Scalable Gaussian Process for Learning Non-Ergodic Ground Motion Model from Physics-Based Simulations with Application to Power Infrastructure Assessment

Abstract

This study presents the development and application of a scalable non-ergodic ground motion model (NGMM) for the Los Angeles area. The NGMM is trained and validated on physics-based simulated ground-motion data from a recent Statewide California Earthquake Center (SCEC) CyberShake study. The NGMM is formulated as a Gaussian Process (GP) regression model, where the prior median is defined as the ASK14 ergodic ground-motion model and the posterior median is obtained by learning the non-ergodic effects embedded in the training data. These non-ergodic effects include systematic site and path effects, which are represented in the GP using Mat\'ern and specialized covariance kernels that explicitly characterize path vectors. Implementing the NGMM requires hyperparameter tuning and inference on large datasets (on the order of one million data points or more), posing significant computational challenges for conventional GP approaches. To address this scalability issue, this paper presents a suite of computational strategies, including sparse Cholesky inversion, parallel computing, GPU acceleration, and stochastic gradient descent minimization. Despite these advances, the full CyberShake dataset (on the order of hundreds of millions of data points) remains computationally prohibitive. Therefore, aleatory variability is modeled separately using a mixed-effects formulation to represent within-event and between-event variability. The developed NGMM has two primary applications: interpolation of partially observed ground-motion fields and predictive modeling for ground motions in unobserved earthquake scenarios. Validation results on independent datasets demonstrate accurate performance in both applications. A case study of power transmission network assessment in an Mw 6.7 Puente Hill scenario further demonstrated that the developed NGMM closely reproduces physics-based simulation results.