Ground motion prediction equations (GMPEs) are crucial for the seismic hazard analysis of infrastructures. Currently, nearly all GMPEs are designed to predict only mainshock; in addition, they are generally based on a pre-assumed function form for data fitting. Historical earthquake records show that the mainshock (MS) is always followed by several aftershocks (ASs), aggravating the structural damage caused by the MS. The direct application of the traditional earthquake-oriented GMPE to predict ASs may not properly reflect their spectral characteristics and relationship with the MS. All pre-defined functions are generally low-order functions, i.e., they include limited number of variables. The newly emerged deep learning method is a powerful tool for revealing and presenting correlations among high-dimensional variables. Thus, the deep learning method was used as a GMPE to predict the spectral accelerations (Sa) of aftershocks in this study. Two popular networks (the deep neural network (DNN) and conditional generative adversarial network (CGAN)) were adopted to build the prediction model. Eight seismic variables and Sa of the mainshock at 21 periods were used as inputs for the deep learning model, and the Sa of the aftershocks at 21 periods were the outputs. A total of 503 sets of MS–AS records were used to develop the model, and the prediction results were compared with real data and that obtained by traditional GMPEs. The comparisons indicated that the deep learning model is a promising tool for predicting the Sa of aftershocks, and the CGAN model is slightly better than the DNN model because of the former's random nature in the generation of new data.

地震动预测方程 (GMPE) 对于基础设施的地震危害分析至关重要。目前，几乎所有 GMPE 都设计为仅预测主震；此外，它们通常基于预先假设的函数形式进行数据拟合。历史地震记录表明，主震（MS）之后总是会发生多次余震（AS），从而加剧了由 MS 引起的结构破坏。直接应用传统的面向地震的 GMPE 预测 AS 可能无法正确反映其频谱特征以及与 MS 的关系。所有预定义函数通常都是低阶函数，即它们包含的变量数量有限。新出现的深度学习方法是揭示和呈现高维变量之间相关性的有力工具。因此，在本研究中，深度学习方法被用作 GMPE 来预测余震的谱加速度 (Sa)。采用两种流行的网络（深度神经网络（DNN）和条件生成对抗网络（CGAN））来构建预测模型。8个地震变量和21个周期的主震Sa作为深度学习模型的输入，21个周期余震的Sa作为输出。总共使用了 503 组 MS-AS 记录来开发模型，并将预测结果与真实数据和传统 GMPE 获得的数据进行比较。比较表明，深度学习模型是预测余震 Sa 的有前景的工具，而 CGAN 模型略优于 DNN 模型，因为前者在生成新数据时具有随机性。