# Bayesian grey-box identification of nonlinear convection effects in heat transfer dynamics

arXiv: https://arxiv.org/abs/2407.01226 · HTML: https://mlsanity.com/paper/2407.01226/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 3 of 3)

- [Gaussian Process Latent Force Models for Learning and Stochastic Control of Physical Systems](https://mlsanity.com/paper/1709.05409/) (2017)
- [Marginalizing Gaussian Process Hyperparameters using Sequential Monte Carlo](https://mlsanity.com/paper/1502.01908/) (2015)
- [A Latent Restoring Force Approach to Nonlinear System Identification](https://mlsanity.com/paper/2109.10681/) (2021)

## Built on by (most cited first, 1 of 1)

- [Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs](https://mlsanity.com/paper/2603.03922/) (2026)

## Abstract (arXiv)

We propose a computational procedure for identifying convection in heat transfer dynamics. The procedure is based on a Gaussian process latent force model, consisting of a white-box component (i.e., known physics) for the conduction and linear convection effects and a Gaussian process that acts as a black-box component for the nonlinear convection effects. States are inferred through Bayesian smoothing and we obtain approximate posterior distributions for the kernel covariance function's hyperparameters using Laplace's method. The nonlinear convection function is recovered from the Gaussian process states using a Bayesian regression model. We validate the procedure by simulation error using the identified nonlinear convection function, on both data from a simulated system and measurements from a physical assembly.