Abstract

Deep generative models are proven to be a useful tool for automatic design synthesis and design space exploration. When applied in engineering design, existing generative models face three challenges: (1) generated designs lack diversity and do not cover all areas of the design space, (2) it is difficult to explicitly improve the overall performance or quality of generated designs, and (3) existing models generally do not generate novel designs, outside the domain of the training data. In this article, we simultaneously address these challenges by proposing a new determinantal point process-based loss function for probabilistic modeling of diversity and quality. With this new loss function, we develop a variant of the generative adversarial network, named “performance augmented diverse generative adversarial network” (PaDGAN), which can generate novel high-quality designs with good coverage of the design space. By using three synthetic examples and one real-world airfoil design example, we demonstrate that PaDGAN can generate diverse and high-quality designs. In comparison to a vanilla generative adversarial network, on average, it generates samples with a 28% higher mean quality score with larger diversity and without the mode collapse issue. Unlike typical generative models that usually generate new designs by interpolating within the boundary of training data, we show that PaDGAN expands the design space boundary outside the training data towards high-quality regions. The proposed method is broadly applicable to many tasks including design space exploration, design optimization, and creative solution recommendation.

References

1.
Chakrabarti
,
A.
,
Shea
,
K.
,
Stone
,
R.
,
Cagan
,
J.
,
Campbell
,
M.
,
Hernandez
,
N. V.
, and
Wood
,
K. L.
,
2011
, “
Computer-Based Design Synthesis Research: An Overview
,”
ASME J. Comput. Inf. Sci. Eng.
,
11
(
2
), p.
021003
. 10.1115/1.3593409
2.
Kingma
,
D. P.
, and
Welling
,
M.
,
2014
, “
Auto-Encoding Variational Bayes
,”
2nd International Conference on Learning Representations
,
Banff, AB, Canada
,
Apr. 14–16
.
3.
Goodfellow
,
I.
,
Pouget-Abadie
,
J.
,
Mirza
,
M.
,
Xu
,
B.
,
Warde-Farley
,
D.
,
Ozair
,
S.
,
Courville
,
A.
, and
Bengio
,
Y.
,
2014
, “
Generative Adversarial Nets
,”
Advances in Neural Information Processing Systems
,
Montreal, Quebec, Canada
,
Dec. 8–13
, pp.
2672
2680
.
4.
Chen
,
W.
,
Fuge
,
M.
, and
Chazan
,
J.
,
2017
, “
Design Manifolds Capture the Intrinsic Complexity and Dimension of Design Spaces
,”
ASME J. Mech. Des.
,
139
(
5
), p.
051102
. 10.1115/1.4036134
5.
Chen
,
W.
, and
Fuge
,
M.
,
2019
, “
Synthesizing Designs With Interpart Dependencies Using Hierarchical Generative Adversarial Networks
,”
ASME J. Mech. Des.
,
141
(
11
), p.
111403
. 10.1115/1.4044076
6.
Chen
,
W.
,
Chiu
,
K.
, and
Fuge
,
M.
,
2019
, “
Aerodynamic Design Optimization and Shape Exploration Using Generative Adversarial Networks
,”
AIAA SciTech Forum
,
San Diego, CA
,
Jan. 7–11
.
7.
Chen
,
W.
,
Chiu
,
K.
, and
Fuge
,
M.
,
2020
, “
Airfoil Design Parameterization and Optimization Using Bézier Generative Adversarial Networks
,”
AIAA J
. 10.2514/1.J059317
8.
Bendsoe
,
M. P.
, and
Sigmund
,
O.
,
2004
,
Topology Optimization: Theory, Methods and Applications
,
Springer
,
New York
.
9.
Ahmed
,
F.
,
Deb
,
K.
, and
Bhattacharya
,
B.
,
2016
, “
Structural Topology Optimization Using Multi-Objective Genetic Algorithm With Constructive Solid Geometry Representation
,”
Appl. Soft. Comput.
,
39
, pp.
240
250
. 10.1016/j.asoc.2015.10.063
10.
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
. 10.1115/1.4045419
11.
