TOuNN: Topology Optimization using Neural Networks
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RESEARCH PAPER
TOuNN: Topology Optimization using Neural Networks Aaditya Chandrasekhar1 · Krishnan Suresh1 Received: 25 April 2020 / Revised: 26 August 2020 / Accepted: 18 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Neural networks, and more broadly, machine learning techniques, have been recently exploited to accelerate topology optimization through data-driven training and image processing. In this paper, we demonstrate that one can directly execute topology optimization (TO) using neural networks (NN). The primary concept is to use the NN’s activation functions to represent the popular Solid Isotropic Material with Penalization (SIMP) density field. In other words, the density function is parameterized by the weights and bias associated with the NN, and spanned by NN’s activation functions; the density representation is thus independent of the finite element mesh. Then, by relying on the NN’s built-in backpropogation, and a conventional finite element solver, the density field is optimized. Methods to impose design and manufacturing constraints within the proposed framework are described and illustrated. A byproduct of representing the density field via activation functions is that it leads to a crisp and differentiable boundary. The proposed framework is simple to implement and is illustrated through 2D and 3D examples. Some of the unresolved challenges with the proposed framework are also summarized. Keywords Neural networks · Machine learning · Topology optimization
1 Introduction Topology optimization (TO) is now a well-established field encompassing numerous methods including Solid Isotropic Material with Penalization (SIMP)-based optimization (Bendsoe and Sigmund 2003; Bendsoe et al. 2008; Sigmund 2001; Chandrasekhar et al. 2020), level set methods (Wang et al. 2003), evolutionary methods (Xie and Steven 1993) and topological sensitivity methods (Suresh 2013; Deng and Suresh 2015; Mirzendehdel et al. 2018; Mirzendehdel and Suresh 2015a). The variety of TO methods not only has added richness to the field but also offers design engineers several TO options to choose from. The objective of this paper is to explore yet another TO method that differs from the above established methods in its construction. The proposed method relies on the
Responsible Editor: Somanath Nagendra Krishnan Suresh
[email protected] 1
Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, USA
popular Solid Isotropic Material with Penalization (SIMP) mathematical formulation, but uses a neural network’s activation functions (Gurney 1997) to represent the SIMP density. In other words, the density function is parameterized by the weights and bias associated with the NN, and spanned by NN’s activation functions; the density representation is thus independent of the finite element mesh. While prior works (see Section 2) have used neural networks (NN) to accelerate topology optimization, the objective here is to directly execute topology optimization using NN. The pr
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