Data-driven multi-oscillator-based modeling of unsteady flows

The phase-reduction analysis can simplify the description of unsteady flows by modeling their dynamics through the lens of oscillators, which enables us to identify efficient perturbation timing to modify the flow. In recent studies, it has been utilized to predict the synchronization conditions between oscillatory inputs and flows, as well as to develop control strategies in aerodynamic applications. However, due to difficulties in addressing chaotic behavior and multiple frequencies in realistic flows, phase-based modeling and analysis are still mostly limited to periodic flows.

In this study, we propose a data-driven framework to model the dynamics of flows based on oscillators representing the dominant features of unsteady flows. We extract the oscillators by sequentially compressing the flow field data into latent spaces using convolutional autoencoders. Frequency identifiers are attached to each latent space of autoencoders, which form the latent spaces of autoencoders as oscillators by introducing a loss associated with the temporal variation of phase variables. For further physical interpretability of extracted oscillators, we impose an additional loss to link the amplitude variable to the strength of oscillators. The interactions between oscillators are modeled by training neural ordinary differential equations. By applying the proposed approach to the 2D laminar mixing layer and the 3D supersonic turbulent cavity flow, we validate that the proposed method successfully extracts unsteady flow features corresponding to the dominant frequencies from flow field data and offers the oscillator interactions that replicate the statistical properties of those flows. The proposed method will contribute to the further investigation of perturbation dynamics for more complex flows and their control.