The Response Surface Method (RSM)-based non-intrusive method has been widely used to reduce the computational cost for stochastic Explosion Risk Analysis (ERA) in oil and gas industry. However, the RSM, which may cause the overfitting problem, can reduce robustness and efficiency of the ERA procedure. Therefore, a more robust Bayesian Regularization Artificial Neural Network (BRANN) is introduced in this study. The BRANN-based non-intrusive method is developed along with its executive procedure for stochastic ERA. The BRANN-Dispersion-Deterministic (BDD) models and the BRANN-Explosion-Deterministic (BED) models are firstly developed based on representative simulations. Optimal simulation input numbers of the aforementioned deterministic models are then identified. Furthermore, the exceedance frequency curve is generated by combing the deterministic models with Latin Hypercube Sampling (LHS). Sensitivity analysis of simulation input numbers with regard to the exceedance frequency curve is conducted. Eventually, comparison of the exceedance probability curves between the BRANN-based method and the RSM-based method is carried out. The ultra-deep-water semi-submersible offshore platform is used to demonstrate the advantages of the BRANN-based non-intrusive method.