An explicit physics-residual learning model for vehicle longitudinal trajectory prediction

In heterogeneous traffic environments, accurate and stable prediction of vehicle longitudinal dynamics is critical for ensuring the operational safety and reliability of Autonomous Vehicles (AVs), necessitating predictive models that achieve both high accuracy and strong interpretability. Although Physics-Informed Neural Networks (PINNs) have demonstrated enhanced predictive performance, challenges remain in terms of training stability and mechanistic interpretability in complex traffic scenarios. To address these limitations, this study propose a physics-residual-driven IDM–GLSTM model, which integrates data-driven residuals into the Intelligent Driver Model (IDM) to explicitly decouple the deterministic longitudinal dynamics from the interaction effects induced by surrounding vehicles. Specifically, the IDM encodes physically interpretable Car-Following (CF) dynamics, while a Graph Attention Network (GAT) combined with a Long Short-Term Memory (LSTM) network adaptively captures temporal dependencies and spatial interaction residuals that are not explicitly represented in the physical model, thereby improving predictive accuracy while preserving the structural interpretability of the system. Empirical evaluation on the Next Generation Simulation (NGSIM) data in the US demonstrates that IDM–GLSTM significantly outperforms baseline models in LoP-RMSE (longitudinal position root mean square error), achieving a reduction of approximately 34%–38% compared with conventional LSTM and Retraining LSTM models. Cross-region transfer experiments further confirm the IDM–GLSTM’s robust generalization capability across different traffic conditions. Complementary analyses using information-theoretic metrics and SHAP (SHapley Additive exPlanations) indicate that the model predominantly leverages physically meaningful features, such as the leading vehicle and nearest neighbors, while effectively compensating for complex multi-vehicle interactions through the learned high-entropy residuals.