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

Abstract

We present a generative modeling framework for global sensitivity analysis (GSA) in complex systems characterized by strong and potentially high-dimensional parameter correlations. Traditional variance-based GSA methods rely on the assumption of independent inputs, which rarely holds for Bayesian-calibrated models. While recent extensions using Rosenblatt transformations and Shapley effects theoretically address this limitation, their implementation requires accurate conditional sampling from correlated joint distributions, a task that remains challenging. Existing solutions suffer from restrictive assumptions on input dependence, which limit their applicability to complex data-driven problems. Our method addresses these challenges by reframing sensitivity analysis as a post calibration task on Bayesian posterior distributions, where parameter correlations are learned from data using generative models, eliminating restrictive dependence assumptions and ensuring data relevant sensitivity estimates. We employ autoregressive architectures to implement Rosenblatt transformations and leverage diffusion models to estimate Shapley effects. These methods impose no predefined distributional assumptions and scale efficiently with both data volume and model complexity. We demonstrate the effectiveness of our approach on two representative applications: a COVID-19 transmission model and a cancer immunotherapy model. Results show that our methods effectively captures parameter sensitivities in the presence of parameter correlations, and achieve notable gains in scalability and flexibility over existing methods.