NTopo: Mesh-free Topology Optimization using Implicit Neural Representations

Jonas Zehnder, Yue Li, Stelian Coros, Bernhard Thomaszewski

Keywords: implicit representations, topology optimization, bilevel optimization, multilayer perceptrons, mesh-free

Abstract: 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.

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TL;DR: We present a mesh-free topology optimization method using implicit neural representations, that also applies to learning solution spaces.

Code: https://github.com/JonasZehn/ntopo/