  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.
