# Neural ODE to model and prognose thermoacoustic instability

arXiv: https://arxiv.org/abs/2106.12758 · HTML: https://mlsanity.com/paper/2106.12758/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 77 references that are in the map.
- First posted on arXiv 24 Jun 2021.

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

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [On Loss Functions for Deep Neural Networks in Classification](https://mlsanity.com/paper/1702.05659/) (2017)
- [Review and Comparison of Commonly Used Activation Functions for Deep Neural Networks](https://mlsanity.com/paper/2010.09458/) (2020)

## Built on by (most cited first, 3 of 3)

- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [Machine-Learned Closure of URANS for Stably Stratified Turbulence: Connecting Physical Timescales & Data Hyperparameters of Deep Time-Series Models](https://mlsanity.com/paper/2404.16141/) (2024)
- [Forecasting with an N-dimensional Langevin Equation and a Neural-Ordinary Differential Equation](https://mlsanity.com/paper/2405.07359/) (2024)

## Abstract (arXiv)

In reacting flow systems, thermoacoustic instability characterized by high amplitude pressure fluctuations, is driven by a positive coupling between the unsteady heat release rate and the acoustic field of the combustor. When the underlying flow is turbulent, as a control parameter of the system is varied and the system approach thermoacoustic instability, the acoustic pressure oscillations synchronize with heat release rate oscillations. Consequently, during the onset of thermoacoustic instability in turbulent combustors, the system dynamics transition from chaotic oscillations to periodic oscillations via a state of intermittency. Thermoacoustic systems are traditionally modeled by coupling the model for the unsteady heat source and the acoustic subsystem, each estimated independently. The response of the unsteady heat source, the flame, to acoustic fluctuations are characterized by introducing external unsteady forcing. This necessitates a powerful excitation module to obtain the nonlinear response of the flame to acoustic perturbations. Instead of characterizing individual subsystems, we introduce a neural ordinary differential equation (neural ODE) framework to model the thermoacoustic system as a whole. The neural ODE model for the thermoacoustic system uses time series of the heat release rate and the pressure fluctuations, measured simultaneously without introducing any external perturbations, to model their coupled interaction. Further, we use the parameters of neural ODE to define an anomaly measure that represents the proximity of system dynamics to limit cycle oscillations and thus provide an early warning signal for the onset of thermoacoustic instability.