Kulesza
,
A.
, and
Taskar
,
B.
,
2012
, “
Determinantal Point Processes for Machine Learning
,”
Found. Trends Mach. Learn.
,
5
(
2–3
), pp.
123
286
. 10.1561/2200000044
12.
Goodfellow
,
I.
,
Bengio
,
Y.
, and
Courville
,
A.
,
2016
,
Deep Learning
,
MIT Press
,
Cambridge, MA
.
13.
Gmeiner
,
T.
, and
Shea
,
K.
,
2013
, “
A Spatial Grammar for the Computational Design Synthesis of Vise Jaws
,”
ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Portland, OR
,
Aug. 4–7
.
14.
Königseder
,
C.
,
Stanković
,
T.
, and
Shea
,
K.
,
2016
, “
Improving Design Grammar Development and Application Through Network-Based Analysis of Transition Graphs
,”
Design Sci.
,
2
, p.
e5
. 10.1017/dsj.2016.5
15.
Shea
,
K.
,
Aish
,
R.
, and
Gourtovaia
,
M.
,
2005
, “
Towards Integrated Performance-Driven Generative Design Tools
,”
Auto. Construction
,
14
(
2
), pp.
253
264
. 10.1016/j.autcon.2004.07.002
16.
Herber
,
D. R.
,
Guo
,
T.
, and
Allison
,
J. T.
,
2017
, “
Enumeration of Architectures With Perfect Matchings
,”
ASME J. Mech. Des.
,
139
(
5
), p.
051403
. 10.1115/1.4036132
17.
Kamesh
,
V. V.
,
Mallikarjuna Rao
,
K.
,
Rao
,
S.
, and
Balaji
,
A.
,
2017
, “
Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial
,”
ASME J. Mech. Des.
,
139
(
6
), p.
062304
. 10.1115/1.4036306
18.
Bryant
,
C. R.
,
Stone
,
R. B.
,
McAdams
,
D. A.
,
Kurtoglu
,
T.
, and
Campbell
,
M. I.
,
2005
, “
Concept Generation From the Functional Basis of Design
,”
ICED 05: 15th International Conference on Engineering Design: Engineering Design and the Global Economy
,
Melbourne, Australia
,
Aug. 15–18
, pp.
280
281
.
19.
Wyatt
,
D. F.
,
Wynn
,
D. C.
,
Jarrett
,
J. P.
, and
Clarkson
,
P. J.
,
2012
, “
Supporting Product Architecture Design Using Computational Design Synthesis With Network Structure Constraints
,”
Res. Eng. Design
,
23
(
1
), pp.
17
52
. 10.1007/s00163-011-0112-y
20.
Wijkniet
,
J.
, and
Hofman
,
T.
,
2018
, “
Modified Computational Design Synthesis Using Simulation-Based Evaluation and Constraint Consistency for Vehicle Powertrain Systems
,”
IEEE Trans. Vehicular Technol.
,
67
(
9
), pp.
8065
8076
. 10.1109/TVT.2018.2844024
21.
Chen
,
X.
,
Diez
,
M.
,
Kandasamy
,
M.
,
Zhang
,
Z.
,
Campana
,
E. F.
, and
Stern
,
F.
,
2015
, “
High-Fidelity Global Optimization of Shape Design by Dimensionality Reduction, Metamodels and Deterministic Particle Swarm
,”
Eng. Optim.
,
47
(
4
), pp.
473
494
. 10.1080/0305215X.2014.895340
22.
D’Agostino
,
D.
,
Serani
,
A.
,
Campana
,
E. F.
, and
Diez
,
M.
,
2017
, “
Nonlinear Methods for Design-Space Dimensionality Reduction in Shape Optimization
,”
Machine Learning, Optimization, and Big Data – Third International Conference
,
Volterra, Italy
,
Sept. 14–17
, pp.
121
132
.
23.
D’Agostino
,
D.
,
Serani
,
A.
,
Campana
,
E. F.
, and
Diez
,
M.
