Study on Effectiveness of Mapping Using Variational Autoencoder for Elucidation of Nonlinear Dynamics in a Rocket Combustor

Abstract

To simulate combustion oscillations occurred in a rocket combustor, numerical calculations were conducted. The output physical variable vectors were subjected to Proper Orthogonal Decomposition (POD) and a Variational Autoencoder (VAE), a type of generative AI, for dimension reduction. A phase plane constructed from latent variables obtained through dimension reduction was used to analyze a nonlinear dynamical system. For dynamical system analysis on the phase plane, it is necessary that the physical variable vectors and the latent variable vectors have a local homeomorphic mapping relationship. This paper proposes and evaluates a method for calculating the error on the mappings for both methods with respect to the local homeomorphic mapping.