Abstract

Function is defined as the ensemble of tasks that enable the product to complete the designed purpose. Functional tools, such as functional modeling, offer decision guidance in the early phase of product design, where explicit design decisions are yet to be made. Function-based design data is often sparse and grounded in individual interpretation. As such, function-based design tools can benefit from automatic function classification to increase data fidelity and provide function representation models that enable function-based intelligent design agents. Function-based design data is commonly stored in manually generated design repositories. These design repositories are a collection of expert knowledge and interpretations of function in product design bounded by function-flow and component taxonomies. In this work, we represent a structured taxonomy-based design repository as assembly-flow graphs, then leverage a graph neural network (GNN) model to perform automatic function classification. We support automated function classification by learning from repository data to establish the ground truth of component function assignment. Experimental results show that our GNN model achieves a micro-average F1-score of 0.617 for tier 1 (broad), 0.624 for tier 2, and 0.415 for tier 3 (specific) functions. Given the imbalance of data features and the subjectivity in the definition of product function, the results are encouraging. Our efforts in this paper can be a starting point for more sophisticated applications in knowledge-based CAD systems and Design-for-X consideration in function-based design.

References

1.
Ullman
,
D.
,
2003
,
The Mechanical Design Process
,
McGraw-Hill Science/Engineering/Math
,
New York
.
2.
Gero
,
J. S.
, and
Kannengiesser
,
U.
,
2004
, “
The Situated Function-Behaviour-Structure Framework
,”
Des. Studies
,
25
(
4
), pp.
373
391
.
3.
Rosenman
,
M. A.
, and
Gero
,
J. S.
,
1998
, “
Purpose and Function in Design: From the Socio-Cultural to the Technophysical
,”
Des. Studies
,
19
(
2
), pp.
161
186
.
4.
Eisenbart
,
B.
,
Gericke
,
K.
, and
Blessing
,
L.
,
2011
, “
A Framework for Comparing Design Modelling Approaches Across Disciplines
,”
DS 68-2: Proceedings of the 18th International Conference on Engineering Design (ICED 11)
,
Copenhagen, Denmark
,
Aug. 15–18
.
5.
Eisenbart
,
B.
,
Gericke
,
K.
, and
Blessing
,
L.
,
2013
, “
An Analysis of Functional Modeling Approaches Across Disciplines
,”
Artificial Intelligence for Engineering Design, Analysis and Manufacturing: AIEDAM
,
27
(
3
), pp.
281
289
.
6.
Hirtz
,
J.
,
Stone
,
R. B.
,
McAdams
,
D. A.
,
Szykman
,
S.
, and
Wood
,
K. L.
,
2002
, “
A Functional Basis for Engineering Design: Reconciling and Evolving Previous Efforts
,”
Res. Eng. Des. – Theory Appl. Concurrent Eng.
,
13
(
2
), pp.
65
82
.
7.
Ferrero
,
V.
,
Wisthoff
,
A.
,
Huynh
,
T.
,
Ross
,
D.
, and
DuPont
,
B.
,
2018
, “
A Sustainable Design Repository for Influencing the Eco-Design of New Consumer Products
,”
EngrXIV, p. Under Review
.
8.
Oman
,
S.
,
Gilchrist
,
B.
,
Tumer
,
I. Y.
, and
Stone
,
R.
,
2014
, “
The Development of a Repository of Innovative Products (RIP) for Inspiration in Engineering Design
,”
Int. J. Des. Creativity Innovation
,
2
(
4
), pp.
186
202
.
9.
Szykman
,
S.
,
Sriram
,
R. D.
,
Bochenek
,
C.
, and
Racz
,
J. W.
,
1999
, “The NIST Design Repository Project,”
Adv. Soft Computing – Eng. Des. Manuf.
,
R.
Roy
,
T.
Furuhashi
, and
P. K.
Chawdry
, eds.,
Springer-Verlag
,
London
, pp.
5
19
.
10.
Feng
,
Y.
,
Zhao
,
Y.
