# Prediction with Approximated Gaussian Process Dynamical Models

arXiv: https://arxiv.org/abs/2006.14551 · HTML: https://mlsanity.com/paper/2006.14551/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

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

- [Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior](https://mlsanity.com/paper/2305.09017/) (2023)
- [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)
- [Sequential Estimation of Gaussian Process-based Deep State-Space Models](https://mlsanity.com/paper/2301.12528/) (2023)
- [Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Models](https://mlsanity.com/paper/2406.11809/) (2024)
- [Learning-Based Optimal Control with Performance Guarantees for Unknown Systems with Latent States](https://mlsanity.com/paper/2303.17963/) (2023)
- [Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspective](https://mlsanity.com/paper/2507.18220/) (2025)
- [Sampling-Based Safe Reinforcement Learning](https://mlsanity.com/paper/2605.19469/) (2026)

## Abstract (arXiv)

The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human-robot interaction, is often challenging or even infeasible due to the complexity of the system dynamics. In contrast, data-driven approaches need only a minimum of prior knowledge and scale with the complexity of the system. In particular, Gaussian process dynamical models (GPDMs) provide very promising results for the modeling of complex dynamics. However, the control properties of these GP models are just sparsely researched, which leads to a "blackbox" treatment in modeling and control scenarios. In addition, the sampling of GPDMs for prediction purpose respecting their non-parametric nature results in non-Markovian dynamics making the theoretical analysis challenging. In this article, we present approximated GPDMs which are Markov and analyze their control theoretical properties. Among others, the approximated error is analyzed and conditions for boundedness of the trajectories are provided. The outcomes are illustrated with numerical examples that show the power of the approximated models while the the computational time is significantly reduced.