Data-driven modeling of geometry-adaptive steady heat conduction based on convolutional neural networks

Abstract A data-driven model for rapid prediction of the steady-state heat conduction of a hot object with arbitrary geometry is developed. Mathematically, the steady-state heat conduction can be described by the Laplace's equation, where a heat (spatial) diffusion term dominates the governing equation. As the intensity of the heat diffusion only depends on the gradient of the temperature field, the temperature distribution of the steady-state heat conduction displays strong features of locality. Therefore, a convolution neural network-based data-driven model is proposed, which is good at capturing local features (sub-invariant) thus can be treated as numerical discretization in some sense. Furthermore, a signed distance function (SDF) is proposed to represent the geometry of the problem, which contains more information than the binary image. The hot objects in the training datasets are composed of simple geometries, the geometry is different in size, shape, orientation, and location. After training, the data-driven model can accurately predict steady-state heat conduction of hot objects with complex geometries which have never been seen by the network; and the prediction speed is more than one order faster than numerical simulation. The outstanding performance of the network model indicates the potential of the approach for applications of engineering optimization and design in future.