,
2018
, “
Deep Autoencoder for Off-Line Design-Space Dimensionality Reduction in Shape Optimization
,”
2018 AIAA/ASCE/AHS/ASC, Structures Structural Dynamics, and Materials Conference
,
Kissimmee, FL
,
Jan. 8–12
.
24.
Burnap
,
A.
,
Liu
,
Y.
,
Pan
,
Y.
,
Lee
,
H.
,
Gonzalez
,
R.
, and
Papalambros
,
P. Y.
,
2016
, “
Estimating and Exploring the Product Form Design Space Using Deep Generative Models
,”
ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Charlotte, NC
,
Aug. 21–24
.
25.
Cunningham
,
J. D.
,
Simpson
,
T. W.
, and
Tucker
,
C. S.
,
2019
, “
An Investigation of Surrogate Models for Efficient Performance-Based Decoding of 3d Point Clouds
,”
ASME J. Mech. Des.
,
141
(
12
), p.
121401
. 10.1115/1.4044597
26.
Cang
,
R.
,
Vipradas
,
A.
, and
Ren
,
Y.
,
2017
, “
Scalable Microstructure Reconstruction With Multi-Scale Pattern Preservation
,”
ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Cleveland, OH
,
Aug. 6–9
.
27.
Yang
,
Z.
,
Li
,
X.
,
Catherine Brinson
,
L.
,
Choudhary
,
A. N.
,
Chen
,
W.
, and
Agrawal
,
A.
,
2018
, “
Microstructural Materials Design Via Deep Adversarial Learning Methodology
,”
ASME J. Mech. Des.
,
140
(
11
), p.
111416
. 10.1115/1.4041371
28.
Chen
,
W.
, and
Fuge
,
M.
,
2018
, “
Béziergan: Automatic Generation of Smooth Curves From Interpretable Low-Dimensional Parameters
,”
Preprint arXiv:1808.08871
.
29.
Oh
,
S.
,
Jung
,
Y.
,
Kim
,
S.
,
Lee
,
I.
, and
Kang
,
N.
,
2019
, “
Deep Generative Design: Integration of Topology Optimization and Generative Models
,”
ASME J. Mech. Des.
,
141
(
11
), p.
111405
. 10.1115/1.4044229
30.
Burnap
,
A.
,
Hauser
,
J. R.
, and
Timoshenko
,
A.
,
2019
, “
Design and Evaluation of Product Aesthetics: A Human-Machine Hybrid Approach
,”
CoRR
, abs/1907.07786. http://arxiv.org/abs/1907.07786
31.
Salimans
,
T.
,
Goodfellow
,
I.
,
Zaremba
,
W.
,
Cheung
,
V.
,
Radford
,
A.
, and
Chen
,
X.
,
2016
, “
Improved Techniques for Training GANs
,”
Advances in Neural Information Processing Systems
,
Barcelona, Spain
,
Dec. 5–10
, pp.
2226
2234
.
32.
Mao
,
X.
,
Li
,
Q.
,
Xie
,
H.
,
Lau
,
R. Y.
,
Wang
,
Z.
, and
Paul Smolley
,
S.
,
2017
, “
Least Squares Generative Adversarial Networks
,”
Proceedings of the IEEE International Conference on Computer Vision
,
Venice, Italy
,
Oct. 22–29
, pp.
2813
2821
.
33.
Bang
,
D.
, and
Shim
,
H.
,
2018
, “
Mggan: Solving Mode Collapse Using Manifold Guided Training
,”
Preprint arXiv:1804.04391
.
34.
Srivastava
,
A.
,
Valkov
,
L.
,
Russell
,
C.
,
Gutmann
,
M. U.
, and
Sutton
,
C.
,
2017
, “
VEEGAN: Reducing Mode Collapse in Gans Using Implicit Variational Learning
,”
Advances in Neural Information Processing Systems
,
Long Beach, CA
,
Dec. 4–9
, pp.
3308
3318
.
35.
Chen
,
X.
,
Duan
,
Y.
,
Houthooft
,
R.
,
Schulman
,
J.
,
Sutskever
,
I.
, and
Abbeel
,
P.
