# A Physics Enhanced Residual Learning (PERL) Framework for Vehicle Trajectory Prediction

arXiv: https://arxiv.org/abs/2309.15284 · HTML: https://mlsanity.com/paper/2309.15284/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 26 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [Residual Policy Learning](https://mlsanity.com/paper/1812.06298/) (2018)
- [An LSTM Network for Highway Trajectory Prediction](https://mlsanity.com/paper/1801.07962/) (2018)
- [Deep Bidirectional and Unidirectional LSTM Recurrent Neural Network for Network-wide Traffic Speed Prediction](https://mlsanity.com/paper/1801.02143/) (2018)
- [STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2209.00225/) (2022)
- [A Physics-Informed Deep Learning Paradigm for Car-Following Models](https://mlsanity.com/paper/2012.13376/) (2020)
- [Learning Discrepancy Models From Experimental Data](https://mlsanity.com/paper/1909.08574/) (2019)
- [Short-term traffic prediction using physics-aware neural networks](https://mlsanity.com/paper/2109.10253/) (2021)
- [IDM-Follower: A Model-Informed Deep Learning Method for Long-Sequence Car-Following Trajectory Prediction](https://mlsanity.com/paper/2210.10965/) (2022)

## Built on by (most cited first, 5 of 5)

- [Traffic expertise meets residual RL: Knowledge-informed model-based residual reinforcement learning for CAV trajectory control](https://mlsanity.com/paper/2408.17380/) (2024)
- [FollowGen: A Scaled Noise Conditional Diffusion Model for Car-Following Trajectory Prediction](https://mlsanity.com/paper/2411.16747/) (2024)
- [Crossfusor: A Cross-Attention Transformer Enhanced Conditional Diffusion Model for Car-Following Trajectory Prediction](https://mlsanity.com/paper/2406.11941/) (2024)
- [Physics Enhanced Residual Policy Learning (PERPL) for safety cruising in mixed traffic platooning under actuator and communication delay](https://mlsanity.com/paper/2409.15595/) (2024)
- [Sky-Drive: A Distributed Multi-Agent Simulation Platform for Human-AI Collaborative and Socially-Aware Future Transportation](https://mlsanity.com/paper/2504.18010/) (2025)

## Abstract (arXiv)

In vehicle trajectory prediction, physics models and data-driven models are two predominant methodologies. However, each approach presents its own set of challenges: physics models fall short in predictability, while data-driven models lack interpretability. Addressing these identified shortcomings, this paper proposes a novel framework, the Physics-Enhanced Residual Learning (PERL) model. PERL integrates the strengths of physics-based and data-driven methods for traffic state prediction. PERL contains a physics model and a residual learning model. Its prediction is the sum of the physics model result and a predicted residual as a correction to it. It preserves the interpretability inherent to physics-based models and has reduced data requirements compared to data-driven methods. Experiments were conducted using a real-world vehicle trajectory dataset. We proposed a PERL model, with the Intelligent Driver Model (IDM) as its physics car-following model and Long Short-Term Memory (LSTM) as its residual learning model. We compare this PERL model with the physics car-following model, data-driven model, and other physics-informed neural network (PINN) models. The result reveals that PERL achieves better prediction with a small dataset, compared to the physics model, data-driven model, and PINN model. Second, the PERL model showed faster convergence during training, offering comparable performance with fewer training samples than the data-driven model and PINN model. Sensitivity analysis also proves comparable performance of PERL using another residual learning model and a physics car-following model.