Physics symbolic learner for discovering ground-motion models via NGA-West2 database

Ground-motion model (GMM) is the basis of many earthquake engineering studies and practices. In this study, a novel physics-informed symbolic learner (PISL) method is proposed to automatically discover mathematical equation operators as symbols. The sequential threshold ridge regression algorithm is utilized to distill a concise and interpretable explicit characterization of complex systems of ground-motions. In addition to the basic variables retrieved from previous GMMs, the current PISL incorporates three priori physical conditions, namely, distance, magnitude, and site amplification saturation. Based on the Next Generation Attenuation West2 database, GMMs developed using the PISL, an empirical regression method (ERM), and an artificial neural network (ANN) are compared in terms of residuals and extrapolation of peak ground acceleration and velocity. The results show that the inter- and intra-event standard deviations of the three methods are similar. The functional form of the PISL is more concise than that of the ERM and ANN. The extrapolation capability of the PISL is more accurate than that of the ANN. The PISL-GMM used in this study provide a new paradigm of regression that considers both physical- and data-driven machine learning and can be used to identify the implied physical relationships and prediction equations of ground-motion variables.