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Abstract

Multilayer perceptron (MLP) and convolutional neural network (CNN) encounter a critical scalability issue when applied to the performance evaluation task for frame structure designs. Specifically, a model of MLP or CNN is limited to structures of a particular topology type and fails immediately when applied to other topology types. In order to tackle this challenge, we propose a scalable performance evaluation method (called FrameGraph) for frame structure designs using graph neural network (GNN), offering applicability to a wide range of topology types simultaneously. FrameGraph consists of two main parts: (1) Components and their connections in a frame structure are denoted as edges and vertices in a graph, respectively. Subsequently, a graph dataset for frame structure designs with different topologies is constructed. (2) A well-defined GNN design space is established with a general GNN layer, and a controlled random search approach is employed to derive the optimal GNN model for this performance evaluation task. In numerical experiments of car door frames and car body frames, FrameGraph achieved the highest prediction precisions (96.28% and 97.87%) across all structural topologies compared to a series of classical GNN algorithms. Furthermore, the comparison with MLP and FEM highlighted FrameGraph's significant efficiency advantage. This verifies the feasibility and optimality of FrameGraph for the performance evaluation task of frame structures with different topologies.

References

1.
Silver
,
D.
,
Huang
,
A.
,
Maddison
,
C. J.
,
Guez
,
A.
,
Sifre
,
L.
,
Van Den Driessche
,
G.
,
Schrittwieser
,
J.
,
Antonoglou
,
I.
, et al
,
2016
, “
Mastering the Game of Go With Deep Neural Networks and Tree Search
,”
Nature
,
529
(
7587
), pp.
484
489
.
2.
Mnih
,
V.
,
Kavukcuoglu
,
K.
,
Silver
,
D.
,
Rusu
,
A. A.
,
Veness
,
J.
,
Bellemare
,
M. G.
,
Graves
,
A.
, et al
,
2015
, “
Human-Level Control Through Deep Reinforcement Learning
,”
Nature
,
518
(
7540
), pp.
529
533
.
3.
Brown
,
N.
, and
Sandholm
,
T.
,
2018
, “
Superhuman Ai for Heads-Up No-Limit Poker: Libratus Beats Top Professionals
,”
Science
,
359
(
6374
), pp.
418
424
.
4.
Raina
,
A.
,
McComb
,
C.
, and
Cagan
,
J.
,
2019
, “
Learning to Design From Humans: Imitating Human Designers Through Deep Learning
,”
ASME J. Mech. Des.
,
141
(
11
), p.
111102
.
5.
Shu
,
D.
,
Cunningham
,
J.
,
Stump
,
G.
,
Miller
,
S. W.
,
Yukish
,
M. A.
,
Simpson
,
T. W.
, and
Tucker
,
C. S.
,
2020
, “
3D Design Using Generative Adversarial Networks and Physics-Based Validation
,”
ASME J. Mech. Des.
,
142
(
7
), p.
071701
.
6.
Zhao
,
P.
,
Liao
,
W.
,
Huang
,
Y.
, and
Lu
,
X.
,
2023
, “
Intelligent Beam Layout Design for Frame Structure Based On Graph Neural Networks
,”
J. Build. Eng.
,
2022
(
63
), p.
105499
.
7.
Asteris
,
P. G.
,
Tsaris
,
A. K.
,
Cavaleri
,
L.
,
Repapis
,
C. C.
,
Papalou
,
A.
,
Di Trapani
,
F.
, and
Karypidis
,
D. F.
,
2016
, “
Prediction of the Fundamental Period of Infilled Rc Frame Structures Using Artificial Neural Networks
,”
Comput. Intell. Neurosci.
,
2016
(
12
), p.
5104907
.
8.
Torky
,
A. A.
, and
Ohno
,
S.
,
2021
, “
Deep Learning Techniques for Predicting Nonlinear Multi-Component Seismic Responses of Structural Buildings
,”
Comput. Struct.
,
252
, p.
106570
.
9.
Aksöz
,
Z.
, and
Preisinger
,
C.
,
2020
, “An Interactive Structural Optimization of Space Frame Structures Using Machine Learning,”
Impact: Design With All Senses. DMSB 2019
,
C.
Gengnagel
,
O.
Baverel
,
J.
Burry
,
M.
Ramsgaard Thomsen
, and
S.
Weinzierl
, eds.,
Springer
,
Cham
, pp.
