# On Simulation and Trajectory Prediction with Gaussian Process Dynamics

arXiv: https://arxiv.org/abs/1912.10900 · HTML: https://mlsanity.com/paper/1912.10900/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2019.

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

- [Machine Learning for Autonomous Vehicle's Trajectory Prediction: A comprehensive survey, Challenges, and Future Research Directions](https://mlsanity.com/paper/2307.07527/) (2023)
- [Targeted Adversarial Attacks against Neural Network Trajectory Predictors](https://mlsanity.com/paper/2212.04138/) (2022)
- [Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework](https://mlsanity.com/paper/2409.08616/) (2024)
- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Models](https://mlsanity.com/paper/2510.02224/) (2025)
- [Safe Machine-Learning-supported Model Predictive Force and Motion Control in Robotics](https://mlsanity.com/paper/2303.04569/) (2023)
- [Exact Inference for Continuous-Time Gaussian Process Dynamics](https://mlsanity.com/paper/2309.02351/) (2023)
- [GRANP: A Graph Recurrent Attentive Neural Process Model for Vehicle Trajectory Prediction](https://mlsanity.com/paper/2404.08004/) (2024)
- [The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Models](https://mlsanity.com/paper/2211.11103/) (2022)
- [Shallow Representation is Deep: Learning Uncertainty-aware and Worst-case Random Feature Dynamics](https://mlsanity.com/paper/2106.13066/) (2021)
- [Gaussian Process for Trajectories](https://mlsanity.com/paper/2110.03712/) (2021)

## Abstract (arXiv)

Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error and underestimation of the prediction uncertainty, potentially leading to failures in safety-critical applications. This paper discusses methods that explicitly take the correlation of successive function evaluations into account. We first describe two sampling-based techniques; one approach provides samples of the true trajectory distribution, suitable for `ground truth' simulations, while the other draws function samples from basis function approximations of the GP. Second, we propose a linearization-based technique that directly provides approximations of the trajectory distribution, taking correlations explicitly into account. We demonstrate the procedures in simple numerical examples, contrasting the results with established methods.