# Physics Embedded Neural Network Vehicle Model and Applications in Risk-Aware Autonomous Driving Using Latent Features

arXiv: https://arxiv.org/abs/2207.07920 · HTML: https://mlsanity.com/paper/2207.07920/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 16 Jul 2022.

## Builds on (most cited first, 10 of 10)

- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Uncertainty-Aware Reinforcement Learning for Collision Avoidance](https://mlsanity.com/paper/1702.01182/) (2017)
- [Low Level Control of a Quadrotor with Deep Model-Based Reinforcement Learning](https://mlsanity.com/paper/1901.03737/) (2019)
- [Smooth Model Predictive Path Integral Control without Smoothing](https://mlsanity.com/paper/2112.09988/) (2021)
- [TOAST: Trajectory Optimization and Simultaneous Tracking using Shared Neural Network Dynamics](https://mlsanity.com/paper/2201.08321/) (2022)
- [Adaptive Probabilistic Vehicle Trajectory Prediction Through Physically Feasible Bayesian Recurrent Neural Network](https://mlsanity.com/paper/1911.04597/) (2019)

## Built on by (most cited first, 12 of 12)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Deep Dynamics: Vehicle Dynamics Modeling with a Physics-Constrained Neural Network for Autonomous Racing](https://mlsanity.com/paper/2312.04374/) (2023)
- [Bridging Active Exploration and Uncertainty-Aware Deployment Using Probabilistic Ensemble Neural Network Dynamics](https://mlsanity.com/paper/2305.12240/) (2023)
- [Risk-Aware Reward Shaping of Reinforcement Learning Agents for Autonomous Driving](https://mlsanity.com/paper/2306.03220/) (2023)
- [Safe Navigation in Unstructured Environments by Minimizing Uncertainty in Control and Perception](https://mlsanity.com/paper/2306.14601/) (2023)
- [Autonomous particles](https://mlsanity.com/paper/2301.10077/) (2023)
- [Meta-Learning Online Dynamics Model Adaptation in Off-Road Autonomous Driving](https://mlsanity.com/paper/2504.16923/) (2025)
- [Analyzing the Impact of Simulation Fidelity on the Evaluation of Autonomous Driving Motion Control](https://mlsanity.com/paper/2602.07984/) (2026)
- [Fine-Tuning Hybrid Physics-Informed Neural Networks for Vehicle Dynamics Model Estimation](https://mlsanity.com/paper/2409.19647/) (2024)
- [Situationally-Aware Dynamics Learning](https://mlsanity.com/paper/2505.19574/) (2025)
- [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)

## Abstract (arXiv)

Non-holonomic vehicle motion has been studied extensively using physics-based models. Common approaches when using these models interpret the wheel/ground interactions using a linear tire model and thus may not fully capture the nonlinear and complex dynamics under various environments. On the other hand, neural network models have been widely employed in this domain, demonstrating powerful function approximation capabilities. However, these black-box learning strategies completely abandon the existing knowledge of well-known physics. In this paper, we seamlessly combine deep learning with a fully differentiable physics model to endow the neural network with available prior knowledge. The proposed model shows better generalization performance than the vanilla neural network model by a large margin. We also show that the latent features of our model can accurately represent lateral tire forces without the need for any additional training. Lastly, We develop a risk-aware model predictive controller using proprioceptive information derived from the latent features. We validate our idea in two autonomous driving tasks under unknown friction, outperforming the baseline control framework.