  The layout optimization of the heat conduction is essential during design in
engineering, especially for thermal sensible products. When the optimization
algorithm iteratively evaluates different loading cases, the traditional
numerical simulation methods used usually lead to a substantial computational
cost. To effectively reduce the computational effort, data-driven approaches
are used to train a surrogate model as a mapping between the prescribed
external loads and various geometry. However, the existing model are trained by
data-driven methods which requires intensive training samples that from
numerical simulations and not really effectively solve the problem. Choosing
the steady heat conduction problems as examples, this paper proposes a
Physics-driven Convolutional Neural Networks (PD-CNN) method to infer the
physical field solutions for random varied loading cases. After that, the
Particle Swarm Optimization (PSO) algorithm is used to optimize the sizes and
the positions of the hole masks in the prescribed design domain, and the
average temperature value of the entire heat conduction field is minimized, and
the goal of minimizing heat transfer is achieved. Compared with the existing
data-driven approaches, the proposed PD-CNN optimization framework not only
predict field solutions that are highly consistent with conventional simulation
results, but also generate the solution space with without any pre-obtained
training data.