18
31
.
10.
Song
,
L. H.
,
Wang
,
C.
,
Fan
,
J. S.
, and
Lu
,
H. M.
,
2023
, “
Elastic Structural Analysis Based On Graph Neural Network Without Labeled Data
,”
Comput.-Aided Civ. Infrastruct. Eng.
,
38
(
10
), pp.
1307
1323
.
11.
You
,
J.
,
Ying
,
Z.
, and
Leskovec
,
J.
,
2020
, “
Design Space for Graph Neural Networks
,”
Adv. Neural Inf. Process. Syst.
,
33
, pp.
17009
17021
.
12.
Bathe
,
K.
,
2006
,
Finite Element Procedures
,
Prentice Hall, Pearson Education, Inc
,
Cambridge, MA
.
13.
Huebner
,
K. H.
,
Dewhirst
,
D. L.
,
Smith
,
D. E.
, and
Byrom
,
T. G.
,
2001
,
The Finite Element Method for Engineers
,
John Wiley & Sons
,
New York
.
14.
Hutton
,
D. V.
,
2004
,
Fundamentals of Finite Element Analysis
,
The McGraw Hill Companies
,
Boston, MA
.
15.
Hou
,
W.
,
Shan
,
C.
,
Yu
,
Y.
,
Hu
,
P.
, and
Zhang
,
H.
,
2017
, “
Modular Platform Optimization in Conceptual Vehicle Body Design Via Modified Graph-Based Decomposition Algorithm and Cost-Based Priority Method
,”
Struct. Multidiscip. Optim.
,
55
(
6
), pp.
2087
2097
.
16.
Oishi
,
A.
, and
Yagawa
,
G.
,
2017
, “
Computational Mechanics Enhanced by Deep Learning
,”
Comput. Meth. Appl. Mech. Eng.
,
327
, pp.
327
351
.
17.
Liang
,
L.
,
Liu
,
M.
,
Martin
,
C.
, and
Sun
,
W.
,
2018
, “
A Deep Learning Approach to Estimate Stress Distribution: A Fast and Accurate Surrogate of Finite-Element Analysis
,”
J. R. Soc. Interface
,
15
(
138
), p.
20170844
.
18.
Raissi
,
M.
,
Perdikaris
,
P.
, and
Karniadakis
,
G. E.
,
2019
, “
Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations
,”
J. Comput. Phys.
,
378
, pp.
686
707
.
19.
Mohan
,
A. T.
, and
Gaitonde
,
D. V.
,
2018
, “
A Deep Learning Based Approach to Reduced Order Modeling for Turbulent Flow Control Using Lstm Neural Networks
,” arxiv.org.
20.
Mallela
,
U. K.
, and
Upadhyay
,
A.
,
2016
, “
Buckling Load Prediction of Laminated Composite Stiffened Panels Subjected to In-Plane Shear Using Artificial Neural Networks
,”
Thin Walled Struct.
,
102
, pp.
158
164
.
21.
Capuano
,
G.
, and
Rimoli
,
J. J.
,
2019
, “
Smart Finite Elements: A Novel Machine Learning Application
,”
Comput. Meth. Appl. Mech. Eng.
,
345
, pp.
363
381
.
22.
Ibragimova
,
O.
,
Brahme
,
A.
,
Muhammad
,
W.
,
Connolly
,
D.
,
Lévesque
,
J.
, and
Inal
,
K.
,
2022
, “
A Convolutional Neural Network Based Crystal Plasticity Finite Element Framework to Predict Localised Deformation in Metals
,”
Int. J. Plast.
,
157
, p.
103374
.
23.
Veličković
,
P.
,
Cucurull
,
G.
,
Casanova
,
A.
,
Romero
,
A.
,
Lio
,
P.
, and
Bengio
,
Y.
,
2017
, “
Graph Attention Networks
,”
In Proc. 6th International Conference on Learning Representations, ICLR 2018
,
Vancouver, BC, Canada
,
Apr. 30–May 3
.
24.
Kipf
,
T. N.
, and
Welling
,
M.
,
2016
, “
Semi-Supervised Classification with Graph Convolutional Networks
,”
Proceedings of the 5th International Conference on Learning Representations
,
Toulon, France
.
25.
Hamilton
,
W.
,
Ying
,
Z.
, and
Leskovec
,
J.
