Neural Level Set Topology Optimization Using Unfitted Finite Elements

Abstract

To facilitate the 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. Without handcrafted initializations, the method produces regular topologies close to the optimal solution for standard benchmark problems whilst maintaining the ability to solve a more general class of problems than standard methods, for example, interface-coupled multiphysics.