To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods with solvers capable of handling arbitrary problems. In this work, a topology optimization method for general multiphysics problems is presented. We leverage a convolutional neural parameterization of a level set for a description of the geometry and use this in an unfitted finite element method that is differentiable with respect to the level set everywhere in the domain. We construct the parameter to objective map in such a way that the gradient can be computed entirely by automatic differentiation at roughly the cost of an objective function evaluation. The method produces optimized topologies that are similar in performance yet exhibit greater regularity than baseline approaches on standard benchmarks whilst having the ability to solve a more general class of problems, e.g., interface-coupled multiphysics.

翻译：为推动自动化工程设计技术的广泛应用，现有方法需进一步提升效率与泛化能力。在拓扑优化领域，这要求将现代优化方法与能够处理任意问题的求解器相结合。本文提出了一种适用于一般多物理场问题的拓扑优化方法。我们采用水平集的卷积神经参数化描述几何结构，并将其应用于非拟合有限元方法，该方法在计算域内对水平集处处可微。通过构建参数至目标映射，梯度可完全通过自动微分计算，其计算成本近似于一次目标函数评估。该方法在标准基准测试中产生的优化拓扑性能与基准方法相当，但具有更好的规则性，同时能够解决更一般的问题类别，例如界面耦合多物理场问题。