Topology Optimization via Machine Learning and Deep Learning A Review Seungyeon Shin1a Dongju Shin12a and Namwoo Kang12

2025-05-06 2 0 2.25MB 50 页 10玖币

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Topology Optimization via Machine Learning and Deep Learning:

A Review

Seungyeon Shin1,a, Dongju Shin1,2,a, and Namwoo Kang1,2,*

1 Cho Chun Shik Graduate School of Mobility,

Korea Advanced Institute of Science and Technology

2 Narnia Labs

*Corresponding author: nwkang@kaist.ac.kr

a Contributed equally to this work.

A previous version of this manuscript was presented at the 2021 World Congress on Advances in Structural

Engineering and Mechanics (ASEM21) (Seoul, Korea, August 23-26, 2021) (Shin et al., 2021)

Abstract

Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary

conditions within a design domain. This method enables effective design without initial design, but has been

limited in use due to high computational costs. At the same time, machine learning (ML) methodology including

deep learning has made great progress in the 21st century, and accordingly, many studies have been conducted to

enable effective and rapid optimization by applying ML to TO. Therefore, this study reviews and analyzes

previous research on ML-based TO (MLTO). Two different perspectives of MLTO are used to review studies:

(1) TO and (2) ML perspectives. The TO perspective addresses “why” to use ML for TO, while the ML perspective

addresses “how” to apply ML to TO. In addition, the limitations of current MLTO research and future research

directions are examined.

1. Introduction

Topology optimization (TO) is a field of design optimization that determines the optimal material layout under

certain constraints on loads and boundaries within a given design space. This method allows the optimal

distribution of materials with desired performance to be determined while meeting the design constraints of the

structure (Bendsøe, 1989). TO is meaningful in that, compared with conventional optimization approaches,

designing is possible without meaningful initial design. Due to these advantages, various TO methodologies have

been studied to date (Bendsøe, 1989; Rozvany et al., 1992; Mlejnek, 1992; Allaire et al., 2002; Wang et al., 2003;

Xie & Steven, 1993). The following four TO methodologies are described in detail in Appendix A: density-based

method (i.e., the solid isotropic material with penalization (SIMP) method), evolutionary structural optimization

(ESO) method, level-set method (LSM), and moving morphable component (MMC) method.

Recent TO methods aim to solve various industrial applications. Examples include TO for patient-specific

osteosynthesis plates (Park et al., 2021), microscale lattice parameter (i.e., the strut diameter) optimization for TO

(Cheng et al., 2019), homogenization of 3D TO with microscale lattices (Zhang et al., 2021b), and multiscale TO

for additive manufacturing (AM) (Kim et al., 2022). Other notable works for more complex TO problems include

a multilevel approach to large-scale TO accounting for linearized buckling criteria (Ferrari & Sigmund, 2020),

the localized parametric level-set method applying a B-spline interpolation method (Wu et al., 2020), the

systematic TO approach for simultaneously designing morphing functionality and actuation in three-dimensional

wing structures (Jensen et al., 2021), the parametrized level-set method combined with the MMA algorithm to

solve nonlinear heat conduction problems with regional temperature constraints (Zhuang et al., 2021b), and the

parametric level-set method for non-uniform mesh of fluid TO problems (Li et al., 2022).

However, although the aforementioned TO methodologies can produce good conceptual designs, one of the

main challenges in performing TO is its high computational cost. The overall cost of the computational scheme is

dominated by finite element analysis (FEA), which computes the sensitivity for each iteration of the optimization

process. The required FEA time increases as the mesh size increases (e.g., when the mesh size is increased by 125

times, the required time increases by 4,137 times (Liu & Tovar, 2014)). Amid this computational challenge,

performing TO for a fine (high-resolution) topological mesh can take a few hours to days (Rade et al., 2020).

