VoroTO: Multiscale Topology Optimization of Voronoi Structures using Surrogate Neural Networks

TL;DR

The paper tackles the high computational cost of multiscale topology optimization for Voronoi-based porous structures by introducing an offline-trained neural-network surrogate that maps Voronoi microstructure parameters (site locations, thickness, anisotropy, orientation) to homogenized elastic properties, ensuring positive definiteness via Cholesky factors. This surrogate enables an end-to-end differentiable, multi-scale optimization framework that promotes macroscale connectivity through parameter smoothing. The authors demonstrate substantial computational savings and maintain accuracy (less than ~10% error in key metrics) on tensile-bar and mid-cantilever benchmarks, showing the method can outperform brute-force fine-scale approaches. The work expands the design space with anisotropic Voronoi cells, validates the approach with real multiscale tests, and suggests promising future directions for 3D extensions and bone-inspired multifunctional materials.

Abstract

Cellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. Many of these structures are Voronoi-like; therefore researchers have proposed Voronoi multi-scale designs for a wide variety of engineering applications. However, designing such structures can be computationally prohibitive due to the multi-scale nature of the underlying analysis and optimization. In this work, we propose the use of a neural network (NN) to carry out efficient topology optimization (TO) of multi-scale Voronoi structures. The NN is first trained using Voronoi parameters (cell site locations, thickness, orientation, and anisotropy) to predict the homogenized constitutive properties. This network is then integrated into a conventional TO framework to minimize structural compliance subject to a volume constraint. Special considerations are given for ensuring positive definiteness of the constitutive matrix and promoting macroscale connectivity. Several numerical examples are provided to showcase the proposed method.

Figures (20)

• Figure 1: Graphical abstract: Offline computation: Given a dataset containing Voronoi microstructure parameters and homogenized constitutive properties, a neural network is trained offline. Multiscale TO: The trained network is used as a surrogate during topology optimization to derive optimized Voronoi structures.
• Figure 2: Heel bone and loading conditions.
• Figure 3: (a) Topology optimization problem. (b) Single scale design. (c) A multiscale porous design.
• Figure 4: Voronoi diagram defined by a set of sites (points). The shape of cell ($\bigstar$) is influenced by its immediate neighbors ($\mathbin{\vcenter{\hbox{$\m@th\bullet$}}}$).
• Figure 5: A typical density field defining a Voronoi structure.