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：为促进自动化工程设计技术的广泛采用，现有方法需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处理任意问题的求解器相结合。本文提出了一种面向多物理场问题的通用拓扑优化方法。我们利用水平集的卷积神经参数化描述几何形态，并将其应用于非拟合有限元法中——该方法在定义域内任意位置均可对水平集进行微分。通过构建参数到目标的映射关系，梯度可完全通过自动微分计算，计算成本与目标函数评估相当。该方法生成的优化拓扑在标准基准测试中性能与基线方法相近，但具有更强的规则性，同时能够解决更广义的问题类别（例如界面耦合多物理场问题）。