Physics-guided symbolic neural network reveals optimal functional forms describing ground motions

This study presents a novel framework for ground motion modelling utilizing Physics-Guided Symbolic Neural Networks (PGSNN). Symbolic neural networks offer a new method for knowledge discovery, providing a unique perspective for automatically uncovering predictive functional forms from data. This approach differs from traditional methods as it does not rely on predefined equations. Instead, it employs symbolic operators to freely combine input parameters in a high-dimensional space. This method addresses the problem of data imbalance by incorporating physical guidance to ensure that the model produces results that are consistent with established physical principles. The resulting equations align with the expectations of the engineering seismology community, particularly within the magnitude-distance ranges, where classical equations are well calibrated. The prediction performance of the PGSNN, evaluated across different intensity measures (PGA, PGV, and PSA), was assessed by calculating the residuals between measured and predicted values and their standard deviations. The predictive capability of this model was verified using new event records. The results indicate that the prediction performance of the PGSNN is comparable to those of traditional methods.