Choosing the steady heat conduction problems as examples, this paper proposes a physics-driven convolutional neural networks (PD-CNNs) method to infer the physical field solutions for randomly varied loading cases. However, the existing model is trained by data-driven methods, which require intensive training samples from numerical simulations and do not effectively solve the problem. 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, when the optimization algorithm iteratively evaluates different loading cases, the traditional numerical simulation methods usually lead to a substantial computational cost. Optimizing heat conduction layout is essential during engineering design, especially for sensible thermal products.
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