Physics-guided residual learning framework for aftershock time history prediction using mainshock acceleration data

Abstract

Accurate aftershock acceleration time history prediction is essential for post-earthquake structural evaluation, particularly under data-scarce conditions. A physics-guided residual learning framework is developed to generate aftershock acceleration time histories from mainshock acceleration time histories and static site parameters. The proposed approach begins with a pseudo-aftershock acceleration time history constructed by applying exponential attenuation to the mainshock, which serves as a physically inspired prior for residual learning. Multiscale convolutional encoders extract temporal features, whereas static variables such as magnitude and site conditions are fused through gated embedding. A residual correction module guided by cross-attention refines the pseudo-aftershock to match the observed aftershock responses. A hybrid loss function ensures consistency in both time and frequency domains. Despite the limited number of training samples, the proposed residual learning model achieved consistently low prediction errors and showed promising predictive performance under a limited-event setting based on 140 paired sequences from 10 seismic events, including 20 test sequences. The architecture further enabled interpretable forecasting, revealing the manner in which mainshock dynamics and static attributes jointly influenced residual adjustments. On an independent test set, the model achieved a mean absolute error of 0.00553 g (where g denotes the gravitational acceleration), a root mean square error of 0.01304 g, and a coefficient of determination of 0.612. These findings highlight the feasibility of residual-based physically guided forecasting for realistic structural demand assessments.