 5: Comparison of simulations (considered as ground truth) and neural operator predictions for one geology in the validation dataset.