  In this paper, based on neural networks, we develop a data-driven model for
extremely fast prediction of steady-state heat convection of a hot object with
arbitrary complex geometry in a two-dimensional space. According to the
governing equations, the steady-state heat convection is dominated by
convection and thermal diffusion terms, thus the distribution of the physical
fields would exhibit stronger correlations between adjacent points. Therefore,
the proposed neural network model uses Convolutional Neural Network (CNN)
layers as the encoder and Deconvolutional Neural Network (DCNN) layers as the
decoder. Compared with fully connected (FC) network model, the CNN based model
is good for capturing and reconstructing the spatial relationships of low-rank
feature spaces, such as edge intersections, parallelism and symmetry.
Furthermore, we applied the signed distance function (SDF) as the network input
for representing the problem geometry, which contains more information compared
to a binary image. For displaying the strong learning and generalization
ability of the proposed network model, the training dataset only contains hot
objects with simple geometries: triangles, quadrilaterals, pentagons, hexagons
and dodecagons; while the validating cases use arbitrary and complex
geometries. According to the study, the trained network model can accurately
predict the velocity and temperature field of the problems with complex
geometries which has never been seen by the network model during the model
training; and the prediction speed is four orders faster than the CFD. The
ability of the accurate and extremely faster prediction of the network model
suggests the potentials of applying such kind of models to the applications of
real-time control, optimization, and design in future.
