Perovskite solar cells (PSCs) have emerged as promising next-generation photovoltaic technology due to their high efficiency, lightweight structure, and low-cost fabrication. However, structural safety and operational serviceability issues—particularly mechanical instability caused by buckling—remain a critical obstacle to large-scale commercialization. This study develops a machine learning–aided probabilistic framework for the buckling analysis of PSCs. A Mixture Density Network (MDN), which integrates deep neural networks with Gaussian mixture modeling, is employed to predict the full probability distribution of critical buckling loads considering various uncertainties. The model is trained using datasets incorporating stochastic variations in material and geometric parameters. The MDN-based approach can accurately capture the nonlinear and stochastic characteristics of PSCs’ buckling behavior, effectively linking uncertainties to probabilistic failure responses. Comprehensive statistical information on buckling responses, entailing the meaning, standard deviation, probability density function, cumulative distribution function, and conditional probability density are provided for safety examination and reliability-based structural design. Furthermore, numerical experiments demonstrate quantitatively the superiority of the developed machine learning scheme against classical meta-model workhorses in prediction accuracy and efficiency.