Bayesian-calibrated global sensitivity analysis for mathematical models using generative AI.

Area of Science:

• Computational Science
• Statistical Modeling
• Systems Biology

Background:

• Traditional global sensitivity analysis (GSA) methods assume independent inputs, which is often violated in Bayesian-calibrated models with parameter correlations.
• Existing extensions for correlated inputs face challenges with accurate conditional sampling and impose restrictive assumptions.
• Complex data-driven problems require GSA methods that can handle high-dimensional parameter correlations without distributional assumptions.

Purpose of the Study:

• To develop a novel generative modeling framework for global sensitivity analysis (GSA) in complex systems with strong parameter correlations.
• To overcome the limitations of existing GSA methods regarding input independence assumptions and sampling challenges.
• To provide data-driven and flexible sensitivity estimates for complex, correlated systems.

Main Methods:

• Reframed sensitivity analysis as a post-calibration task on Bayesian posterior distributions.
• Utilized generative models, specifically autoregressive architectures and diffusion models, to learn parameter correlations from data.
• Employed autoregressive architectures for Rosenblatt transformations and diffusion models for Shapley effect estimation.

Main Results:

• The proposed framework effectively captures parameter sensitivities in the presence of parameter correlations.
• Demonstrated significant gains in scalability and flexibility compared to existing GSA methods.
• Validated the approach on a COVID-19 transmission model and a cancer immunotherapy model.

Conclusions:

• The generative modeling framework offers a robust solution for GSA in complex systems with correlated parameters.
• The method eliminates restrictive dependence assumptions, ensuring data-relevant sensitivity estimates.
• The approach is scalable and flexible, applicable to a wide range of complex data-driven problems.