Scalable Scenario-based Earthquake Risk Modeling via Linearized Ground-Motion–Fragility Coupling and PPCA

In scenario-based regional risk modeling, the traditional workflow simulates spatially correlated ground motions, and subsequently samples building damage states from lognormal fragility functions. In this procedure, the dimensionality grows with the number of assets and quickly becomes computationally prohibitive for large cities. To overcome this limitation, we introduce a scalable computational framework that (i) reformulates the ground-motion--fragility coupling through an exact linearization and (ii) employs probabilistic principal component analysis (PPCA) to identify low-dimensional latent variables for efficient simulation. We validate the proposed approach on San Francisco’s downtown portfolio of 1,000 buildings, benchmarking against SimCenter R2D's computational testbed. The modal damage states of > 95% buildings match exactly, with a mean difference below 0.04 (on a 0–4 ordinal scale representing none to complete damage), confirming the framework’s accuracy. The achievable dimensionality reduction depends primarily on the portfolio’s spatial extent rather than building density, implying that—given a fixed spatial region—the computational burden remains nearly constant with portfolio size, unlike current approaches. In tests on downtown San Francisco (15,836 buildings) and the broader Bay Area, a single latent dimension and 20 dimensions, respectively, reproduce the benchmark loss distributions within < 2.5%. The method reduces pre-processing complexity from O(N^3) to O(N^2) and simulation complexity from O(N^2) to O(N), where N denotes the number of buildings, yielding roughly 3x faster pre-processing and 110x faster simulation for a 30,000-building subset, with speedups growing linearly with portfolio size. The framework substantially lowers the computational barrier for high-resolution regional seismic risk assessment.