Linear and Nonlinear Latent-Space Reduced-Order Models for the Rayleigh--Taylor Instability
We use a large database of direct numerical simulations to investigate the transition of the Rayleigh--Taylor instability to turbulence and its evolution toward a late-time self-similar regime. In addition to tracking the growth of the mixing layer through the mean heavy-fluid concentration profile, we analyze one-dimensional profiles of turbulent kinetic energy and dissipation, two key quantities in classical turbulent-mixing models. We consider two reduced-order modeling strategies that differ in where nonlinearity is introduced: either in the construction of the latent space or in the description of its temporal evolution. The first method uses a linear encoder--decoder obtained using Proper Orthogonal Decomposition (POD), with nonlinear reduced dynamics learned by a physics-informed neural network (PINN). The second uses a nonlinear encoder--decoder learned by an autoencoder, while constraining the latent dynamics to remain linear and satisfy physical constraints. Both approaches achieve satisfactory performance in reconstructing, interpolating, and extrapolating the dynamics of the Rayleigh--Taylor instability.