Low-voltage electrical contacts are core components of power distribution systems, renewable energy installations, and industrial automation equipment. The electric arc generated during contact switching is the primary cause of contact erosion, material transfer, and equipment failure, posing significant threats to system reliability and operational safety. The accurate prediction of arc parameters is hindered by two challenges: the high scatter in available data undermines empirical models, and purely data-driven approaches risk physically implausible results. To address this, a Gaussian Mixture-enhanced Bayesian-optimized Physics-Informed Neural Network (GB-PINN) is proposed. Three core contributions are made: (1) High-fidelity MHD simulation foundation: A magnetohydrodynamic (MHD) multi-physics coupling model of the contact arc was constructed and validated against experiments, showing high fidelity with only 1.63% error in arc duration and 1.82% in arc energy. A multivariate simulation dataset was generated by varying key contact parameters based on this validated model. (2) GMM-based data augmentation: The measured and simulated data were modeled and sampled via Gaussian Mixture Model (GMM) to enrich the dataset while preserving physical consistency. (3) BOHB-optimized PINN prediction: The Bayesian Optimization and Hyperband (BOHB) algorithm was employed to optimize the PINN hyperparameters, enhancing training efficiency and predictive accuracy. Experimental results demonstrated that the proposed GB-PINN achieved superior performance in predicting arc duration and energy, with mean absolute errors (MAE) of 0.079 ms and 0.624 mJ, root mean square errors (RMSE) of 0.099 ms and 0.774 mJ, and coefficients of determination (R²) of 0.980 and 0.979, significantly outperforming grey model (GM (1, N)), long short-term memory (LSTM), and Transformer models. As a physics-informed data-driven tool, GB-PINN enables high-precision arc prediction, providing reliable support for electrical contact design.