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The layout optimization of the heat conduction is essential during design inengineering, especially for thermal sensible products. When the optimizationalgorithm iteratively evaluates different loading cases, the traditionalnumerical simulation methods used usually lead to a substantial computationalcost. To effectively reduce the computational effort, data-driven approachesare used to train a surrogate model as a mapping between the prescribedexternal loads and various geometry. However, the existing model are trained bydata-driven methods which requires intensive training samples that fromnumerical simulations and not really effectively solve the problem. Choosingthe steady heat conduction problems as examples, this paper proposes aPhysics-driven Convolutional Neural Networks (PD-CNN) method to infer thephysical field solutions for random varied loading cases. After that, theParticle Swarm Optimization (PSO) algorithm is used to optimize the sizes andthe positions of the hole masks in the prescribed design domain, and theaverage temperature value of the entire heat conduction field is minimized, andthe goal of minimizing heat transfer is achieved. Compared with the existingdata-driven approaches, the proposed PD-CNN optimization framework not onlypredict field solutions that are highly consistent with conventional simulationresults, but also generate the solution space with without any pre-obtainedtraining data.

Heat Conduction Plate Layout Optimization using Physics-driven Convolutional Neural Networks