,
Zheng
,
H.
,
Li
,
Z.
, and
Tan
,
J.
,
2020
, “
Data-Driven Product Design Toward Intelligent Manufacturing: A Review
,”
Int. J. Adv. Robot. Syst.
,
17
(
2
), pp.
1
18
.
11.
Bertoni
,
A.
,
2020
, “
Data-Driven Design in Concept Development: Systematic Review and Missed Opportunities
,”
Proceedings of the Design Society: DESIGN Conference
,
Cavtat, Croatia
,
Oct. 26–29
, Vol. 1, pp.
101
110
.
12.
Halevy
,
A.
,
Norvig
,
P.
, and
Pereira
,
F.
,
2009
, “
The Unreasonable Effectiveness of Data
,”
IEEE Intelligent Syst.
,
24
(
2
), pp.
8
12
.
13.
Sun
,
C.
,
Shrivastava
,
A.
,
Singh
,
S.
, and
Gupta
,
A.
,
2017
, “
Revisiting Unreasonable Effectiveness of Data in Deep Learning Era
,”
IEEE International Conference on Computer Vision (ICCV)
,
Venice, Italy
,
Oct. 22–29
, pp.
843
852
.
14.
Cheong
,
H.
,
Li
,
W.
,
Cheung
,
A.
,
Nogueira
,
A.
, and
Iorio
,
F.
,
2017
, “
Automated Extraction of Function Knowledge From Text
,”
ASME J. Mech. Des.
,
139
(
11
), p.
111407
.
15.
Law
,
M. V.
,
Kwatra
,
A.
,
Dhawan
,
N.
,
Einhorn
,
M.
,
Rajesh
,
A.
, and
Hoffman
,
G.
,
2020
, “
Design Intention Inference for Virtual Co-Design Agents
,”
Proceedings of the 20th ACM International Conference on Intelligent Virtual Agents
,
Virtual
,
Oct. 20–22
.
16.
Zhang
,
Y.
,
Liu
,
X.
,
Jia
,
J.
, and
Luo
,
X.
,
2019
, “
Knowledge Representation Framework Combining Case-Based Reasoning With Knowledge Graphs for Product Design
,”
Comput.-Aided Des. Appl.
,
17
(
4
), pp.
763
782
.
17.
Angrish
,
A.
,
Craver
,
B.
, and
Starly
,
B.
,
2019
, “
“fabsearch”: A 3D CAD Model-Based Search Engine for Sourcing Manufacturing Services
,”
J. Comput. Inf. Sci. Eng.
,
19
(
4
), p.
041006
.
18.
Dering
,
M. L.
, and
Tucker
,
C. S.
,
2017
, “
A Convolutional Neural Network Model for Predicting a Products Function, Given Its Form
,”
ASME J. Mech. Des.
,
139
(
11
), p.
111408
.
19.
Han
,
J.
,
Sarica
,
S.
,
Shi
,
F.
, and
Luo
,
J.
,
2020
, “
Semantic Networks for Engineering Design: A Survey
,”
Proceedings of the Design Society
, pp.
2621
2630
.
20.
Lupinetti
,
K.
,
Pernot
,
J.-P.
,
Monti
,
M.
, and
Giannini
,
F.
,
2019
, “
Content-Based Cad Assembly Model Retrieval: Survey and Future Challenges
,”
Comput.-Aided Des.
,
113
, pp.
62
81
.
21.
Zhang
,
Z.
,
Cui
,
P.
, and
Zhu
,
W.
,
2020
, “
Deep Learning on Graphs: A Survey
,”
IEEE Trans. Knowledge Data Eng.
,
1
(
1
), p.
99
.
22.
Wu
,
Z.
,
Pan
,
S.
,
Chen
,
F.
,
Long
,
G.
,
Zhang
,
C.
, and
Philip
,
S. Y.
,
2019
, “
A Comprehensive Survey on Graph Neural Networks
,”
IEEE Trans. Neural Netw. Learning Syst
.
23.
Bang
,
H.
