Seismic Structural Response and Loss Estimation for Dense Urban Districts Using Neural Network Parameterized Gaussian Process

Earthquakes pose a major threat to urban areas, causing fatalities, injuries, and significant economic losses. This study proposes a Gaussian process parametrized by deep neural networks (DNN–GP) as an efficient surrogate for assessing seismic losses of building structures at a regional scale. The framework constructs a GP surrogate using three DNN models that predict the mean, standard deviation, and correlation of structural responses. These models are trained on a seismic demand database developed from a large number of dynamic analyses of structural systems, composed of nonlinear single‐degree‐of‐freedom systems subjected to ground motions with various scaling factors. The DNN–GP model targets assessing an aggregated loss over a cluster of buildings within a limited spatial domain that are subjected to identical ground motion. A key feature of the proposed method is its ability to refine initial estimates from the component DNN models by incorporating reference points, localized nonlinear responses obtained from a selected subset of structures within the considered building portfolio. This study demonstrates the effectiveness of the surrogate model through two numerical studies: (1) prediction of seismic responses for a set of structural systems, and (2) estimation of seismic losses for a building cluster. The results show that the DNN–GP significantly reduces the need for exhaustive nonlinear simulations while maintaining accuracy and quantifying prediction uncertainty. This enables rapid, simulation‐informed decision‐making using the surrogate model for managing seismic risk and enhancing the resilience of urban infrastructure.