# Learning physics-based reduced-order models for a single-injector combustion process

arXiv: https://arxiv.org/abs/1908.03620 · HTML: https://mlsanity.com/paper/1908.03620/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2019.

## Built on by (most cited first, 20 of 20)

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- [Dimensionality Reduction and Dynamical Mode Recognition of Circular Arrays of Flame Oscillators Using Deep Neural Network](https://mlsanity.com/paper/2312.02462/) (2023)
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- [In-context learning from self-generated trajectories for adaptive model reduction](https://mlsanity.com/paper/2607.02937/) (2026)

## Abstract (arXiv)

This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method combines the perspectives of model reduction and machine learning. Model reduction brings in the physics of the problem, constraining the ROM predictions to lie on a subspace defined by the governing equations. This is achieved by defining the ROM in proper orthogonal decomposition (POD) coordinates, which embed the rich physics information contained in solution snapshots of a high-fidelity computational fluid dynamics (CFD) model. The machine learning perspective brings the flexibility to use transformed physical variables to define the POD basis. This is in contrast to traditional model reduction approaches that are constrained to use the physical variables of the high-fidelity code. Combining the two perspectives, the approach identifies a set of transformed physical variables that expose quadratic structure in the combustion governing equations and learns a quadratic ROM from transformed snapshot data. This learning does not require access to the high-fidelity model implementation. Numerical experiments show that the ROM accurately predicts temperature, pressure, velocity, species concentrations, and the limit-cycle amplitude, with speedups of more than five orders of magnitude over high-fidelity models. Our ROM simulation is shown to be predictive 200% past the training interval. Moreover, ROM-predicted pressure traces accurately match the phase of the pressure signal and yield good approximations of the limit-cycle amplitude.