Global Sensitivity Analysis Using Polynomial Chaos Expansion on the Grassmann Manifold

Traditional global sensitivity analysis (GSA) techniques, such as variance- and density-based approaches, are limited in cases where a comprehensive understanding of temporal dynamics is critical, especially for models with diverse timescales and structural complexity, such as system dynamics and agent-based models (ABMs). To address this, we propose a novel manifold learning-based method for GSA in systems exhibiting complex spatiotemporal processes. Our method employs Grassmannian diffusion maps to reduce the dimensionality of the data and polynomial chaos expansion (PCE) to map stochastic input parameters to diffusion coordinates of the reduced space. We calculate sensitivity indices from PCE coefficients, aggregating multiple outputs and their entire trajectories for a more general estimation of parameter sensitivities. We demonstrate the capabilities of the proposed approach by applying it to the Lotka-Volterra model and an epidemic dynamics ABM and capturing diverse temporal dynamics. We establish that the new methodology meets all “good” properties of a global sensitivity measure, making it a valuable alternative to traditional GSA techniques. We anticipate that it will potentially expand the application of manifold-based approaches and deepen the understanding of complex spatiotemporal processes.