<p>Due to their high specific strength and excellent energy absorption capacity, Y-frame core sandwich panels have attracted increasing attention for impact-resistant structures in the aerospace industry. However, the numerical simulation of the impact process is highly nonlinear and computationally intensive, which poses significant challenges to design optimization based on conventional surrogate models. To address this issue, a Bayesian polynomial chaos neural network (BPCNN) surrogate model is proposed to efficiently approximate highly nonlinear responses and is subsequently applied to the optimization of a Y-frame core sandwich panel. Within the proposed framework, a Bayesian formulation is established to determine the parameters of the polynomial chaos neural network by leveraging Gaussian process regression with an explicit noise term. Christoffel function-based weighted sampling method combined with low-discrepancy sequences is developed to generate training samples, and Christoffel priors are assigned to the variance of the noise term. The effectiveness of the proposed BPCNN is validated through representative numerical examples, demonstrating improved accuracy and convergence compared with several widely used surrogate models. Finally, the proposed method is employed for the analysis and multi-objective optimization of the Y-frame core sandwich panel.</p>