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：为了促进自动化工程设计技术的广泛采用，现有方法必须变得更加高效和通用。在拓扑优化领域，这需要将现代优化方法与能够处理任意问题的求解器相结合。本文介绍了一种适用于一般多物理问题的拓扑优化方法。我们利用水平集的卷积神经参数化来描述几何形状，并将其用于非配对有限元方法中，该方法在整个域内都可以与水平集微分。我们以这种方式构建参数到目标的映射，以便梯度可以通过自动微分在大约一个目标函数评估的代价下进行计算。该方法产生的优化拓扑在标准基准测试中与基准方法相似性能，同时比基准方法更具规则性，并具有解决更一般类别问题的能力，例如，接口耦合多物理问题。