# Vehicle single track modeling using physics guided neural differential equations

arXiv: https://arxiv.org/abs/2403.11648 · HTML: https://mlsanity.com/paper/2403.11648/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Mar 2024.

## Built on by (most cited first, 2 of 2)

- [Model Predictive Path Integral PID Control for Learning-Based Path Following](https://mlsanity.com/paper/2603.29499/) (2026)
- [What Do Latent Predictive Vehicle Representations Retain? Measuring State, Geometry, and Local Response](https://mlsanity.com/paper/2609.32512/) (2026)

## Abstract (arXiv)

In this paper, we follow the physics guided modeling approach and integrate a neural differential equation network into the physical structure of a vehicle single track model. By relying on the kinematic relations of the single track ordinary differential equations (ODE), a small neural network and few training samples are sufficient to substantially improve the model accuracy compared with a pure physics based vehicle single track model. To be more precise, the sum of squared error is reduced by 68% in the considered scenario. In addition, it is demonstrated that the prediction capabilities of the physics guided neural ODE model are superior compared with a pure black box neural differential equation approach.