,
2017
, “
Inductive Representation Learning On Large Graphs
,”
Adv. Neural Inf. Process. Syst.
,
30
, pp.
1025
1035
.
26.
Xu
,
K.
,
Hu
,
W.
,
Leskovec
,
J.
, and
Jegelka
,
S.
,
2018
, “
How Powerful Are Graph Neural Networks?
,” Arxiv Preprint Arxiv:1810.00826.
27.
Daigavane
,
A.
,
Ravindran
,
B.
, and
Aggarwal
,
G.
,
2021
, “
Understanding Convolutions On Graphs
,”
Distill
. https://distill.pub/2021/understanding-gnns
28.
Stokes
,
J. M.
,
Yang
,
K.
,
Swanson
,
K.
,
Jin
,
W.
,
Cubillos-Ruiz
,
A.
,
Donghia
,
N. M.
,
MacNair
,
C. R.
, et al
,
2020
, “
A Deep Learning Approach to Antibiotic Discovery
,”
Cell
,
180
(
4
), pp.
688
702
.
29.
Sanchez-Gonzalez
,
A.
,
Godwin
,
J.
,
Pfaff
,
T.
,
Ying
,
R.
,
Leskovec
,
J.
, and
Battaglia
,
P.
,
2020
, “
Learning to Simulate Complex Physics With Graph Networks
,”
Proceedings of the 37th International Conference on Machine Learning
,
Online
,
July 13–18
, pp.
8459
8468
.
30.
Jiang
,
W.
, and
Luo
,
J.
,
2022
, “
Graph Neural Network for Traffic Forecasting: A Survey
,”
Expert Syst. Appl.
,
207
, p.
117921
.
31.
Eksombatchai
,
C.
,
Jindal
,
P.
,
Liu
,
J. Z.
,
Liu
,
Y.
,
Sharma
,
R.
,
Sugnet
,
C.
,
Ulrich
,
M.
, and
Leskovec
,
J.
,
2018
, “
Pixie: A System for Recommending 3+ Billion Items to 200+ Million Users in Real-Time
,”
Proceedings of the 2018 World Wide Web Conference
,
Lyon, France
,
Apr. 23–28
, pp.
1775
1784
.
32.
Wu
,
Z.
,
Pan
,
S.
,
Chen
,
F.
,
Long
,
G.
,
Zhang
,
C.
, and
Yu
,
P. S.
,
2021
, “
A Comprehensive Survey On Graph Neural Networks
,”
IEEE Trans. Neural Netw. Learn. Syst.
,
32
(
1
), pp.
4
24
.
33.
Ju
,
W.
,
Fang
,
Z.
,
Gu
,
Y.
,
Liu
,
Z.
,
Long
,
Q.
,
Qiao
,
Z.
,
Qin
,
Y.
,
Shen
,
J.
,
Sun
,
F.
, and
Xiao
,
Z.
,
2023
, “
A Comprehensive Survey On Deep Graph Representation Learning
,” arxiv preprint arxiv:2304.05055.
34.
Zhou
,
J.
,
Cui
,
G.
,
Hu
,
S.
,
Zhang
,
Z.
,
Yang
,
C.
,
Liu
,
Z.
,
Wang
,
L.
,
Li
,
C.
, and
Sun
,
M.
,
2020
, “
Graph Neural Networks: A Review of Methods and Applications
,”
Ai Open
,
1
, pp.
57
81
.
35.
Zhao
,
P.
,
Liao
,
W.
,
Huang
,
Y.
, and
Lu
,
X.
,
2023
, “
Intelligent Design of Shear Wall Layout Based On Graph Neural Networks
,”
Adv. Eng. Inform.
,
55
, p.
101886
.
36.
Li
,
M.
,
Liu
,
Y.
,
Wong
,
B. C. L.
,
Gan
,
V. J. L.
, and
Cheng
,
J. C. P.
,
2023
, “
Automated Structural Design Optimization of Steel Reinforcement Using Graph Neural Network and Exploratory Genetic Algorithms
,”
Autom. Constr.
,
146
, p.
104677
.
37.
Fogelson
,
M. B.
,
Tucker
,
C.
, and
Cagan
,
J.
,
2023
, “
GCP-HOLO: Generating High-Order Linkage Graphs for Path Synthesis
,”
ASME J. Mech. Des.
,
145
(
7
), p.
073303
.
38.
Xiao
,
Y.
