# Online parameter inference for the simulation of a Bunsen flame using heteroscedastic Bayesian neural network ensembles

arXiv: https://arxiv.org/abs/2104.13201 · HTML: https://mlsanity.com/paper/2104.13201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 26 Apr 2021.

## Builds on (most cited first, 5 of 5)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Ensembling geophysical models with Bayesian Neural Networks](https://mlsanity.com/paper/2010.03561/) (2020)
- [Combined State and Parameter Estimation in Level-Set Methods](https://mlsanity.com/paper/1903.00321/) (2019)
- [Real-time parameter inference in reduced-order flame models with heteroscedastic Bayesian neural network ensembles](https://mlsanity.com/paper/2011.02838/) (2020)

## Abstract (arXiv)

This paper proposes a Bayesian data-driven machine learning method for the online inference of the parameters of a G-equation model of a ducted, premixed flame. Heteroscedastic Bayesian neural network ensembles are trained on a library of 1.7 million flame fronts simulated in LSGEN2D, a G-equation solver, to learn the Bayesian posterior distribution of the model parameters given observations. The ensembles are then used to infer the parameters of Bunsen flame experiments so that the dynamics of these can be simulated in LSGEN2D. This allows the surface area variation of the flame edge, a proxy for the heat release rate, to be calculated. The proposed method provides cheap and online parameter and uncertainty estimates matching results obtained with the ensemble Kalman filter, at less computational cost. This enables fast and reliable simulation of the combustion process.