Learning Rocking Dynamics From Sparse Shake-Table Data With Interpretable Physics-Informed Neural Networks

Abstract

We present a hybrid interpretable Physics-Informed Neural Network Long-Short Term Memory (Hybrid PINN LSTM) framework for predicting the seismic response of rocking blocks. Existing analytical models rely on uncertain idealizations, while purely data-driven and machine-learning approaches lack physical consistency and interpretability. Our framework addresses these limitations by integrating the governing physics of rocking motion with a limited number of shake-table data. Taking the ground acceleration series as input, our model predicts the rotational response of rocking blocks and its associated peak quantities with lower error and higher accuracy than classical rocking theories, while predictions of angular velocity and angular acceleration remain more challenging. Physical consistency is enforced through mechanics-based loss terms, while data-driven losses are calibrated using a small set of laboratory measurements obtained with “off-the-shelf” experimental equipment. Besides, to enhance engineering insight, explainable AI tools at both the surrogate and sequence levels are used to interpret the learned relationships and identify the structural and ground-motion parameters, and excitation time windows governing the rocking response. Our explainability analysis shows that for high-intensity earthquakes, velocity-based measures and related displacement measures dominate overturning behavior, whereas for moderate intensities, the response becomes more interactive, with temporal characteristics, such as duration, playing a comparable role. For non-overturning cases, large safe rocking amplitudes are governed jointly by velocity, displacement, dominant period, and duration of the ground motion. Overall, this work pioneers an accurate, physically consistent and interpretable tool for seismic rocking response prediction. It could be used for assessing the seismic performance of critical equipment on the basis of limited experimental data without relying on current idealistic assumptions on key parameters like the coefficient of restitution.