,
Martin
,
A. V.
,
Prat
,
A.
, and
Selva
,
D.
,
2018
, “
Daphne: An Intelligent Assistant for Architecting Earth Observing Satellite Systems
,”
2018 AIAA Information Systems-AIAA Infotech @ Aerospace
24.
Berquand
,
A.
,
Murdaca
,
F.
,
Riccardi
,
A.
,
Soares
,
T.
,
Genere
,
S.
,
Brauer
,
N.
, and
Kumar
,
K.
,
2019
, “
Artificial Intelligence for the Early Design Phases of Space Missions
,”
2019 IEEE Aerospace Conference
,
Big Sky, MT
,
Mar. 2–9
.
25.
Coyne
,
R. D.
,
Rosenman
,
M. A.
,
Radford
,
A. D.
, and
Gero
,
J. S.
,
1990
,
Knowledge-Based Design Systems
,
Addison-Wesley
,
Boston, MA
.
26.
Erden
,
M.
,
Komoto
,
H.
,
Beek
,
T. V.
,
Damelio
,
V.
,
Echavarria
,
E.
, and
Tomiyama
,
T.
,
2008
, “
A Review of Function Modeling: Approaches and Applications
,”
Artif. Intell. Eng. Des. Anal. Manuf.
,
22
(
2
), pp.
147
169
.
27.
Davis
,
N.
,
Hsiao
,
C.-P.
,
Popova
,
Y.
, and
Magerko
,
B.
,
2015
, “
An Enactive Model of Creativity for Computational Collaboration and Co-Creation
,”
Creativity in the Digital Age Springer Series on Cultural Computing
, pp.
109
133
.
28.
Bohm
,
M. R.
, and
Stone
,
R. B.
,
2004
, “
Product Design Support: Exploring a Design Repository System
,”
ASME International Mechanical Engineering Congress and Exposition
,
Anaheim, CA
,
Aug. 13–19
, CED, pp.
55
65
.
29.
Bohm
,
M. R.
,
Stone
,
R. B.
,
Simpson
,
T. W.
, and
Steva
,
E. D.
,
2008
, “
Introduction of a Data Schema to Support a Design Repository
,”
CAD Comput. Aided Des.
,
40
(
7
), pp.
801
811
.
30.
Arlitt
,
R.
,
Van Bossuyt
,
D. L.
,
Stone
,
R. B.
, and
Tumer
,
I. Y.
,
2017
, “
The Function-Based Design for Sustainability Method
,”
J. Mech. Des.
,
139
(
4
), pp.
1
12
.
31.
Devanathan
,
S.
,
Ramanujan
,
D.
,
Bernstein
,
W. Z.
,
Zhao
,
F.
, and
Ramani
,
K.
,
2010
, “
Integration of Sustainability Into Early Design Through the Function Impact Matrix
,”
ASME J. Mech. Des.
,
132
(
8
), p. 081004.
32.
Gilchrist
,
B. P.
,
Tumer
,
I. Y.
,
Stone
,
R. B.
,
Gao
,
Q.
, and
Haapala
,
K. R.
,
2012
, “
Comparison of Environmental Impacts of Innovative and Common Products
,”
International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
,
Chicago, IL
,
Aug. 12–15
, ASME, pp.
1
10
.
33.
Soria Zurita
,
N. F.
,
Stone
,
R. B.
,
Onan Demirel
,
H.
, and
Tumer
,
I. Y.
,
2020
, “
Identification of Human–System Interaction Errors During Early Design Stages Using a Functional Basis Framework
,”
ASCE-ASME J. Risk Uncert. Engrg. Sys. Part B Mech. Engrg.
,
6
(
1
).
34.
Soria Zurita
,
N. F.
,
Stone
,
R. B.
,
Demirel
,
O.
, and
Tumer
,
I. Y.
,
2018
, “
The Function-Human Error Design Method (FHEDM)
,”
ASME International Design Engineering Technical Conferences
,
Quebec City, Quebec, Canada
,
Aug. 26–29
.
