# A Physics-Informed Deep Learning Paradigm for Car-Following Models

arXiv: https://arxiv.org/abs/2012.13376 · HTML: https://mlsanity.com/paper/2012.13376/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2020.

## Built on by (most cited first, 30 of 41)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2209.00225/) (2022)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Applications of deep learning in traffic congestion detection, prediction and alleviation: A survey](https://mlsanity.com/paper/2102.09759/) (2021)
- [On the Limitations of Physics-informed Deep Learning: Illustrations Using First Order Hyperbolic Conservation Law-based Traffic Flow Models](https://mlsanity.com/paper/2302.12337/) (2023)
- [Dynamic Hypergraph Structure Learning for Traffic Flow Forecasting](https://mlsanity.com/paper/2309.12028/) (2023)
- [Fourier neural operator for learning solutions to macroscopic traffic flow models: Application to the forward and inverse problems](https://mlsanity.com/paper/2308.07051/) (2023)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [GenAI-powered Multi-Agent Paradigm for Smart Urban Mobility: Opportunities and Challenges for Integrating Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) with Intelligent Transportation Systems](https://mlsanity.com/paper/2409.00494/) (2024)
- [A Generative Car-following Model Conditioned On Driving Styles](https://mlsanity.com/paper/2112.05399/) (2021)
- [Car-Following Models: A Multidisciplinary Review](https://mlsanity.com/paper/2304.07143/) (2023)
- [Enhancing System-Level Safety in Mixed-Autonomy Platoon via Safe Reinforcement Learning](https://mlsanity.com/paper/2401.11148/) (2024)
- [Quantifying Uncertainty In Traffic State Estimation Using Generative Adversarial Networks](https://mlsanity.com/paper/2206.09349/) (2022)
- [Traffic expertise meets residual RL: Knowledge-informed model-based residual reinforcement learning for CAV trajectory control](https://mlsanity.com/paper/2408.17380/) (2024)
- [A Physics Enhanced Residual Learning (PERL) Framework for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2309.15284/) (2023)
- [MetaFollower: Adaptable Personalized Autonomous Car Following](https://mlsanity.com/paper/2406.16978/) (2024)
- [EditFollower: Tunable Car Following Models for Customizable Adaptive Cruise Control Systems](https://mlsanity.com/paper/2407.02516/) (2024)
- [Position: Biology is the Challenge Physics-Informed ML Needs to Evolve](https://mlsanity.com/paper/2510.25368/) (2025)
- [IDM-Follower: A Model-Informed Deep Learning Method for Long-Sequence Car-Following Trajectory Prediction](https://mlsanity.com/paper/2210.10965/) (2022)
- [Markov Regime-Switching Intelligent Driver Model for Interpretable Car-Following Behavior](https://mlsanity.com/paper/2506.14762/) (2025)
- [Perimeter Control with Heterogeneous Metering Rates for Cordon Signals: A Physics-Regularized Multi-Agent Reinforcement Learning Approach](https://mlsanity.com/paper/2308.12985/) (2023)
- [Privacy-Preserving Data Fusion for Traffic State Estimation: A Vertical Federated Learning Approach](https://mlsanity.com/paper/2401.11836/) (2024)
- [COOL: A Conjoint Perspective on Spatio-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2403.01091/) (2024)
- [PITA: Physics-Informed Trajectory Autoencoder](https://mlsanity.com/paper/2403.11728/) (2024)
- [Communication-Aware Reinforcement Learning for Cooperative Adaptive Cruise Control](https://mlsanity.com/paper/2407.08964/) (2024)
- [Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis](https://mlsanity.com/paper/2505.11491/) (2025)
- [Inverting the Fundamental Diagram and Forecasting Boundary Conditions: How Machine Learning Can Improve Macroscopic Models for Traffic Flow](https://mlsanity.com/paper/2303.12740/) (2023)
- [TrTr: A Versatile Pre-Trained Large Traffic Model based on Transformer for Capturing Trajectory Diversity in Vehicle Population](https://mlsanity.com/paper/2309.12677/) (2023)
- [RACER: Rational Artificial Intelligence Car-following-model Enhanced by Reality](https://mlsanity.com/paper/2312.07003/) (2023)
- [Discovering Car-following Dynamics from Trajectory Data through Deep Learning](https://mlsanity.com/paper/2408.00251/) (2024)

## Abstract (arXiv)

Car-following behavior has been extensively studied using physics-based models, such as the Intelligent Driver Model. These models successfully interpret traffic phenomena observed in the real-world but may not fully capture the complex cognitive process of driving. Deep learning models, on the other hand, have demonstrated their power in capturing observed traffic phenomena but require a large amount of driving data to train. This paper aims to develop a family of neural network based car-following models that are informed by physics-based models, which leverage the advantage of both physics-based (being data-efficient and interpretable) and deep learning based (being generalizable) models. We design physics-informed deep learning car-following (PIDL-CF) architectures encoded with two popular physics-based models - IDM and OVM, on which acceleration is predicted for four traffic regimes: acceleration, deceleration, cruising, and emergency braking. Two types of PIDL-CFM problems are studied, one to predict acceleration only and the other to jointly predict acceleration and discover model parameters. We also demonstrate the superior performance of PIDL with the Next Generation SIMulation (NGSIM) dataset over baselines, especially when the training data is sparse. The results demonstrate the superior performance of neural networks informed by physics over those without. The developed PIDL-CF framework holds the potential for system identification of driving models and for the development of driving-based controls for automated vehicles.