[Paper Review] A Two-Stage Bayesian Framework for Multi-Fidelity Online Updating of Spatial Fragility Fields

Abdullah M. Braik, Maria Koliou|arXiv (Cornell University)|Jan 19, 2026

Meteorological Phenomena and Simulations0 citations

TL;DR

The paper proposes a two-stage Bayesian framework that online updates spatial fragility fields by unifying physics-based fragility with real-time post-disaster observations, using a Probit-Normal representation and a probit-warped Gaussian Process.

ABSTRACT

This paper addresses a long-standing gap in natural hazard modeling by unifying physics-based fragility functions with real-time post-disaster observations. It introduces a Bayesian framework that continuously refines regional vulnerability estimates as new data emerges. The framework reformulates physics-informed fragility estimates into a Probit-Normal (PN) representation that captures aleatory variability and epistemic uncertainty in an analytically tractable form. Stage 1 performs local Bayesian updating by moment-matching PN marginals to Beta surrogates that preserve their probability shapes, enabling conjugate Beta-Bernoulli updates with soft, multi-fidelity observations. Fidelity weights encode source reliability, and the resulting Beta posteriors are re-projected into PN form, producing heteroscedastic fragility estimates whose variances reflect data quality and coverage. Stage 2 assimilates these heteroscedastic observations within a probit-warped Gaussian Process (GP), which propagates information from high-fidelity sites to low-fidelity and unobserved regions through a composite kernel that links space, archetypes, and correlated damage states. The framework is applied to the 2011 Joplin tornado, where wind-field priors and computer-vision damage assessments are fused under varying assumptions about tornado width, sampling strategy, and observation completeness. Results show that the method corrects biased priors, propagates information spatially, and produces uncertainty-aware exceedance probabilities that support real-time situational awareness.

Motivation & Objective

• Bridge physics-based fragility models with real-time post-disaster observations to improve regional vulnerability estimates.
• Develop a tractable PN (Probit-Normal) representation to capture aleatory variability and epistemic uncertainty in fragility estimates.
• Enable local updates via Beta-Bernoulli conjugacy with multi-fidelity observations and fidelity-weighted posteriors.
• Propagate information spatially to low-fidelity and unobserved regions through a probit-warped GP.
• Demonstrate the framework on the 2011 Joplin tornado with fused wind-field priors and computer-vision damage assessments.

Proposed method

• Stage 1 local Bayesian updating by moment-matching PN marginals to Beta surrogates while preserving probability shapes.
• Use fidelity weights to encode source reliability and obtain Beta posteriors that re-project into PN form to yield heteroscedastic fragility estimates.
• Stage 2 assimilates heteroscedastic observations in a probit-warped Gaussian Process to propagate information via a composite kernel linking space, archetypes, and damage states.
• Combine multi-fidelity observations to update regional vulnerability in an online setting.
• Provide uncertainty-aware exceedance probabilities for real-time situational awareness.

Experimental results

Research questions

• RQ1 How can physics-informed fragility estimates be reformulated for tractable Bayesian updating with real-time data?
• RQ2 Can a two-stage framework effectively fuse multi-fidelity observations to update spatial fragility fields and quantify uncertainty?
• RQ3 How does a probit-warped GP propagate information from high-fidelity to lower-fidelity and unobserved regions?
• RQ4 What is the impact of observation completeness and sampling strategy on updating fragility fields in natural hazard scenarios?
• RQ5 Does the approach improve exceedance probability estimates for real-time decision support?

Key findings

• Stage 1 yields Beta posteriors that, when re-projected to PN form, produce heteroscedastic fragility estimates reflecting data quality and coverage.
• Stage 2 propagates information through a probit-warped GP, enabling spatial updating across space, archetypes, and correlated damage states.
• The method corrects biased priors and enables spatial information propagation with uncertainty-aware exceedance probabilities.
• Applied to the 2011 Joplin tornado, the framework fuses wind-field priors with computer-vision damage assessments under different assumptions about tornado width and sampling.
• Results support real-time situational awareness through uncertainly-informed predictions.