Low-Dimensional Latent Space Representation of the Parametric Dependence of Transient Instability Growth

We consider data-driven modeling of the transient growth phase of

Ritchmeyer Meshkov instability before the flow has transitioned to

turbulence. We rely on nonlinear autoencoders to reduce dimensionality

of the system to then learn dynamical evolution in the corresponding

latent space. In this study, the data comprises of the observation of

the evolution of the unstable interface between two materials subject

to impulsive acceleration when parameters related to the equation of

state and the initial perturbation of the interface are varied. In

this setting, we find that linear evolution in a very low dimensional

latent space is capable of capturing the spatiotemporal dynamics with

resonable accuracy. We seek to better understand this surprising

finding from different perspectives including, e.g. in terms of the

interplay between the representations of spatial domain/features and

temporal dynamics. Next, we show how this low-dimensional latent space

representation can be leveraged to develop a parameterized

reduced-order model that captures the parametric dependence of the

growth of the instability. Finally, we present results from multiple

approaches that render more efficient the process of generating

plausible solutions to inverse modeling problems that use the

parameterized reduced order model.