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In this paper, based on neural networks, we develop a data-driven model forextremely fast prediction of steady-state heat convection of a hot object witharbitrary complex geometry in a two-dimensional space. According to thegoverning equations, the steady-state heat convection is dominated byconvection and thermal diffusion terms, thus the distribution of the physicalfields 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 thedecoder. Compared with fully connected (FC) network model, the CNN based modelis good for capturing and reconstructing the spatial relationships of low-rankfeature spaces, such as edge intersections, parallelism and symmetry.Furthermore, we applied the signed distance function (SDF) as the network inputfor representing the problem geometry, which contains more information comparedto a binary image. For displaying the strong learning and generalizationability of the proposed network model, the training dataset only contains hotobjects with simple geometries: triangles, quadrilaterals, pentagons, hexagonsand dodecagons; while the validating cases use arbitrary and complexgeometries. According to the study, the trained network model can accuratelypredict the velocity and temperature field of the problems with complexgeometries which has never been seen by the network model during the modeltraining; and the prediction speed is four orders faster than the CFD. Theability of the accurate and extremely faster prediction of the network modelsuggests the potentials of applying such kind of models to the applications ofreal-time control, optimization, and design in future.

Data-Driven Modeling of Geometry-Adaptive Steady Heat Transfer based on Convolutional Neural Networks: Heat Convection