Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network
This work addresses the problem of accurate and efficient turbulent flow modeling for fluid dynamics researchers, offering a novel hybrid method that is incremental in combining existing techniques.
The paper tackles the challenge of predicting chaotic spatiotemporal turbulent flows by proposing a reduced-order model that combines a convolutional autoencoder for spatial decomposition and an echo state network for temporal prediction, achieving a latent representation with less than 1% of the degrees of freedom and computational time compared to solving governing equations.
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state for a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live (i.e., it is a numerical approximation of the turbulent attractor). The latent space is found by a series of nonlinear filtering operations, which are performed by a convolutional autoencoder (CAE). The CAE provides the decomposition in space. Second, we predict the time evolution of the turbulent state in the latent space, which is performed by an echo state network (ESN). The ESN provides the decomposition in time. Third, by assembling the CAE and the ESN, we obtain an autonomous dynamical system: the convolutional autoncoder echo state network (CAE-ESN). This is the reduced-order model of the turbulent flow. We test the CAE-ESN on a two-dimensional flow. We show that, after training, the CAE-ESN (i) finds a latent-space representation of the turbulent flow that has less than 1% of the degrees of freedom than the physical space; (ii) time-accurately and statistically predicts the flow in both quasiperiodic and turbulent regimes; (iii) is robust for different flow regimes (Reynolds numbers); and (iv) takes less than 1% of computational time to predict the turbulent flow than solving the governing equations. This work opens up new possibilities for nonlinear decompositions and reduced-order modelling of turbulent flows from data.