Learning unsteady trajectories in a latent space for studying ignition in rocket combustors

Laser-based ignition success of rocket engines presents a highly challenging scenario for machine learning surrogate models due to the unsteady multi-physics interactions, involving thermodynamics, turbulent mixing, laser deposition, and combustion. The first step we take is high-fidelity simulation of this problem through large scale computations that accurately resolves physics in the combustor. These computations lead to the binary outcome of successful/unsuccessful ignition as a response to system inputs. Thereafter, high-fidelity data output is used to tune and correct a low-fidelity model with dramatically reduced scale-resolution, achieving a bi-fidelity prediction. An ensemble of simulations with sampling of the physical variabilities in the system is then constructed, as a precursor to an ML model. Convolutional autoencoders (AE) can first compress images from time-series associated with transport of a laser-deposited energy kernel into a low-dimensional latent space. Thereafter, a neural ordinary differential equation (NODE) extracts dynamical system information of trajectories in the uncovered latent space. Together, compression of the simulation ensemble by an AE, and the dynamical evolution uncovered by the NODE constructs a framework in which physical inputs to the system, corresponding to physical uncertainties in the rocket combustor, generate latent space trajectories, that are then decoded into a physical output. This outcome then supersedes and replaces the tuned low-fidelity CFD pathway, a reference output of the ML model is shown in Figure 1. As part of this work, we therefore comment on tested compression strategies, particularly in relation to the dimension of the AE’s latent-space vector, and training policies for a NODE on curvy trajectories in the latent space.