35.
Tensa
,
M.
,
Edmonds
,
K.
,
Ferrero
,
V.
,
Mikes
,
A.
,
Soria Zurita
,
N.
,
Stone
,
R.
, and
DuPont
,
B.
,
2019
, “
Toward Automated Functional Modeling: An Association Rules Approach for Mining the Relationship Between Product Components and Function
,”
Proc. Des. Soc.: Int. Conf. Eng. Des.
,
1
(
1
), pp.
1713
1722
.
36.
Mikes
,
A.
,
Edmonds
,
K.
,
Stone
,
R. B.
, and
DuPont
,
B.
,
2020
, “
Optimizing An Algorithm for Data Mining a Design Repository to Automate Functional Modeling
,”
ASME International Design Engineering Technical Conferences
,
Virtual
,
Aug. 17–19
, pp.
1
12
.
37.
Edmonds
,
K.
,
Mikes
,
A.
,
DuPont
,
B.
, and
Stone
,
R. B.
,
2020
, “
A Weighted Confidence Metric to Improve Automated Functional Modeling
,”
Proceedings of the ASME Design Engineering Technical Conference
,
Virtual
,
Aug. 17–19
, pp.
1
13
.
38.
Ferrero
,
V. J.
,
Alqseer
,
N.
,
Tensa
,
M.
, and
DuPont
,
B.
,
2020
, “
Using Decision Trees Supported by Data Mining to Improve Function-Based Design
,”
ASME International Design Engineering and Technical Conferences
,
Virtual
,
Aug. 17–19
, pp.
1
11
.
39.
Singh
,
A.
, and
Tucker
,
C. S.
,
2017
, “
A Machine Learning Approach to Product Review Disambiguation Based on Function, Form and Behavior Classification
,”
Decision Support Syst.
,
97
, pp.
81
91
.
40.
Szykman
,
S.
,
Sriram
,
R. D.
,
Bochenek
,
C.
,
Racz
,
J. W.
, and
Senfaute
,
J.
,
2000
, “
Design Repositories: Engineering Design’s New Knowledge Base
,”
IEEE Intell. Syst. Appl.
,
15
(
3
), pp.
48
55
.
41.
Phelan
,
K.
,
Wilson
,
C.
, and
Summers
,
J. D.
,
2014
, “
Development of a Design for Manufacturing Rules Database for Use in Instruction of DFM Practices
,”
Proceedings of the ASME International Design Engineering Technical Conference
,
Buffalo, NY
,
Aug. 17–20
, Vol. 1A, pp.
1
7
.
42.
Bharadwaj
,
A.
,
Xu
,
Y.
,
Angrish
,
A.
,
Chen
,
Y.
, and
Starly
,
B.
,
2019
, “
Development of a Pilot Manufacturing Cyberinfrastructure With An Information Rich Mechanical CAD 3D Model Repository
,”
ASME 2019 14th International Manufacturing Science and Engineering Conference, MSEC 2019
,
Erie, PA
,
June 10–14
, pp.
1
8
.
43.
Kurtoglu
,
T.
,
Campbell
,
M. I.
,
Bryant
,
C. R.
,
Stone
,
R. B.
, and
Mcadams
,
D. A.
,
2005
, “
Deriving a Component Basis for Computational Functional Synthesis
,”
ICED 05: 15th International Conference on Engineering Design: Engineering Design and the Global Economy
,
Melbourne, Australia
,
Aug. 15–18
.
44.
Cheong
,
H.
,
Chiu
,
I.
,
Shu
,
L. H.
,
Stone
,
R. B.
, and
McAdams
,
D. A.
,
2011
, “
Biologically Meaningful Keywords for Functional Terms of the Functional Basis
,”
ASME J. Mech. Des.
,
133
(
2
), p.
021007
.
45.
Ferrero
,
V.
,
2020
,
PyDamp: Python-based Data Addition and Management of PSQL. 10.5281/zenodo.3873370
.
46.
Fayyad
,
U.
