Using Unfitted Finite Elements in Topology Optimization of Neural Surface Ensembles

Since the introduction of topology optimization in structural design, significant research has focused on improving the robustness and applicability of these automated design techniques to a wider range of problems. Achieving this goal in topology optimization necessitates the integration of advanced optimization strategies with numerical solvers that can accommodate complex and heterogeneous physics. In this study, we propose a topology optimization framework tailored for general Multiphysics applications. The geometry is represented through a convolutional neural network-based parameterization of a level set function, which is embedded within an unfitted finite element formulation that remains differentiable with respect to the level set across the entire computational domain. The mapping from design parameters to the objective function is constructed such that gradients are obtained exclusively via automatic differentiation, with a computational cost comparable to a single objective evaluation. Without relying on problem-specific initialization strategies, the proposed approach generates smooth and well-structured topologies that closely match optimal solutions for standard benchmark cases, while also extending naturally to more complex scenarios, including interface-coupled Multiphysics problems.