Scalable Scenario-based Regional Earthquake Risk Assessment via Gaussianized Ground-motion--damage Modeling 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 (N) and quickly becomes computationally prohibitive for large cities. To overcome this limitation, we introduce a scalable computational framework that (i) recasts the traditional two-step (ground-motion, then damage) simulation as a single, N-dimensional Gaussian sampling problem via an exact change of variables, and (ii) identifies low-dimensional latent variables that make this sampling efficient by employing probabilistic principal component analysis (PPCA). 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. 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 achievable dimensionality reduction depends primarily on the portfolio’s spatial extent rather than building density. As a result, the computational complexity drops by one order in N relative to the traditional approach -- from O(N^3) to O(N^2) in the pre-processing step and from O(N^2M) to O(NM) in the simulation step, where M is the number of simulations. For 30,000 buildings, the method yields roughly 9x faster pre-processing and 97x faster simulation, with speedups growing linearly with portfolio size, resulting in 63x faster total computation time for M=10^5, compared to the traditional framework. Overall, the framework substantially lowers the computational barrier for regional seismic risk assessment of dense urban building portfolios.