Multi-scale Topology Optimization using Neural Networks
Hongrui Chen Xingchen Liu Levent Burak Kara
A long-standing challenge is designing multi-scale structures with good
connectivity between cells while optimizing each cell to reach close to the
theoretical performance limit. We propose a new method for direct multi-scale
topology optimization using neural networks. Our approach focuses on inverse
homogenization that seamlessly maintains compatibility across neighboring
microstructure cells. Our approach consists of a topology neural network that
optimizes the microstructure shape and distribution across the design domain as
a continuous field. Each microstructure cell is optimized based on a specified
elasticity tensor that also accommodates in-plane rotations. The neural network
takes as input the local coordinates within a cell to represent the density
distribution within a cell, as well as the global coordinates of each cell to
design spatially varying microstructure cells. As such, our approach models an
n-dimensional multi-scale optimization problem as a 2n-dimensional inverse
homogenization problem using neural networks. During the inverse homogenization
of each unit cell, we extend the boundary of each cell by scaling the input
coordinates such that the boundaries of neighboring cells are combined. Inverse
homogenization on the combined cell improves connectivity. We demonstrate our
method through the design and optimization of graded multi-scale structures.