A hierarchical deep neural-network for long-term prediction of turbulent flow*

A hierarchical neural-network method is developed to stably predict the future of turbulent flow over long periods using recursive predictions. This method introduces a reconstruction network in addition to a base prediction network, aiming to restore turbulent fluctuations in the output fields of the prediction network. The reconstruction network is trained using a statistical loss function to match the statistical properties of turbulence. In tests with turbulent channel flow, the method accurately predicted instantaneous and mean flow fields over 15 flow-through times, whereas the base prediction model became unstable. Turbulent kinetic energy budget analysis revealed significant errors in kinetic energy dissipation and production rates near the wall in predictions without the reconstruction model. Conversely, the reconstruction network provided accurate predictions of these rates, ensuring stable long-term predictions. Additionally, the method was tested on predicting unsteady wake flow over a square cylinder, yielding flow fields in good agreement with large-eddy simulation results, while predictions without the reconstruction model diverged.