Development of reduced order modeling-based linear system extracting method for efficient data handling with a minimal nonlinearity

Flexible control of fluid flow phenomena is not only of scientific interest but also of engineering importance. However, its high degrees of freedom and strong nonlinearity pose challenges for designing control laws. A solution extensively studied is the application of reduced-order modeling (ROM), which efficiently handles high-dimensional data. In particular, one of the machine learning-based order reduction methods called autoencoder (AE) has attracted attention, leading to various AE-based analysis methods. This is achieved by its ability to map high-dimensional data into a low-dimensional space. However, even with the AE-based ROM, another problem still remains; namely, the extracted low-dimensional features still exhibit strong nonlinearity. Hence, we have investigated a linear system extraction autoencoder (LEAE), which improves the capability of AE to extract a complete linear system from fluid flow phenomena. In this study, we propose an enhanced LEAE, i.e., a partially nonlinear LEAE, using a scheme of time variation of the orbit radius to freely adapt to the time evolution of the latent variables with the flow development. The model extracts a system that can represent the temporal evolution of latent variables by targeting continuously changing flow fields. To achieve this, we focus on both 1) transient and 2) steady flows around a circular cylinder at Re_D=100. Finally, we assess the extracted linear system with minimal nonlinearity and demonstrate its effectiveness.