Predictive Framework for the Track Quality Index Using a Physics-Regularized Neural Network

Abstract Accurate prediction of the Track Quality Index (TQI) is essential for proactive railway maintenance planning, yet purely data-driven approaches may violate fundamental degradation physics, producing predictions of spontaneous track improvement that are operationally misleading. This paper presents a physics-regularized neural network that integrates a domain-informed degradation model with a neural network residual correction, enforcing monotonicity and physically admissible degradation rates through a composite loss function while retaining the flexibility to capture multivariate patterns. Using 147,566 track geometry measurements spanning 34 months across seven geometry parameters, the model is evaluated against three baselines: a vanilla neural network, a posthoc clipped baseline, and a gamma process, across five forecast horizons (1–5 months). Architecture selection and loss-weight configuration are validated through sensitivity analysis and ablation studies; physics parameter stability is assessed via five-fold geographic cross-validation. The physics-regularized model reduces monotonicity violations by 83.9% and improves constraint adherence by 35 percentage points relative to the vanilla baseline, at an average root mean square error (RMSE) cost of 11.5%, mean absolute error (MAE) of 3.1%, and mean absolute percentage error (MAPE) of 3.9%. Posthoc clipping achieves full monotonicity at more than twice this accuracy cost, confirming that structural enforcement during training is superior to mechanical posthoc correction. The gamma process has an ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R squared equals 0.3470" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.3470</mml:mn> </mml:math> at 5 months), demonstrating that constraint adherence without multivariate feature integration has no operational value. Learned physics parameters exhibit coefficients of variation below 7% across geographic folds, confirming interpretable and stable degradation properties. The framework offers a practical path to physically trustworthy TQI forecasting for safety-critical maintenance scheduling.