Ground-motion model (GMM) is the basis of many earthquake engineering
studies. In this study, a novel physics-informed symbolic learner (PISL) method
based on the Nest Generation Attenuation-West2 database 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 two a priori physical conditions, namely,
distance and amplitude saturation. GMMs developed using the PISL, an empirical
regression method (ERM), and an artificial neural network (ANN) are compared in
terms of residuals and extrapolation based on obtained data 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 in
different regions.

本文提出了一种新的物理启发符号学习方法（PISL），并使用 Nest Generation Attenuation-West2 数据库，使用序列阈值岭回归算法自动发现数学运算符作为符号，提取由复杂系统发出的地面运动的简洁且易于理解的显式特征描述。通过对峰值地面加速度和速度的数据进行比较和外推来评估使用 PISL、经验回归方法和人工神经网络开发的 GMM 的残差和外推能力，并发现 PISL-GMM 提供了同时考虑物理学和数据驱动机器学习的新型回归算法，可以用于在不同区域中识别地震运动变量的预测方程式。