# A Priori Uncertainty Quantification of Reacting Turbulence Closure Models using Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2402.18729 · HTML: https://mlsanity.com/paper/2402.18729/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 106 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 30 of 32)

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- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
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- [Specifying Weight Priors in Bayesian Deep Neural Networks with Empirical Bayes](https://mlsanity.com/paper/1906.05323/) (2019)
- [Deep Ensembles from a Bayesian Perspective](https://mlsanity.com/paper/2105.13283/) (2021)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Bayesian Learning for Neural Networks: an algorithmic survey](https://mlsanity.com/paper/2211.11865/) (2022)
- [Active Learning and Bayesian Optimization: a Unified Perspective to Learn with a Goal](https://mlsanity.com/paper/2303.01560/) (2023)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)
- [Out-of-distribution Detection and Generation using Soft Brownian Offset Sampling and Autoencoders](https://mlsanity.com/paper/2105.02965/) (2021)
- [Learning Subgrid-scale Models with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2212.09967/) (2022)
- [Meaningful uncertainties from deep neural network surrogates of large-scale numerical simulations](https://mlsanity.com/paper/2010.13749/) (2020)

## Abstract (arXiv)

While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulation (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. In this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.