Reconstruction of natural convection within an enclosure using deep neural network

Abstract

The deep neural network (DNN) is an extensively used technique to fit the high dimensional data. Fluid flow and heat transfer in macroscale are one of the complex physical phenomena which are governed by the Navier-Stokes (N-S) equation. The conventional numerical method (e.g., finite difference method) can solve the equation with corresponding boundary conditions using kinds of spatial discretized methods. In the present paper, the deep neural network can also be used to train and compute the results even if the training data only comes from boundary conditions of velocities and temperature. For the natural convection with few computational fluid dynamics (CFD) based velocities and temperature, the loss function of deep neural network, which mixes the explicit constraint of N-S equation, can reconstruct the fluid and heat field accurately. Usually, the complex geometry or high Rayleigh (Ra) number are corresponding to the complicate distribution of velocities and temperature field, which need more training points to achieve impressive accuracy. The present paper comprehensively investigates reconstructing results with different training data when Ra=103, and finds that only 1.48% points of CFD based data can obtain the impressive conclusion. Besides, the attempt of predicting velocities and temperature of the whole domain from partial region training data has been conducted. Global relative errors of velocities and temperature of Ra=105converge to the value, which is a little larger thanRa=104, although the latter case possesses more training points. When increasing the Rayleigh number to 106, the reconstruction of unsteady natural convection still remains high accuracy even if only 10 snapshots are considered. For the reconstruction of natural convection with complex geometry, the results show that more training points should be fed into the deep neural network to train and learn accurate results.