,
Piatetsky-Shapiro
,
G.
, and
Smyth
,
P.
,
1996
, “
The KDD Process for Extracting Useful Knowledge From Volumes of Data
,”
Commun. ACM
,
39
(
11
), pp.
27
34
.
47.
Fayyad
,
U.
,
Piatetsky-Shapiro
,
G.
, and
Smyth
,
P.
,
1996
, “
Knowledge Discovery and Data Mining: Towards a Unifying Framework
,”
AAAI KDD-96 Proceedings
,
Portland, OR
,
Aug. 2–4
, Vol. 14, pp.
82
88
.
48.
Fayyad
,
U.
,
Piatetsky-Shapiro
,
G.
, and
Smyth
,
P.
,
1996
, “
From Data Mining to Knowledge Discovery in Databases
,”
AI Magazine
,
17
(
2
), pp.
37
54
.
49.
Williams
,
G.
,
Meisel
,
N. A.
,
Simpson
,
T. W.
, and
McComb
,
C.
,
2019
, “
Design Repository Effectiveness for 3D Convolutional Neural Networks: Application to Additive Manufacturing
,”
ASME J. Mech. Des.
,
141
(
11
), p.
111701
.
50.
Wang
,
Q.
,
Mao
,
Z.
,
Wang
,
B.
, and
Guo
,
L.
,
2017
, “
Knowledge Graph Embedding: A Survey of Approaches and Applications
,”
IEEE Trans. Knowl. Data Eng.
,
29
(
12
), pp.
2724
2743
.
51.
Ji
,
S.
,
Pan
,
S.
,
Cambria
,
E.
,
Marttinen
,
P.
, and
Yu
,
P. S.
,
2020
, “
A Survey on Knowledge Graphs: Representation, Acquisition and Applications
,”
arXiv:2002.00388
.
52.
Miller
,
G. A.
,
1995
, “
WordNet
,”
Commun. ACM
,
38
(
11
), pp.
39
41
.
53.
Liu
,
H.
, and
Singh
,
P.
,
2004
, “
ConceptNet – A Practical Commonsense Reasoning Tool-Kit
,”
BT Technol. J.
,
22
(
4
), pp.
211
226
.
54.
Sarica
,
S.
,
Luo
,
J.
, and
Wood
,
K. L.
,
2020
, “
TechNet: Technology Semantic Network Based on Patent Data
,”
Expert Syst. Appl.
,
142
.
55.
Sarica
,
S.
,
Song
,
B.
,
Luo
,
J.
, and
Wood
,
K.
,
2019
, “
Technology Knowledge Graph for Design Exploration: Application to Designing the Future of Flying Cars
,”
Proceedings of the ASME International Design Engineering Technical Conference
,
Anaheim, CA
,
Aug. 18–21
, Vol. 1, pp.
1
8
.
56.
Shi
,
F.
,
Chen
,
L.
,
Han
,
J.
, and
Childs
,
P.
,
2017
, “
A Data-Driven Text Mining and Semantic Network Analysis for Design Information Retrieval
,”
ASME J. Mech. Des.
,
139
(
11
), p.
111402
.
57.
Han
,
J.
,
Forbes
,
H.
,
Shi
,
F.
,
Hao
,
J.
, and
Schaefer
,
D.
,
2020
, “
A Data-Driven Approach for Creative Concept Generation and Evaluation
,”
Proc. Des. Soc.: Des. Conf.
,
1
, pp.
167
176
.
58.
Zhang
,
Y.
,
Liu
,
X.
,
Jia
,
J.
, and
Luo
,
X.
,
2019
, “
Knowledge Representation Framework Combining Case-Based Reasoning with Knowledge Graphs for Product Design
,”
Comput.-Aided Des. Appl.
,
17
(
4
), pp.
763
782
.
59.
Hassani
,
K.
, and
Khasahmadi
,
A. H.
,
2020
, “
Contrastive Multi-View Representation Learning on Graphs
,”
International Conference on Machine Learning
,
Vienna, Austria
,
July 13–18
, pp.
