# Deep Dynamics: Vehicle Dynamics Modeling with a Physics-Constrained Neural Network for Autonomous Racing

arXiv: https://arxiv.org/abs/2312.04374 · HTML: https://mlsanity.com/paper/2312.04374/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 7 Dec 2023.

## Builds on (most cited first, 7 of 7)

- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)
- [F1/10: An Open-Source Autonomous Cyber-Physical Platform](https://mlsanity.com/paper/1901.08567/) (2019)
- [Physics Embedded Neural Network Vehicle Model and Applications in Risk-Aware Autonomous Driving Using Latent Features](https://mlsanity.com/paper/2207.07920/) (2022)
- [Indy Autonomous Challenge -- Autonomous Race Cars at the Handling Limits](https://mlsanity.com/paper/2202.03807/) (2022)
- [RACECAR -- The Dataset for High-Speed Autonomous Racing](https://mlsanity.com/paper/2306.03252/) (2023)
- [BayesRace: Learning to race autonomously using prior experience](https://mlsanity.com/paper/2005.04755/) (2020)
- [Hybrid Physics and Deep Learning Model for Interpretable Vehicle State Prediction](https://mlsanity.com/paper/2103.06727/) (2021)

## Built on by (most cited first, 8 of 8)

- [Fine-Tuning Hybrid Physics-Informed Neural Networks for Vehicle Dynamics Model Estimation](https://mlsanity.com/paper/2409.19647/) (2024)
- [MVAdapt: Zero-Shot Multi-Vehicle Adaptation for End-to-End Autonomous Driving](https://mlsanity.com/paper/2604.11854/) (2026)
- [VeMo: A Lightweight Data-Driven Approach to Model Vehicle Dynamics](https://mlsanity.com/paper/2510.07447/) (2025)
- [PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles](https://mlsanity.com/paper/2511.15522/) (2025)
- [Verifying Physics-Informed Neural Network Fidelity using Classical Fisher Information from Differentiable Dynamical System](https://mlsanity.com/paper/2601.11638/) (2026)
- [White-Box Neural Ensemble for Vehicular Plasticity: Quantifying the Efficiency Cost of Symbolic Auditability in Adaptive NMPC](https://mlsanity.com/paper/2602.01516/) (2026)
- [Dynamics Distillation for Efficient and Transferable Control Learning](https://mlsanity.com/paper/2605.01516/) (2026)
- [Scalable Identification of Physics-Based and Neural Dynamics from Partial Measurements](https://mlsanity.com/paper/2610.16559/) (2026)

## Abstract (arXiv)

Autonomous racing is a critical research area for autonomous driving, presenting significant challenges in vehicle dynamics modeling, such as balancing model precision and computational efficiency at high speeds (>280km/h), where minor errors in modeling have severe consequences. Existing physics-based models for vehicle dynamics require elaborate testing setups and tuning, which are hard to implement, time-intensive, and cost-prohibitive. Conversely, purely data-driven approaches do not generalize well and cannot adequately ensure physical constraints on predictions. This paper introduces Deep Dynamics, a physics-constrained neural network (PCNN) for vehicle dynamics modeling of an autonomous racecar. It combines physics coefficient estimation and dynamical equations to accurately predict vehicle states at high speeds and includes a unique Physics Guard layer to ensure internal coefficient estimates remain within their nominal physical ranges. Open-loop and closed-loop performance assessments, using a physics-based simulator and full-scale autonomous Indy racecar data, highlight Deep Dynamics as a promising approach for modeling racecar vehicle dynamics.