# An Ensemble-Based Deep Framework for Estimating Thermo-Chemical State Variables from Flamelet Generated Manifolds

arXiv: https://arxiv.org/abs/2211.14098 · HTML: https://mlsanity.com/paper/2211.14098/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 6 of 6)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Challenges in Markov chain Monte Carlo for Bayesian neural networks](https://mlsanity.com/paper/1910.06539/) (2019)
- [Measurement of Hybrid Rocket Solid Fuel Regression Rate for a Slab Burner using Deep Learning](https://mlsanity.com/paper/2108.11276/) (2021)
- [ChemTab: A Physics Guided Chemistry Modeling Framework](https://mlsanity.com/paper/2202.09855/) (2022)

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

- [UQ of 2D Slab Burner DNS: Surrogates, Uncertainty Propagation, and Parameter Calibration](https://mlsanity.com/paper/2411.16693/) (2024)

## Abstract (arXiv)

Complete computation of turbulent combustion flow involves two separate steps: mapping reaction kinetics to low-dimensional manifolds and looking-up this approximate manifold during CFD run-time to estimate the thermo-chemical state variables. In our previous work, we showed that using a deep architecture to learn the two steps jointly, instead of separately, is 73% more accurate at estimating the source energy, a key state variable, compared to benchmarks and can be integrated within a DNS turbulent combustion framework. In their natural form, such deep architectures do not allow for uncertainty quantification of the quantities of interest: the source energy and key species source terms. In this paper, we expand on such architectures, specifically ChemTab, by introducing deep ensembles to approximate the posterior distribution of the quantities of interest. We investigate two strategies of creating these ensemble models: one that keeps the flamelet origin information (Flamelets strategy) and one that ignores the origin and considers all the data independently (Points strategy). To train these models we used flamelet data generated by the GRI--Mech 3.0 methane mechanism, which consists of 53 chemical species and 325 reactions. Our results demonstrate that the Flamelets strategy is superior in terms of the absolute prediction error for the quantities of interest, but is reliant on the types of flamelets used to train the ensemble. The Points strategy is best at capturing the variability of the quantities of interest, independent of the flamelet types. We conclude that, overall, ChemTab Deep Ensembles allows for a more accurate representation of the source energy and key species source terms, compared to the model without these modifications.