4116
4126
.
60.
Li
,
Y.
,
Tarlow
,
D.
,
Brockschmidt
,
M.
, and
Zemel
,
R.
,
2015
, “
Gated Graph Sequence Neural Networks
,”
International Conference on Learning Representations
,
San Juan, Puerto Rico
,
May 2–4
.
61.
Hamilton
,
W.
,
Ying
,
Z.
, and
Leskovec
,
J.
,
2017
, “
Inductive Representation Learning on Large Graphs
,”
Advances in Neural Information Processing Systems
,
Long Beach, CA
,
Dec. 4–9
, pp.
1024
1034
.
62.
Kipf
,
T. N.
, and
Welling
,
M.
,
2017
, “
Semi-Supervised Classification With Graph Convolutional Networks
,”
International Conference on Learning Representations
,
Toulon, France
,
Apr. 24–26
.
63.
Veličković
,
P.
,
Cucurull
,
G.
,
Casanova
,
A.
,
Romero
,
A.
,
Liò
,
P.
, and
Bengio
,
Y.
,
2018
, “
Graph Attention Networks
,”
International Conference on Learning Representations
,
Vancouver, Canada
,
Apr. 30–May 3
.
64.
Xu
,
K.
,
Hu
,
W.
,
Leskovec
,
J.
, and
Jegelka
,
S.
,
2019
, “
How Powerful are Graph Neural Networks?
International Conference on Learning Representations
,
New Orleans, LA
,
May 6–9
.
65.
Duvenaud
,
D. K.
,
Maclaurin
,
D.
,
Iparraguirre
,
J.
,
Bombarell
,
R.
,
Hirzel
,
T.
,
Aspuru-Guzik
,
A.
, and
Adams
,
R. P.
,
2015
, “
Convolutional Networks on Graphs for Learning Molecular Fingerprints
,”
Advances in Neural Information Processing Systems
,
Montreal, Quebec, Canada
,
Dec. 7–12
, pp.
2224
2232
.
66.
Hanocka
,
R.
,
Hertz
,
A.
,
Fish
,
N.
,
Giryes
,
R.
,
Fleishman
,
S.
, and
Cohen-Or
,
D.
,
2019
, “
Meshcnn: A Network With An Edge
,”
ACM Trans. Graphics (TOG)
,
38
(
4
), pp.
1
12
.
67.
Hassani
,
K.
, and
Haley
,
M.
,
2019
, “
Unsupervised Multi-Task Feature Learning on Point Clouds
,”
International Conference on Computer Vision
,
Seoul, South Korea
,
Oct. 27–Nov. 2
, pp.
8160
8171
.
68.
Wang
,
T.
,
Zhou
,
Y.
,
Fidler
,
S.
, and
Ba
,
J.
,
2019
, “
Neural Graph Evolution: Automatic Robot Design
,”
International Conference on Learning Representations
,
New Orleans, LA
,
May 6–9
.
69.
Sanchez-Gonzalez
,
A.
,
Heess
,
N.
,
Springenberg
,
J. T.
,
Merel
,
J.
,
Riedmiller
,
M.
,
Hadsell
,
R.
, and
Battaglia
,
P.
,
2018
, “
Graph Networks As Learnable Physics Engines for Inference and Control
,”
International Conference on Machine Learning
,
Stockholm, Sweden
,
July 10–15
, pp.
4470
4479
.
70.
Sanchez-Gonzalez
,
A.
,
Godwin
,
J.
,
Pfaff
,
T.
,
Ying
,
R.
,
Leskovec
,
J.
, and
Battaglia
,
P.
,
2020
, “
Learning to Simulate Complex Physics With Graph Networks
,”
International Conference on Machine Learning, PMLR
,
Vienna, Austria
,
July 12–18
, pp.
8459
8468
.
71.
Shlomi
,
J.
,
Battaglia
,
P.
, and
Vlimant
,
J.-R.
