Physics-Informed Bayesian Inference for Virtual Testing and Prediction of Train Performance

This paper proposes a physics-informed Bayesian framework for virtual testing and predictive modeling of train performance, specifically addressing stopping-distance prediction. The approach unifies physical simulation models with data-driven statistical inference to achieve uncertainty-aware predictions under limited or noisy measurements. By embedding governing equations of motion into a hierarchical Bayesian structure, the method systematically accounts for both model-form and data uncertainty, allowing explicit decomposition into aleatoric and epistemic components. A Gaussian process surrogate is employed to efficiently emulate high-fidelity physics simulations while preserving key dynamic behaviors and parameter sensitivities. The Bayesian formulation enables probabilistic calibration and validation, providing predictive distributions and confidence bounds. As a representative application, the framework is applied to the virtual prediction of train stopping distances, demonstrating how the proposed methodology captures nonlinear braking dynamics and quantifies uncertainty in safety-relevant performance metrics directly compatible with statistical verification standards such as EN 16834. The results confirm that the physics-informed Bayesian approach enables accurate, interpretable, and standards-aligned virtual testing across a wide range of dynamical systems.