Chaotic systems are often computationally expensive to investigate due to the very high degrees of freedom required to perform direct numerical simulation (DNS), creating a bottleneck in the downstream analysis of these systems. Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions and limits the achievable drag reduction using polymer additives. DNS of EIT is highly computationally expensive due to the need to resolve the multiscale nature of the system. While DNS of two-dimensional EIT typically requires a million degrees of freedom, in this talk we will demonstrate that an accurate reduced order model of the dynamics can be constructed using machine learning, which captures its dynamics roughly a million times faster than the DNS. 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 are 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 statistics. This model can accelerate the downstream analysis such as the investigation of coherent structures underlying the dynamics and the design of control strategies to suppress EIT to reduce turbulent drag beyond the Maximum Drag Reduction (MDR) limit.
