# Learning Constrained Dynamics with Gauss Principle adhering Gaussian Processes

arXiv: https://arxiv.org/abs/2004.11238 · HTML: https://mlsanity.com/paper/2004.11238/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2020.

## Built on by (most cited first, 13 of 13)

- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [Structure-preserving Gaussian Process Dynamics](https://mlsanity.com/paper/2102.01606/) (2021)
- [Probabilistic Robust Linear Quadratic Regulators with Gaussian Processes](https://mlsanity.com/paper/2105.07668/) (2021)
- [On Foundation Models for Dynamical Systems from Purely Synthetic Data](https://mlsanity.com/paper/2412.00395/) (2024)
- [Structure-Preserving Learning Using Gaussian Processes and Variational Integrators](https://mlsanity.com/paper/2112.05451/) (2021)
- [Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guarantees](https://mlsanity.com/paper/2105.03397/) (2021)
- [Incorporating Sum Constraints into Multitask Gaussian Processes](https://mlsanity.com/paper/2202.01793/) (2022)
- [Physics-enhanced Gaussian Process Variational Autoencoder](https://mlsanity.com/paper/2305.09006/) (2023)
- [Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equations](https://mlsanity.com/paper/2411.16663/) (2024)
- [Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control](https://mlsanity.com/paper/2301.03565/) (2023)
- [Learning Hybrid Dynamics Models With Simulator-Informed Latent States](https://mlsanity.com/paper/2309.02873/) (2023)
- [Newtonian and Lagrangian Neural Networks: A Comparison Towards Efficient Inverse Dynamics Identification](https://mlsanity.com/paper/2506.17994/) (2025)
- [LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE](https://mlsanity.com/paper/2505.12360/) (2025)

## Abstract (arXiv)

The identification of the constrained dynamics of mechanical systems is often challenging. Learning methods promise to ease an analytical analysis, but require considerable amounts of data for training. We propose to combine insights from analytical mechanics with Gaussian process regression to improve the model's data efficiency and constraint integrity. The result is a Gaussian process model that incorporates a priori constraint knowledge such that its predictions adhere to Gauss' principle of least constraint. In return, predictions of the system's acceleration naturally respect potentially non-ideal (non-)holonomic equality constraints. As corollary results, our model enables to infer the acceleration of the unconstrained system from data of the constrained system and enables knowledge transfer between differing constraint configurations.