Accelerated topology optimization by means of deep learning
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RESEARCH PAPER
Accelerated topology optimization by means of deep learning Nikos Ath. Kallioras 1 & Georgios Kazakis 1 & Nikos D. Lagaros 1 Received: 13 February 2019 / Revised: 4 January 2020 / Accepted: 11 February 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study is focused on enhancing the computational efficiency of the solid isotropic material with penalization (SIMP) approach implemented for solving topology optimization problems. Solving such problems might become extremely timeconsuming; in this direction, machine learning (ML) and specifically deep neural computing are integrated in order to accelerate the optimization procedure. The capability of ML-based computational models to extract multiple levels of representation of nonlinear input data has been implemented successfully in various problems ranging from time series prediction to pattern recognition. The later one triggered the development of the methodology proposed in the current study that is based on deep belief networks (DBNs). More specifically, a DBN is calibrated on transforming the input data to a new higher-level representation. Input data contains the density fluctuation pattern of the finite element discretization provided by the initial steps of SIMP approach, and output data corresponds to the resulted density values distribution over the domain as obtained by SIMP. The representation capabilities and the computational advantages offered by the proposed DBN-based methodology coupled with the SIMP approach are investigated in several benchmark topology optimization test examples where it is observed more than one order of magnitude reduction on the iterations that were originally required by SIMP, while the advantages become more pronounced in case of large-scale problems. Keywords Topology optimization . Deep learning . Deep belief networks . Restricted Boltzmann machines . Pattern recognition . SIMP
1 Introduction Since the 1970s, structural optimization has been the topic of intensive scientific development and several methods for achieving improved structural designs have been advocated (Moses 1974; Gallagher and Zienklewicz 1973; Haug and Arora 1974; Sheu and Prager 1968; Spunt 1971); structural optimization matured from simple academic problems to becoming the core of contemporary design in case of extremely complicated structural systems (Lagaros 2018). Topology optimization represents a material distribution numerical
Responsible Editor: Felipe A. C. Viana * Nikos D. Lagaros [email protected]; [email protected]; [email protected] 1
Institute of Structural Analysis & Antiseismic Research, Department of Structural Engineering, School of Civil Engineering, National Technical University of Athens, 9, Heroon Polytechniou Str., Zografou Campus, GR-15780 Athens, Greece
procedure for synthesizing structural layouts without any preconceived form. Many approaches have been proposed so far, specially tailored for solving the topology optimization problem, where the most widely used ones
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