Furthermore, the 3D TO process requires much higher computational costs with increasing demands in the order

SIMP, BESO, and level set method in terms of the number of iterations (Yago et al., 2022). Therefore, various

studies have aimed to reduce the computation of solving these analysis equations in TO (Amir et al., 2009; Amir

et al., 2010). For instance, by using an approximate approach to solve the nested analysis equation in the minimum

compliance TO problem, Amir and Sigmund (2011) reduced the computational cost by one order of magnitude

for an FE mesh with 40,500 elements.

Similarly, aiming to improve this computational challenge, various methods have been developed to accelerate

TO (e.g., Limkilde et al. (2018) discussed the computational complexity of TO, while Ferrari and Sigmund (2020)

conducted large-scale TO with reduced computational cost. Martínez-Frutos et al. (2017) performed efficient

computation using GPU, while Borrvall and Petersson (2001) and Aage et al. (2015) attempted to accelerate TO

by parallel computing. Despite the aforementioned efforts to reduce TO computing time, the computational costs

remain high. This challenge has encouraged several researchers to develop ML-based TO to accelerate TO.

Figure 1 Overview of AI, ML, and DL (Kaluarachchi et al., 2021)

Artificial intelligence (AI) includes any technology that allows machines to emulate human behavior, and

machine learning (ML) is a subset of AI, aimed at learning meaningful patterns from data by using statistical

methods (Figure 1). Deep learning (DL) is a subset of ML, inspired by the neuron structure of the human brain,

seeks to improve learning ability through methods of training hierarchical neural network (NN) structures

consisting of multiple layers from the data itself (LeCun et al., 2015; Goodfellow et al., 2016).

Data-based TO methodologies complement the problem of conventional TO methodologies with computational

cost problems due to design iterations over thousands of times, and many studies have been conducted to improve

TO algorithms through AI (Sosnovik & Oseledets, 2019; Oh et al., 2019; Banga et al., 2018, Guo et al., 2018;

Cang et al., 2019; Chandrasekhar & Suresh, 2021c). TO methods applying AI can quickly and effectively optimize

the initial topology. In this study, ML-based TO (MLTO) is expressed throughout studies that incorporate ML or

DL. In particular, we focus more on various methodologies by using DL.

This material intends to review various MLTO studies currently developed and analyze each characteristic.

Section 2 and Section 3 present the existing studies from a TO point of view and an ML point of view, respectively,

and analyzed the characteristics of the study. Section 2 groups and introduces studies focusing on the purpose,

i.e., “why” ML is applied to TO from a TO perspective. Section 3 groups and introduces studies focusing on the

ML method, i.e., “how” TO can be converted to ML problems from an ML perspective. In Section 4, the

limitations of MLTO studies and the desirable future directions of the field are presented. Appendixes A and B

introduce the fundamental background of TO and basic DL methodologies required to understand this study.

Figure 2 presents various analytical perspectives on MLTO to be described in Sections 2 and 3.

Figure 2 MLTO Review Framework

2. TO Perspective: Why Use ML

From the perspective of TO, studies that focus on ML/DL to improve the existing TO techniques have seven

main purposes: acceleration of iteration, non-iterative optimization, meta-modeling, dimensionality reduction of

design space, improvement of optimizer, generative design (design exploration), and postprocessing. Each

purpose is shown in Figure 3, and the studies corresponding to each purpose are organized in Table 1.

Figure 3 Visualization of the methodology by MLTO purpose

Table 1 Classification of relevant studies by MLTO purpose

Purpose of MLTO

in TO perspective

Corresponding Research

Acceleration of

Iteration

Banga et al., 2018; Lin et al., 2018; Sosnovik & Oseledets, 2019; Bi et al., 2020; Kallioras

et al., 2020; Kallioras & Lagaros, 2021a

Non-Iterative

Optimization

Rawat & Shen, 2018; Cang et al., 2019; Li et al., 2019a; Rawat & Shen, 2019a; Rawat &

