This presentation will detail some of my recent works related to the formulation and computation of data-driven reduced-order models for fluid flows.

In the first part, the concept of Flame Transfer Function (FTF) is introduced. This low-order model, based on a simple Fourier transform, is one of the most common in thermoacoustics, where it is used to represent the dynamical response of a flame to acoustic perturbations. The challenge of the present work lies in the configuration for which a FTF is computed: it consists of a doubly-transcritical LO2-LCH4 coaxial jet-flame, typical of those found in future reusable liquid-rocket engines. The FTF is computed from data simulated with the “real-gas'' version of the unstructured Large Eddy Simulation (LES) solver AVBP (CERFACS, France). Physical interpretations of the FTF are provided, with a particular emphasis on the contributions to the heat-release fluctuations; the effect of heat losses at the injector are also briefly discussed.

In a second independent part, a Deep Neural Network for the identification and reduction of high-dimensional systems is presented. This type of auto-encoder architecture has become ubiquitous in Scientific Machine Learning, due to its applicability to any video-like data obtained either from experiments or simulations. It presents however a major shortcoming, characterized by a strong time-step bias, which prevents accurate model prediction at arbitrary instants. A method is therefore introduced to remediate this point. It relies on the inversion of a Linear Multistep Method, to convert a discrete-time model into a continuous-time model. The approach is illustrated on simple, synthetic data.