NTopo: Mesh-free Topology Optimization using Implicit Neural Representations
This addresses topology optimization problems in engineering design by offering a mesh-free approach, though it appears incremental as it builds on existing neural representation techniques.
The paper tackled topology optimization, an inverse problem with high-dimensional parameters, by using implicit neural representations to parameterize density and displacement fields in a mesh-free manner, resulting in a method that is highly competitive for minimizing structural compliance and enables self-supervised learning of continuous solution spaces.
Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization -- an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural representations in the context of mesh-free topology optimization, we use multilayer perceptrons to parameterize both density and displacement fields. Our experiments indicate that our method is highly competitive for minimizing structural compliance objectives, and it enables self-supervised learning of continuous solution spaces for topology optimization problems.