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

## TL;DR

This paper introduces a physics-informed machine learning approach to develop reduced-order models for a single-injector combustion process, achieving high accuracy and significant computational speedups without needing access to the high-fidelity model implementation.

## Contribution

It combines physics-based model reduction with machine learning to identify transformed variables and learn quadratic ROMs directly from data, enhancing predictive capabilities.

## Key findings

- ROM predicts key combustion variables accurately
- Speedups of over five orders of magnitude compared to high-fidelity models
- ROM remains predictive 200% beyond training interval

## Abstract

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.