# Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems

arXiv: https://arxiv.org/abs/1709.05409 · HTML: https://mlsanity.com/paper/1709.05409/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2017.

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

- [Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients](https://mlsanity.com/paper/2212.14319/) (2022)
- [Machine Learning in Orbit Estimation: a Survey](https://mlsanity.com/paper/2207.08993/) (2022)
- [Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes](https://mlsanity.com/paper/2108.06430/) (2021)
- [Data-efficient Kernel Methods for Learning Hamiltonian Systems](https://mlsanity.com/paper/2509.17154/) (2025)
- [System identification using Bayesian neural networks with nonparametric noise models](https://mlsanity.com/paper/2104.12119/) (2021)
- [Approximate Latent Force Model Inference](https://mlsanity.com/paper/2109.11851/) (2021)
- [Bayesian grey-box identification of nonlinear convection effects in heat transfer dynamics](https://mlsanity.com/paper/2407.01226/) (2024)
- [A Kronecker product accelerated efficient sparse Gaussian Process (E-SGP) for flow emulation](https://mlsanity.com/paper/2312.10023/) (2023)

## Abstract (arXiv)

This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first-principles physical model part and a non-parametric GP model part. We briefly review the statistical inference and learning methods for this kind of models, introduce stochastic control methodology for the models, and provide new theoretical observability and controllability results for them.