A Physics-Constrained Residual Learning Framework for Robust Freeway Traffic Prediction

Accurate freeway Improvements in traffic state prediction accuracy and enhanced stability enable more proactive traffic control and demand management strategies, thereby reducing congestion spillover effects, unnecessary acceleration–deceleration cycles, and the resulting fuel consumption and emissions. Yet, this remains challenging due to the interplay between deterministic traffic flow mechanisms and stochastic disturbances. Purely data-driven models suffer from error accumulation under out-of-distribution conditions, while physics-based models lack flexibility in capturing nonlinear deviations. This paper proposes MDURP, a physics-constrained residual learning framework that reformulates prediction as a residual-space learning problem. A calibrated Cell Transmission Model generates a physically admissible baseline; deep learning models are then restricted to learning the residuals. Wavelet decomposition and GARCH volatility modeling address the multi-scale and heteroskedastic characteristics of these residuals. Experimental results demonstrate that MDURP consistently outperforms baseline models, reducing MAE by an average of 6.8%, RMSE by an average of 4%. The framework also suppresses long-term error accumulation, with MAPE escalation slowing from 0.79% to 0.58% per step. These gains confirm that anchoring deep learning within a physics-defined residual space enhances both accuracy and stability.