This article introduces a methodology for updating the nonlinear stochastic dynamics of a nozzle with uncertain computational model. The approach focuses on a high-dimensional nonlinear computational model constrained by a small target dataset. Challenges include the large number of degrees-of-freedom, geometric nonlinearities, material uncertainties, stochastic external loads, underobservability, and high computational costs. A detailed dynamic analysis of the nozzle is presented. An updated statistical surrogate model relating the observations of interest to the control parameters is constructed. Despite small training and target datasets and partial observability, the study successfully applies probabilistic learning on manifolds (PLoM) to address these challenges. PLoM captures geometric nonlinear effects and uncertainty propagation, improving conditional mean statistics compared to training data. The conditional confidence region demonstrates the ability of the methodology to accurately represent both observed and unobserved output variables, contributing to advancements in modeling complex systems.