Accelerating gradient-based topology optimization design with dual-model artificial neural networks
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RESEARCH PAPER
Accelerating gradient-based topology optimization design with dual-model artificial neural networks Chao Qian 1 & Wenjing Ye 1 Received: 2 June 2020 / Revised: 12 October 2020 / Accepted: 23 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Topology optimization (TO) is a common technique used in free-form designs. However, conventional TO-based design approaches suffer from high computational cost due to the need for repetitive forward calculations and/or sensitivity analysis, which are typically done using high-dimensional simulations such as finite element analysis (FEA). In this work, artificial neural networks are used as efficient surrogate models for forward and sensitivity calculations in order to greatly accelerate the design process of topology optimization. To improve the accuracy of sensitivity analyses, dual-model artificial neural networks that are trained with both forward and sensitivity data are constructed and are integrated into the Solid Isotropic Material with Penalization (SIMP) method to replace the FEA. The performance of the accelerated SIMP method is demonstrated on two benchmark design problems namely minimum compliance design and metamaterial design. The efficiency gained in the problem with size of 64 × 64 is 137 times in forward calculation and 74 times in sensitivity analysis. In addition, effective data generation methods suitable for TO designs are investigated and developed, which lead to a great saving in training time. In both benchmark design problems, a design accuracy of 95% can be achieved with only around 2000 training data. Keywords Topology optimization . SIMP . Deep learning . Artificial neural network . Structural and metamaterial design
1 Introduction Topology optimization is a mathematical technique commonly used in free-form designs. Since its invention (Bendsøe and Kikuchi 1988), various topology optimization (TO)–based design approaches have been developed (Jakiela et al. 2000; Wang et al. 2003; Juan et al. 2008; Schevenels et al. 2011; Guo et al. 2014; Zhang et al. 2017, 2019; Zhao et al. 2020) and applied to design a wide range of structures and products such as automobile and aircraft parts/components (Cavazzuti et al. 2011; Zhu et al. 2016). The advent in additive manufacturing technologies has further broadened the application scope of TO. Advanced materials such as phononic materials (Sigmund and Jensen 2003), various metamaterials (Diaz and Sigmund 2010; Matsumoto et al. 2011; Rong and Ye Responsible Editor: Yoojeong Noh * Wenjing Ye [email protected] 1
Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
2019) and artificial bone scaffolds and orthopedic implants (Wang et al. 2016) have been successfully designed using TO methods. However, almost all TO methods are cursed with the exorbitant computational cost. The major bottleneck in the TO process is the repetitive evaluation of the objective function, constraints, and/or s
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