,
2020
, “
Graph Neural Networks in Particle Physics
,”
Mach. Learning: Sci. Technol.
,
2
(
2
), pp.
1
19
.
72.
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
.
73.
Park
,
J.
, and
Park
,
J.
,
2019
, “
Physics-Induced Graph Neural Network: An Application to Wind-Farm Power Estimation
,”
Energy
,
187
, p.
115883
.
74.
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
.
75.
2020
,
Oregon State Design Repository, https://design.engr.oregonstate.edu/repo
.
76.
Hagberg
,
A. A.
,
Schult
,
D. A.
, and
Swart
,
P. J.
,
2008
, “
Exploring Network Structure, Dynamics, and Function Using networkx
,”
Proceedings of the 7th Python in Science Conference
,
G.
Varoquaux
,
T.
Vaught
, and
J.
Millman
, eds., pp.
11
15
.
77.
Hagberg
,
A.
,
Swart
,
P.
, and
S Chult
,
D.
,
2008
, “
Exploring Network Structure, Dynamics, and Function Using Networkx
,”
Technical Report
,
Los Alamos National Lab. (LANL)
,
Los Alamos, NM (United States)
.
78.
Williams
,
R. J.
, and
Zipser
,
D.
,
1989
, “
A Learning Algorithm for Continually Running Fully Recurrent Neural Networks
,”
Neural Comput.
,
1
(
2
), pp.
270
280
.
79.
Glorot
,
X.
, and
Bengio
,
Y.
,
2010
, “
Understanding the Difficulty of Training Deep Feedforward Neural Networks
,”
International Conference on Artificial Intelligence and Statistics
,
Sardinia, Italy
,
May 13–15
, pp.
249
256
.
80.
Kingma
,
D. P.
, and
Ba
,
J. L.
,
2014
, “
ADAM: Amethod for Stochastic Optimization
,”
International Conference on Learning Representation
,
Banff, Canada
,
Apr. 14–16
.
81.
Loshchilov
,
I.
, and
Hutter
,
F.
,
2016
, “
SGDR: Stochastic Gradient Descent With Warm Restarts
,”
International Conference on Learning Representations
,
San Juan, Puerto Rico
,
May 2–4
.
82.
Maas
,
A. L.
,
Hannun
,
A. Y.
, and
Ng
,
A. Y.
,
2013
, “
Rectifier Nonlinearities Improve Neural Network Acoustic Models
,”
International Conference on Machine Learning
,
Atlanta, GA
,
June 16–21
.
83.
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
(
56
), pp.
1929
1958
.
84.
Paszke
,
A.
,
Gross
,
S.
,
Massa
,
F.
,
Lerer
,
A.
,
Bradbury
,
J.
,
Chanan
,
G.
,
Killeen
,
T.
, et al.,
2019
, “
Pytorch: An Imperative Style, High-Performance Deep Learning Library
,”
Advances in Neural Information Processing Systems 32
,
H.
Wallach
,
H.
Larochelle
,
A.
Beygelzimer
,
F.
d’Alché-Buc
,
E.
Fox
,
R.
Garnett
, eds.,
Curran Associates, Inc.
, pp.
8024
8035
.
85.
Fey
,
M.
, and
Lenssen
,
J. E.
,
2019
, “
Fast Graph Representation Learning With PyTorch Geometric
,”
ICLR Workshop on Representation Learning on Graphs and Manifolds
,
New Orleans, LA
,
May 6–9
.
86.
Cheng
,
Z.
, and
Ma
,
Y.
,
2017
, “
Explicit Function-Based Design Modelling Methodology With Features
,”
J. Eng. Des.
,
28
(
3
), pp.
205
231
.
87.
Bohm
,
M. R.
,
Haapala
,
K. R.
,
Poppa
,
K.
,
Stone
,
R. B.
, and
Tumer
,
I. Y.
,
2010
, “
Integrating Life Cycle Assessment Into the Conceptual Phase of Design Using a Design Repository
,”
ASME J. Mech. Des.
,
132
(
9
), p.
091005
.
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