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

TL;DR

This work tackles uncertainty quantification for data-driven closure models in large-eddy simulations of reacting turbulent flows by employing Bayesian neural networks to jointly capture epistemic and aleatoric uncertainties in the sub-filter progress-variable dissipation rate, $\chi_{\rm SFS}$. It formulates a data-driven closure within a probabilistic framework, characterizes uncertainty sources, and demonstrates a priori evaluation on diverse flame datasets. A key novelty is the explicit treatment of extrapolation behavior through synthetic data (including normalizing flows) to enable robust OOD detection and to guide data acquisition, while maintaining in-distribution accuracy. The findings indicate that aleatoric uncertainty dominates predictive uncertainty, that epistemic uncertainty is localized in phase space, and that NF-based synthetic data provides superior extrapolation performance; the work also discusses pathways to propagate uncertainty through simulations and uses a trainable prior to regularize learning. Overall, the approach offers a principled, uncertainty-aware route to deploy data-driven closures in reacting-flow simulations and informs data-collection and OOD detection strategies for safer, more reliable predictions.

Abstract

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.

Figures (16)

• Figure 1: A dataset that has a region of high epistemic uncertainty and low aleatoric uncertainty (left of origin) as well as a region with low epistemic uncertainty and high aleatoric uncertainty (right of origin).
• Figure 2: (a) A in the style of blundell2015weight that captures epistemic uncertainty only and (b) a in the style of kendall2017uncertainties that captures both epistemic and aleatoric uncertainty.
• Figure 3: Comparison of two Bayesian neural networks trained on the dataset presented in Fig. \ref{['fig:uncertainty-cartoon']}, (a) models only the epistemic (model-form) uncertainty, while (b) models both epistemic and aleatoric uncertainty.
• Figure 4: Demonstration of "catastrophic forgetting" when a model is (a) first trained to a prior-enforcing dataset and then the true dataset (the warm-start method) and (b) trained on combined dataset.
• Figure 5: Histogram plot in log-scale showing the mean prediction, $\mathbb{E}_{q(\mathbf{w}|\theta)}\left[ \chi_{\rm SFS} \right]$, from model and $\chi_{\rm SFS}$ from data. The dashed black line represents a perfect model.