Abstract
Stochastic gene regulatory networks exhibit complex dynamics that require efficient methods for parameter inference and uncertainty quantification. In this work, we propose a surrogate modelling framework that combines a partial integro-differential equation (PIDE) formulation with polynomial chaos expansions (PCE) to efficiently approximate the stochastic dynamics of gene expression models under parametric uncertainty. The approach represents the time evolution of low-order statistical moments as polynomial functions of uncertain kinetic parameters, enabling fast evaluations and tractable inference. The method is demonstrated on a self-regulating gene network, achieving accurate parameter estimation and a reduction of approximately two orders of magnitude in computational cost compared to direct PIDE-based optimisation.