# Discovering Car-following Dynamics from Trajectory Data through Deep Learning

arXiv: https://arxiv.org/abs/2408.00251 · HTML: https://mlsanity.com/paper/2408.00251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 64 references that are in the map.
- First posted on arXiv 1 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [How does this interaction affect me? Interpretable attribution for feature interactions](https://mlsanity.com/paper/2006.10965/) (2020)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [A Physics-Informed Deep Learning Paradigm for Car-Following Models](https://mlsanity.com/paper/2012.13376/) (2020)
- [Learning concise representations for regression by evolving networks of trees](https://mlsanity.com/paper/1807.00981/) (2018)
- [Epsilon-Lexicase Selection for Regression](https://mlsanity.com/paper/1905.13266/) (2019)
- [Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection](https://mlsanity.com/paper/2209.09326/) (2022)
- [I-24 MOTION: An instrument for freeway traffic science](https://mlsanity.com/paper/2301.11198/) (2023)
- [Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants](https://mlsanity.com/paper/2211.10575/) (2022)
- [Improving exploration in policy gradient search: Application to symbolic optimization](https://mlsanity.com/paper/2107.09158/) (2021)
- [Discovering State Variables Hidden in Experimental Data](https://mlsanity.com/paper/2112.10755/) (2021)
- [Influence of CAV Clustering Strategies on Mixed Traffic Flow Characteristics: An Analysis of Vehicle Trajectory Data](https://mlsanity.com/paper/2003.08290/) (2020)

## Built on by (most cited first, 1 of 1)

- [NOVA: Symbolic Regression Discovery of Interpretable Car-Following and Lane-Change Models with Driver Heterogeneity](https://mlsanity.com/paper/2606.10583/) (2026)

## Abstract (arXiv)

This study aims to discover the governing mathematical expressions of car-following dynamics from trajectory data directly using deep learning techniques. We propose an expression exploration framework based on deep symbolic regression (DSR) integrated with a variable intersection selection (VIS) method to find variable combinations that encourage interpretable and parsimonious mathematical expressions. In the exploration learning process, two penalty terms are added to improve the reward function: (i) a complexity penalty to regulate the complexity of the explored expressions to be parsimonious, and (ii) a variable interaction penalty to encourage the expression exploration to focus on variable combinations that can best describe the data. We show the performance of the proposed method to learn several car-following dynamics models and discuss its limitations and future research directions.