Elastoinertial turbulence: data-driven reduced-order model based on manifold dynamics

Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensive due to the need to resolve the multiscale nature of the system. While DNS of two-dimensional (2-D) EIT typically requires $O(10^6)$ degrees of freedom, we demonstrate here that a data-driven modelling framework allows for the construction of an accurate model with 50 degrees of freedom. We achieve a low-dimensional representation of the full state by first applying a viscoelastic variant of proper orthogonal decomposition to DNS results, and then using an autoencoder. The dynamics of this low-dimensional representation is learned using the neural ordinary differential equation (NODE) method, which approximates the vector field for the reduced dynamics as a neural network. The resulting low-dimensional data-driven model effectively captures short-time dynamics over the span of one correlation time, as well as long-time dynamics, particularly the self-similar, nested travelling wave structure of 2-D EIT in the parameter range considered.