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.

翻译：随着神经算子的兴起，科学机器学习为量化高保真数值模拟中的不确定性提供了新方案。传统神经网络（如卷积神经网络或物理信息神经网络）仅能预测预定配置下的解。而神经算子可学习偏微分方程（如弹性波方程）随参数变化的通解。目前神经算子在地震学中的应用极为有限，尽管三维效应的重要性已广为人知，但所有相关研究均局限于二维场景。本研究首次将傅里叶神经算子（FNO）应用于基于三维地质描述的地面运动时程预测。我们采用高保真模拟代码SEM3D构建了由30,000种不同地质模型生成的地面运动数据库。基于该数据库发现，即便底层地质存在显著非均质性，FNO仍能精确生成地面运动响应，尤其在中长周期强度指标的再现方面表现优异。本文展示了三维傅里叶神经算子在首个地震学应用中的成果。凭借数据库的泛化能力，我们相信该模型可用于评估沉积盆地等地质特征对地面运动的影响——这对场地效应评估至关重要。