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

Numerical simulation of steady-state heat conduction is common for thermal engineering. The simulation process usually involves mathematical formulation, numerical discretization and iteration of discretized ordinary or partial differential equations depending on complexity of problems. In current work, we develop a data-driven model for extremely fast prediction of steady-state heat conduction of a hot object with arbitrary geometry in a two-dimensional space. 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, in current approach the data-driven model is developed using convolution neural networks (CNNs), which is good at capturing local features (sub-invariant) thus can be treated as numerical discretization in some sense. Furthermore, in our model, a signed distance function (SDF) is proposed to represent the geometry of the problem, which contains more information compared to a binary image. For the training datasets, the hot objects are consisting of five simple geometries: triangles, quadrilaterals, pentagons, hexagons and dodecagons. All the geometries are different in size, shape, orientation and location. After training, the data-driven network model is able to accurately predict steady-state heat conduction of hot objects with complex geometries which has never been seen by the network model; and the prediction speed is three to four orders faster than numerical simulation. According to the outstanding performance of the network model, it is hoped that this approach can serve as a valuable tool for applications of engineering optimization and design in future.