Physical enhanced residual learning (PERL) framework for vehicle trajectory prediction

While physics models for predicting system states can reveal fundamental insights owing to their parsimonious structure, they may not always yield the most accurate predictions, particularly for complex systems. As an alternative, neural network (NN) models usually yield more accurate predictions; however, they lack interpretable physical insights. To articulate the advantages of both physics and NN models while circumventing their limitations, this study proposes a physics-enhanced residual learning (PERL) framework that adjusts a physics model prediction with a corrective residual predicted from a residual learning NN model. The integration of the physics model preserves interpretability and tremendously reduces the amount of training data compared with pure NN models. We apply PERL to a vehicle trajectory prediction problem with real-world trajectory data of both a human-driven vehicle (HV) and an autonomous vehicle (AV), using an adapted Newell car-following model as the physics model and four kinds of neural networks (Gated Recurrent Unit (GRU), Convolution long short-term memory (CLSTM), Variational Autoencoder (VAE), and the Informer model) as the residual learning model. We compare this PERL model with pure physics models, NN models, and other physics-informed neural network (PINN) models. The results reveal that PERL yields the best prediction when the training data are small. The PERL model converges quickly during training. Moreover, compared with the NN and PINN models, the PERL model requires fewer parameters to achieve similar predictive performance. A sensitivity analysis revealed that the PERL model consistently outperforms the physics models, NN models and PINN models with different physics and residual learning models given a small training dataset. Among these, the PERL model based on CLSTM achieved the most accurate predictions.