# Efficient nonlinear flame response modeling for propulsion thermoacoustic analysis using limited numerical data

arXiv: https://arxiv.org/abs/2409.05885 · HTML: https://mlsanity.com/paper/2409.05885/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 72 references that are in the map.
- First posted on arXiv 26 Aug 2024.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [Independently Recurrent Neural Network (IndRNN): Building A Longer and Deeper RNN](https://mlsanity.com/paper/1803.04831/) (2018)

## Abstract (arXiv)

Characterizing nonlinear flame response is critical for predicting thermoacoustic instabilities in propulsion combustors, yet obtaining a comprehensive response map through high-fidelity simulations remains computationally prohibitive. This study proposes a data-driven approach for learning nonlinear flame-response dynamics from limited numerical samples. Instead of requiring exhaustive harmonic-forcing simulations, a frequency-sweeping dataset with multiple perturbation amplitudes is designed to capture the coupled effects of excitation frequency and amplitude, enabling efficient learning of the nonlinear input-output relationship between flow perturbations and heat-release-rate fluctuations. A dual-path temporal surrogate model is developed to represent nonlinear response evolution in the time domain, where complementary temporal features are extracted to retain both global response trends and local nonlinear characteristics. The proposed framework is validated using numerical simulations of a laminar premixed flame. It accurately predicts nonlinear single-frequency responses over a wide range of forcing amplitudes and frequencies, with an average mean relative error of 6.69% for 72 independent test cases. Further evaluation using a modified n-τ model demonstrates that the framework can capture stronger nonlinear responses by increasing the diversity of the training data. This work provides an efficient alternative for constructing nonlinear flame-response models and offers a promising approach for rapid thermoacoustic stability analysis of propulsion combustors.