New HSIC framework separates aleatory and epistemic uncertainty for high-dimensional models

A new method for global sensitivity analysis (GSA) under hybrid uncertainty has been introduced by Shijie Zhong, Jiangfeng Fu, and Pengfei Wei in a June 2026 arXiv paper. The work addresses a critical limitation of existing Hilbert-Schmidt Independence Criterion (HSIC) approaches, which are typically restricted to single-output settings and cannot separate aleatory (stochastic) uncertainty from epistemic (model/parameter ignorance) uncertainty. Their solution is a double-space tensor-product reproducing kernel Hilbert space (RKHS) framework that constructs factorized kernels over both the latent input space and the multidimensional output space.

By deriving a concurrent double Möbius inversion, the method orthogonally decomposes the global dependence measure into three components: pure aleatory effects, pure epistemic effects, and their interaction contributions. This yields dimension-wise sensitivity indices that preserve the uncertainty attribution structure across all output dimensions. To satisfy independence assumptions, the authors introduce an auxiliary-variable representation via the inverse probability integral transform, enabling treatment of hierarchical uncertainties and Copula-induced correlations within a unified latent space. A fully vectorized single-loop implementation avoids the computational burden of nested Monte Carlo simulation, while statistical significance and estimation uncertainty are quantified through permutation testing and bootstrap confidence intervals. Numerical studies on a modified multi-output Ishigami function and an aerodynamic pressure-field problem confirm the framework's accuracy, scalability, and practical applicability in engineering and machine learning contexts.