Quantifying the dynamic predictability of train delay with uncertainty-aware neural networks

The digital transformation of railway systems has sparked research in train delay prediction. While efforts have predominantly set on maximizing prediction accuracy, there remains a significant need to explore a deeper understanding of the prediction -associated uncertainty. This study proposes uncertainty -aware neural networks, extended with test -time -dropout and loss attenuation, to predict train delays and also estimate the level of associated confidence. Our approach outperforms commonly -used stochastic methods in terms of accuracy and precision. We further introduce a dynamic prediction horizon framework (DPHF) to systematically compare and validate uncertainty -enhanced predictions over time. We suggest the likeliness of realization (LoR) to evaluate predictions with confidence estimates and to quantify dynamic predictability, which we find to be best described by an exponential decay for an increasing prediction horizon. While the model -driven (epistemic) uncertainty remains relatively small and constant as the prediction horizon increases, the data -inherent (aleatoric) uncertainty is substantially larger and grows significantly. This indicates that the observed decay in predictability is not an artefact of the modelling process but indeed an inherent property of train delays. This study thus provides new insights that can be used to increase the robustness and reliability of railway operations, emphasizing innovative modelling and the utilization of emerging data sources.