Neural Level Set Topology Optimization Using Unfitted Finite Elements

Abstract: 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.