Uncertainty and sensitivity analyses of deterministic parameters based optimal aerogel glazing system are necessary due to multi-dimensional uncertainties in the real working condition, whereas thermal and energy performances of aerogel glazing system, in the academia, are normally characterized by deterministic parameters. In this study, a generic uncertainty quantification methodology was proposed using the two-dimensional Markov Chain Monte Carlo to quantify both aleatory and epistemic uncertainties of scenario parameters in the aerogel glazing system. A surrogate model, trained by mathematical heat and optical models using the machine-learning based data-driven method, was developed to predict the thermal and energy performances under multi-level scenario uncertainties. Results showed that, the developed surrogate model is efficient to deal with computational complexity of sophisticated light and heat transfer processes. When considering scenario uncertainties, the annual value of heat flux is reduced from 237.2 to 185.3 kWh/(m2.a) by 21.9%, and the annual value of total heat gain is reduced from 267.2 to 209.5 kWh/m2.a by 21.6%. This study proposes a generic methodology for multi-dimensional uncertainties’ quantification and a surrogate model for thousands of cases-based uncertainty analysis. Approaches for the stochastic uncertainty analysis on aerogel glazing system were presented, which can promote the optimal design in buildings.