,
Ahmed
,
F.
, and
Sha
,
Z.
,
2023
, “
Graph Neural Network-Based Design Decision Support for Shared Mobility Systems
,”
ASME J. Mech. Des.
,
145
(
9
), p.
091703
.
39.
Ferrero
,
V.
,
DuPont
,
B.
,
Hassani
,
K.
, and
Grandi
,
D.
,
2022
, “
Classifying Component Function in Product Assemblies With Graph Neural Networks
,”
ASME J. Mech. Des.
,
144
(
2
), p.
021406
.
40.
Heyrani Nobari
,
A.
,
Rey
,
J.
,
Kodali
,
S.
,
Jones
,
M.
, and
Ahmed
,
F.
,
2024
, “
Meshpointnet: 3D Surface Classification Using Graph Neural Networks and Conformal Predictions On Mesh-Based Representations
,”
ASME J. Mech. Des.
,
146
(
5
), p.
051712
.
41.
Whalen
,
E.
, and
Mueller
,
C.
,
2022
, “
Toward Reusable Surrogate Models: Graph-Based Transfer Learning On Trusses
,”
ASME J. Mech. Des.
,
144
(
2
), p.
021704
.
42.
Brandstetter
,
J.
,
Worrall
,
D.
, and
Welling
,
M.
,
2022
, “
Message Passing Neural Pde Solvers
,” arxiv preprint arxiv:2202.03376.
43.
Boussif
,
O.
,
Bengio
,
Y.
,
Benabbou
,
L.
, and
Assouline
,
D.
,
2022
, “
Magnet: Mesh Agnostic Neural Pde Solver
,”
Adv. Neural Inf. Process. Syst.
,
35
, pp.
31972
31985
.
44.
Sanchez-Lengeling
,
B.
,
Reif
,
E.
,
Pearce
,
A.
, and
Wiltschko
,
A. B.
,
2021
, “
A Gentle Introduction to Graph Neural Networks
,”
Distill
. .
45.
Li
,
G.
,
Xiong
,
C.
,
Thabet
,
A.
, and
Ghanem
,
B.
,
2020
, “
Deepergcn: All You Need to Train Deeper Gcns
,” arxiv preprint arxiv:2006.07739.
46.
Fey
,
M.
, and
Lenssen
,
J. E.
,
2019
, “
Fast Graph Representation Learning With Pytorch Geometric
,” Arxiv Preprint Arxiv:1903.02428.
47.
Guo
,
K.
, and
Buehler
,
M. J.
,
2020
, “
A Semi-Supervised Approach to Architected Materials Design Using Graph Neural Networks
,”
Extreme Mech. Lett.
,
41
, p.
101029
.
48.
Law
,
J. N.
,
Pandey
,
S.
,
Gorai
,
P.
, and
St. John
,
P. C.
,
2022
, “
Upper-Bound Energy Minimization to Search for Stable Functional Materials With Graph Neural Networks
,”
JACS Au
,
3
(
1
), pp.
113
123
.
49.
Zhang
,
Z.
,
Lin
,
X.
,
Li
,
M.
, and
Wang
,
Y.
,
2021
, “
A Customized Deep Learning Approach to Integrate Network-Scale Online Traffic Data Imputation and Prediction
,”
Transp. Res. Part C Emerg. Technol.
,
132
, p.
103372
.
50.
Zhang
,
K.
,
He
,
F.
,
Zhang
,
Z.
,
Lin
,
X.
, and
Li
,
M.
,
2021
, “
Graph Attention Temporal Convolutional Network for Traffic Speed Forecasting on Road Networks
,”
Transportmetrica B: Transp. Dyn.
,
9
(
1
), pp.
153
171
.
51.
He
,
K.
,
Zhang
,
X.
,
Ren
,
S.
, and
Sun
,
J.
,
2016
, “
Deep Residual Learning for Image Recognition
,”
Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
,
Las Vegas, NV
,
June 26–July 1
, pp.
770
778
.
52.
Ioffe
,
S.
, and
Szegedy
,
C.
,
2015
, “
Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
,”
International Conference on Machine Learning
,
Lille, France
,
July 6–11
, pp.
448
456
.
53.
Srivastava
,
N.
,
Hinton
,
G.
,
Krizhevsky
,
A.
,
Sutskever
,
I.
, and
Salakhutdinov
,
R.
