Spatially correlated multi-state fragility via a warped Gaussian process

• Fragility is redefined as a spatially correlated random field with dual uncertainty. • Analytically derived from first principles with closed-form uncertainty quantification. • Multi-output Gaussian process with a composite kernel across space, damage states, and archetypes. • San Francisco case study demonstrates spatial and cross-state correlations. • Sparse variational Gaussian process scales efficiently to over 15,000 buildings. This study introduces a novel probabilistic methodology for spatial fragility modeling based on a warped Gaussian Process (GP), offering a unified framework for estimating building damage probabilities with uncertainty quantification. Unlike conventional approaches that treat damage probabilities as conditionally independent point estimates, the proposed method models fragility as a spatially and structurally correlated random field governed by both aleatory and epistemic uncertainty. A latent fragility index is defined in probit space and modeled using a GP over spatial coordinates, damage states, and structural archetypes. A structured multi-output kernel captures correlations across these dimensions, while sparse variational inference allows scalability to large-scale building inventories. Fragility probabilities are derived through a nonlinear warping of the latent GP, yielding a multivariate Probit-Normal distribution with a closed-form joint density, as well as analytic expressions for expectation, variance, and correlation. Application to over 15,000 buildings in the San Francisco Bay Area under a regional seismic hazard demonstrates the method’s ability to generate spatially coherent fragility maps with quantified uncertainty. Violations of ordinality across damage states are suppressed in expectation and strongly reduced in the joint distribution learned by the model, and correlation among spatially proximate and structurally similar buildings is explicitly modeled. The result is a scalable, interpretable, and uncertainty-aware spatial fragility modeling framework for high-resolution regional risk assessment and resilience planning.