# A Black-Box Physics-Informed Estimator based on Gaussian Process Regression for Robot Inverse Dynamics Identification

arXiv: https://arxiv.org/abs/2310.06585 · HTML: https://mlsanity.com/paper/2310.06585/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems](https://mlsanity.com/paper/1907.04489/) (2019)
- [A Tutorial on Sparse Gaussian Processes and Variational Inference](https://mlsanity.com/paper/2012.13962/) (2020)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Derivative-free online learning of inverse dynamics models](https://mlsanity.com/paper/1809.05074/) (2018)
- [Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes](https://mlsanity.com/paper/2206.12272/) (2022)
- [Online semi-parametric learning for inverse dynamics modeling](https://mlsanity.com/paper/1603.05412/) (2016)
- [Incremental Semiparametric Inverse Dynamics Learning](https://mlsanity.com/paper/1601.04549/) (2016)
- [Cascaded Gaussian Processes for Data-efficient Robot Dynamics Learning](https://mlsanity.com/paper/1910.02291/) (2019)
- [A data-efficient geometrically inspired polynomial kernel for robot inverse dynamics](https://mlsanity.com/paper/1904.13317/) (2019)
- [Proprioceptive Robot Collision Detection through Gaussian Process Regression](https://mlsanity.com/paper/1905.08689/) (2019)

## Built on by (most cited first, 4 of 4)

- [Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)](https://mlsanity.com/paper/2508.07775/) (2025)
- [Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes](https://mlsanity.com/paper/2511.05330/) (2025)
- [Diffusion Sequence Models for Generative In-Context Meta-Learning of Robot Dynamics](https://mlsanity.com/paper/2604.13366/) (2026)
- [Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations](https://mlsanity.com/paper/2605.06246/) (2026)

## Abstract (arXiv)

Learning the inverse dynamics of robots directly from data, adopting a black-box approach, is interesting for several real-world scenarios where limited knowledge about the system is available. In this paper, we propose a black-box model based on Gaussian Process (GP) Regression for the identification of the inverse dynamics of robotic manipulators. The proposed model relies on a novel multidimensional kernel, called textitLagrangian Inspired Polynomial (kernelInitials) kernel. The kernelInitials kernel is based on two main ideas. First, instead of directly modeling the inverse dynamics components, we model as GPs the kinetic and potential energy of the system. The GP prior on the inverse dynamics components is derived from those on the energies by applying the properties of GPs under linear operators. Second, as regards the energy prior definition, we prove a polynomial structure of the kinetic and potential energy, and we derive a polynomial kernel that encodes this property. As a consequence, the proposed model allows also to estimate the kinetic and potential energy without requiring any label on these quantities. Results on simulation and on two real robotic manipulators, namely a 7 DOF Franka Emika Panda, and a 6 DOF MELFA RV4FL, show that the proposed model outperforms state-of-the-art black-box estimators based both on Gaussian Processes and Neural Networks in terms of accuracy, generality and data efficiency. The experiments on the MELFA robot also demonstrate that our approach achieves performance comparable to fine-tuned model-based estimators, despite requiring less prior information.