Multi-domain physics-based loss design for seismic response prediction

Accurate prediction of time-history responses is essential for evaluating structural performance under dynamic loading. Machine learning regression models offer the advantages of rapid, real-time, and high-accuracy predictions. However, their “black-box” nature poses challenges to interpretability and limits their broader application in structural engineering. To address this limitation, we propose a multi-domain physics-informed seismic response prediction strategy. This approach incorporates physics knowledge from the time, frequency, and energy domains into deep learning models via a customized loss function. Building upon conventional time-domain loss, we present a multi-scale frequency-domain loss to capture low-frequency components that are strongly correlated with structural characteristics, as well as momentum-based and energy-based losses that enforce consistency with fundamental dynamic principles. Experimental evaluations on two numerical simulation datasets and two shaking table test datasets indicate that the proposed strategy significantly enhances the prediction accuracy of both purely data-driven and data–knowledge-driven models. Specifically, it achieves an average improvement of 4 % in prediction confidence level within a ± 10 % confidence interval. Furthermore, ablation studies illustrate the positive contribution of the multi-scale frequency-domain and energy-domain losses to overall predictive performance.