Shen, 2019b; Sharpe & Seepersad, 2019; Yu et al., 2019; Zhang et al., 2019; Abueidda et al.,

2020; Almasri et al., 2020; Kollmann et al., 2020; Rade et al., 2020; Keshavarzzadeh et al.,

2021; Nie et al., 2021; Lew & Buehler, 2021; Qiu et al., 2021a

Meta-Modeling

Patel & Choi, 2012; Aulig & Olhofer, 2014; Xia et al., 2017; Zhou & Saitou, 2017; Doi et

al., 2019; Li et al., 2019b; Sasaki & Igarashi, 2019a; Sasaki & Igarashi, 2019b; Takahashi et

al., 2019; White et al., 2019; Asanuma et al., 2020; Deng et al., 2020; Keshavarzzadeh et al.,

2020; Lee et al., 2020; Chi et al., 2021; Kim et al., 2021; Qian & Ye, 2021; Zheng et al., 2021

Dimensionality

Reduction

of Design Space

Ulu et al., 2016; Guo et al., 2018; Li et al., 2019c

Improvement of

Optimizer

Bujny et al., 2018; Hoyer et al., 2019; Lei et al., 2019; Lynch et al., 2019; Deng & To, 2020;

Jiang et al., 2020; Chandrasekhar & Suresh, 2021a; Chandrasekhar & Suresh, 2021b;

Chandrasekhar & Suresh, 2021c; Halle et al., 2021; Zehnder et al., 2021; Zhang et al., 2021a

Generative Design

Oh et al., 2018; Gillhofer et al., 2019; Jiang & Fan, 2019a; Jiang & Fan, 2019b; Jiang et al.,

2019; Oh et al., 2019; Shen & Chen, 2019; Wen et al., 2019; Greminger, 2020; Ha et al., 2020;

Kallioras & Lagaros, 2020; Malviya, 2020; Sun & Ma, 2020; Wang et al., 2020; Wen et al.,

2020; Blanchard-Dionne & Martin, 2021; Kallioras & Lagaros, 2021b; Kudyshev et al., 2021;

Li et al., 2021; Sim et al., 2021; Yamasaki et al., 2021; Jang et al., 2022

Postprocessing

Yildiz et al., 2003; Chu et al., 2016; Strömberg, 2019; Karlsson et al., 2020; Napier et al.,

2020; Strömberg, 2020; Wang et al., 2021; Xue et al., 2021

Others

Liu et al., 2015; Gaymann & Montomoli, 2019; Hayashi & Ohsaki, 2020; Kumar & Suresh,

2020; Qiu et al., 2021b; Brown et al., 2022

2.1. Acceleration of Iteration

The optimization process of iterative TO can be divided into two stages: the early stage, in which the design

change is significant, and the latter stage, in which the design changes slowly until it converges. Studies applying

ML techniques supplement the latter step of the optimization process, which is especially time-consuming. Thus,

studies that aim at accelerating iterative TO consist of two stages as follows:

(1) Until the intermediate stage of the iteration, the iterative TO is performed.

(2) In the intermediate stage, the optimal topology can be directly predicted by ML by using the intermediate

topology obtained from (1).

This process can accelerate the time-consuming and costly latter stage in the conventional optimization process.

Figure 4 Architecture of acceleration of iterative optimization from a representative paper

(Sosnovik & Oseledets, 2019)

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TopologyOptimizationviaMachineLearningandDeepLearning:AReviewSeungyeonShin1,a,DongjuShin1,2,a,andNamwooKang1,2,*1ChoChunShikGraduateSchoolofMobility,KoreaAdvancedInstituteofScienceandTechnology2NarniaLabs*Correspondingauthor:nwkang@kaist.ac.kraContributedequallytothiswork.Apreviousversionofthismanus...

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Topology Optimization via Machine Learning and Deep Learning A Review Seungyeon Shin1a Dongju Shin12a and Namwoo Kang12

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