Accelerating Seismic Response Distribution Estimation With Scalable Mixture Density Network Stochastic Surrogate Models

ABSTRACT Accurate seismic risk assessment can be computationally intensive, requiring numerous nonlinear analyses to propagate uncertainties. Surrogate models offer an efficient alternative via emulating the costly structural models. For earthquake engineering applications, a practical strategy to promote efficient emulation is to employ explanatory variables (seismicity characteristics, ground motion features, or their combination) as explicit surrogate inputs, while simultaneously treating the inherent aleatoric variability in ground motion acceleration time‐series as latent surrogate model input variables. This results in aleatoric uncertainty in the engineering demand parameter (EDP) predictions, which cannot be captured by standard deterministic surrogates. Stochastic emulation overcomes this challenge by establishing a stochastic input–output mapping to account for the aleatoric uncertainties in the EDP distributions. This study introduces the use of mixture density networks (MDNs) to approximate EDP distributions. Key advantages of MDN are its compatibility with non‐replicated training samples and its inherent scalability to high‐dimensional inputs, allowing for an easier incorporation of full ground motion features, a significant advantage over many state‐of‐the‐art surrogates. Case studies on two representative structures, evaluated with three different stochastic ground motion models, demonstrate that the proposed MDN‐based approach outperforms established stochastic surrogate workhorses. It provides more accurate seismic risk estimates at a substantially lower computational training cost, highlighting its practical utility for complex, real‐world seismic applications.