The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and parametrizations. One of the key challenges of all these methods is the massive computational cost associated with 3D topology optimization problems.

We introduce a transfer learning method based on a convolutional neural network that (1) can handle high-resolution 3D design domains of various shapes and topologies; (2) supports real-time design space explorations as the domain and boundary conditions change; (3) requires a much smaller set of high-resolution examples for the improvement of learning in a new task compared to traditional deep learning networks; (4) is multiple orders of magnitude more efficient than the established gradient-based methods, such as SIMP. We provide numerous 2D and 3D examples to showcase the effectiveness and accuracy of our proposed approach, including for design domains that are unseen to our source network, as well as the generalization capabilities of the transfer learning-based approach. Our experiments achieved an average binary accuracy around 95% at real-time prediction rates. These properties, in turn, suggest that the proposed transfer-learning method may serve as the first practical underlying framework for real-time 3D design exploration based on topology optimization.

在过去的二十年中，有关拓扑优化的已出版文献激增，包括使用形状和拓扑导数的方法或基于各种几何表示和参数化制定的演化算法的方法。所有这些方法的主要挑战之一是与3D拓扑优化问题相关的大量计算成本。

我们介绍一种基于卷积神经网络的转移学习方法，该方法（1）可以处理各种形状和拓扑结构的高分辨率3D设计域；（2）支持随着域和边界条件的变化进行实时设计空间探索；（3）与传统的深度学习网络相比，需要更少的高分辨率示例集来改善新任务中的学习；（4）比已建立的基于梯度的方法（如SIMP）效率高多个数量级。我们提供了许多2D和3D实例，以展示我们提出的方法的有效性和准确性，包括看不见的设计领域到我们的源网络，以及基于迁移学习的方法的泛化功能。我们的实验在实时预测率下实现了约95％的平均二进制精度。这些特性反过来表明，所提出的转移学习方法可以用作基于拓扑优化的实时3D设计探索的第一个实用基础框架。