,
2014
, “
Dropout: A Simple Way to Prevent Neural Networks From Overfitting
,”
J. Mach. Learn. Res.
,
15
(
1
), pp.
1929
1958
.
54.
You
,
J.
,
Gomes-Selman
,
J. M.
,
Ying
,
R.
, and
Leskovec
,
J.
,
2021
, “
Identity-Aware Graph Neural Networks
,”
Proceedings of the AAAI Conference on Artificial Intelligence
,
Online
,
Feb. 2–9
.
55.
Cao
,
K.
,
You
,
J.
, and
Leskovec
,
J.
,
2023
, “
Relational Multi-Task Learning: Modeling Relations Between Data and Tasks
,” arxiv preprint arxiv:2303.07666.
56.
L
,
G.
,
M
,
M.
,
T
,
A.
, and
G
,
B.
,
2019
, “
Deepgcns: Can GCNs Go as Deep as CNNs?
Proceedings of the 2019 IEEE/CVF International Conference on Computer Vision (ICCV)
,
Seoul, South Korea
,
Oct. 27– Nov. 2
, pp.
9266
9275
.
57.
Xu
,
K.
,
Li
,
C.
,
Tian
,
Y.
,
Sonobe
,
T.
,
Kawarabayashi
,
K.
, and
Jegelka
,
S.
,
2018
, “
Representation Learning On Graphs with Jumping Knowledge Networks
,”
Proceedings of the 35th International Conference on Machine Learning
,
Stockholm, Sweden
,
July 10–15
, pp.
5453
5462
.
58.
Ying
,
Z.
,
You
,
J.
,
Morris
,
C.
,
Ren
,
X.
,
Hamilton
,
W.
, and
Leskovec
,
J.
,
2018
, “
Hierarchical Graph Representation Learning With Differentiable Pooling
,”
Adv. Neural Inf. Process. Syst.
,
31
, pp.
4805
4815
.
59.
Chen
,
B. S.
,
2016
, “
Advancements of Design and Development for Sipesc—A Software Integration Platform of Numerical Simulation
,”
Sci. Technol. Innov. Herald
,
13
(
19
), pp.
178
179
.
60.
Hu
,
W.
,
Liu
,
B.
,
Gomes
,
J.
,
Zitnik
,
M.
,
Liang
,
P.
,
Pande
,
V.
, and
Leskovec
,
J.
,
2019
, “
Strategies for Pre-Training Graph Neural Networks
,”
In International Conference on Learning Representations
,
Online
.
61.
Shi
,
Y.
,
Huang
,
Z.
,
Feng
,
S.
,
Zhong
,
H.
,
Wang
,
W.
, and
Sun
,
Y.
,
2020
, “
Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification
,” arxiv preprint arxiv:2009.03509.
62.
Rozemberczki
,
B.
,
Englert
,
P.
,
Kapoor
,
A.
,
Blais
,
M.
, and
Perozzi
,
B.
,
2021
, “
Pathfinder Discovery Networks for Neural Message Passing
,”
Proceedings of the Web Conference 2021
,
Online
,
Apr. 19–23
, pp.
2547
2558
.
63.
Malen
,
D. E.
,
2011
,
Fundamentals of Automobile Body Structure Design
,
SAE International
,
Warrendale, PA
.
64.
Gilmer
,
J.
,
Schoenholz
,
S. S.
,
Riley
,
P. F.
,
Vinyals
,
O.
, and
Dahl
,
G. E.
,
2017
, “
Neural Message Passing for Quantum Chemistry
,”
International Conference on Machine Learning
,
Sydney, Australia
,
Aug. 6–11
, pp.
1263
1272
.
65.
Katoch
,
S.
,
Chauhan
,
S. S.
, and
Kumar
,
V.
,
2021
, “
A Review On Genetic Algorithm: Past, Present, and Future
,”
Multimed. Tools Appl.
,
80
(
5
), pp.
8091
8126
.
66.
Elsken
,
T.
,
Metzen
,
J. H.
, and
Hutter
,
F.
,
2019
, “
Neural Architecture Search: A Survey
,”
J. Mach. Learn. Res.
,
20
(
1
), pp.
1997
2017
.
67.
He
,
X.
,
Zhao
,
K.
, and
Chu
,
X.
,
2021
, “
Automl: A Survey of the State-of-the-Art
,”
Knowledge Based Syst.
,
212
, p.
106622
.
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