# Physics Constrained Motion Prediction with Uncertainty Quantification

arXiv: https://arxiv.org/abs/2302.01060 · HTML: https://mlsanity.com/paper/2302.01060/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [THOMAS: Trajectory Heatmap Output with learned Multi-Agent Sampling](https://mlsanity.com/paper/2110.06607/) (2021)
- [On Adversarial Robustness of Trajectory Prediction for Autonomous Vehicles](https://mlsanity.com/paper/2201.05057/) (2022)
- [Adaptive Conformal Prediction for Motion Planning among Dynamic Agents](https://mlsanity.com/paper/2212.00278/) (2022)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)

## Built on by (most cited first, 11 of 11)

- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Four Principles for Physically Interpretable World Models](https://mlsanity.com/paper/2503.02143/) (2025)
- [Multi-Modal Conformal Prediction Regions with Simple Structures by Optimizing Convex Shape Templates](https://mlsanity.com/paper/2312.07434/) (2023)
- [Physically Interpretable World Models via Weakly Supervised Representation Learning](https://mlsanity.com/paper/2412.12870/) (2024)
- [Single Trajectory Conformal Prediction](https://mlsanity.com/paper/2406.01570/) (2024)
- [Differentiable Predictive Control for Large-Scale Urban Road Networks](https://mlsanity.com/paper/2406.10433/) (2024)
- [A Generalizable Physics-guided Causal Model for Trajectory Prediction in Autonomous Driving](https://mlsanity.com/paper/2602.13936/) (2026)
- [Towards Safe and Reliable Autonomous Driving: Dynamic Occupancy Set Prediction](https://mlsanity.com/paper/2402.19385/) (2024)
- [AdaptNC: Adaptive Nonconformity Scores for Conformal Prediction under Distribution Shift](https://mlsanity.com/paper/2602.01629/) (2026)

## Abstract (arXiv)

Predicting the motion of dynamic agents is a critical task for guaranteeing the safety of autonomous systems. A particular challenge is that motion prediction algorithms should obey dynamics constraints and quantify prediction uncertainty as a measure of confidence. We present a physics-constrained approach for motion prediction which uses a surrogate dynamical model to ensure that predicted trajectories are dynamically feasible. We propose a two-step integration consisting of intent and trajectory prediction subject to dynamics constraints. We also construct prediction regions that quantify uncertainty and are tailored for autonomous driving by using conformal prediction, a popular statistical tool. Physics Constrained Motion Prediction achieves a 41% better ADE, 56% better FDE, and 19% better IoU over a baseline in experiments using an autonomous racing dataset.