Multi-Material Topology Optimization Using Neural Networks

The focus of this paper is on multi-material topology optimization (MMTO), where the objective is to not only compute the optimal topology, but also the distribution of two or more materials within the topology. In the popular density-based MMTO, the underlying pseudo-density fields are typically represented using an underlying mesh. While mesh-based MMTO ties in well with mesh-based finite element analysis, there are inherent challenges, namely the extraction of thin features, and the computation of the gradients of the density fields. The objective of this paper is to present a neural network (NN) based MMTO method where the density fields are represented in a mesh-independent manner, using the NN's activation functions, with the weights and biases associated with the NN serving as the design variables. Then, by relying on the NN's built-in optimization routines, and a conventional finite element solver, the MMTO problem is solved. The salient features of the proposed method include: (1) thin features can be extracted through a simple post-processing step, (2) gradients and sensitivities can be computed accurately through back-propagation, (3) the NN construction implicitly guarantees the partition of unity between constituent materials, (4) the NN designs often exhibit better performance than mesh-based designs, and (5) the number of design variables is relatively small. Finally, the proposed framework is simple to implement, and is illustrated through several examples. (C) 2021 Elsevier Ltd. All rights reserved.