,
2016
, “
InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets
,”
Advances in Neural Information Processing Systems
,
Barcelona, Spain
,
Dec. 5–10
, pp.
2172
2180
.
36.
Elfeki
,
M.
,
Couprie
,
C.
,
Riviere
,
M.
, and
Elhoseiny
,
M.
,
2019
, “
GDPP: Learning Diverse Generations Using Determinantal Point Processes
,”
International Conference on Machine Learning
,
Long Beach, CA
,
June 9–15
, pp.
1774
1783
.
37.
Dube
,
A.
, and
Helkkula
,
A.
,
2016
, “
Customer Approach to the Use of Big Data: Wearables for Service
,”
Proceedings of SERVSIG 2016 Conference
,
Maastricht, The Netherlands
,
June 17–19
.
38.
Lin
,
H.
, and
Bilmes
,
J.
,
2011
, “
A Class of Submodular Functions for Document Summarization
,”
Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies–Volume 1
,
Portland, OR
,
June 19–24
, pp.
510
520
.
39.
Shah
,
J. J.
,
Kulkarni
,
S. V.
, and
Vargas-Hernandez
,
N.
,
2000
, “
Evaluation of Idea Generation Methods for Conceptual Design: Effectiveness Metrics and Design of Experiments
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
377
384
. 10.1115/1.1315592
40.
Fuge
,
M.
,
Stroud
,
J.
, and
Agogino
,
A.
,
2013
, “
Automatically Inferring Metrics for Design Creativity
,”
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Portland, OR
,
Aug. 4–7
.
41.
Ahmed
,
F.
,
Ramachandran
,
S. K.
,
Fuge
,
M.
,
Hunter
,
S.
, and
Miller
,
S.
,
2019
, “
Measuring and Optimizing Design Variety Using Herfindahl Index
,”
ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Anaheim, CA
,
Aug. 18–21
.
42.
Ahmed
,
F.
, and
Fuge
,
M.
,
2017
, “
Ranking Ideas for Diversity and Quality
,”
ASME J. Mech. Des.
,
140
(
1
), p.
011101
. 10.1115/1.4038070
43.
Ahmed
,
F.
,
Fuge
,
M.
, and
Gorbunov
,
L. D.
,
2016
, “
Discovering Diverse, High Quality Design Ideas From a Large Corpus
,”
ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Charlotte, NC
,
Aug. 21–24
.
44.
Kulesza
,
A.
, and
Taskar
,
B.
,
2011
, “
k-dpps: Fixed-Size Determinantal Point Processes
,”
Proceedings of the 28th International Conference on Machine Learning, ICML 2011
,
Scheffer
,
T.
, and
Getoor
,
L.
, eds.
Bellevue, WA
,
June 28–July 2
,
Omnipress
, pp.
1193
1200
.
45.
Borodin
,
A.
,
2009
,
The Oxford Handbook of Random Matrix Theory
,
Oxford University Press
,
Oxford, UK
.
46.
Drela
,
M.
,
1989
, “Xfoil: An Analysis and Design System for Low Reynolds Number Airfoils,”
Low Reynolds Number Aerodynamics
,
T. J.
Mueller
, ed.,
Springer
,
New York
, pp.
1
12
.
47.
He
,
K.
,
Zhang
,
X.
,
Ren
,
S.
, and
Sun
,
J.
,
2016
, “
Deep Residual Learning for Image Recognition
,”
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
,
Las Vegas, NV
,
June 27–30
, pp.
770
778
.
48.
Kingma
,
D. P.
, and
Ba
,
J.
,
2015
, “
Adam: A Method for Stochastic Optimization
,”
3rd International Conference on Learning Representations
,
San Diego, CA
,
May 7–9
.
49.
Gómez-Bombarelli
,
R.
,
Wei
,
J. N.
,
Duvenaud
,
D.
,
Hernández-Lobato
,
J. M.
,
Sánchez-Lengeling
,
B.
,
Sheberla
,
D.
,
Aguilera-Iparraguirre
,
J.
,
Hirzel
,
T. D.
,
Adams
,
R. P.
, and
Aspuru-Guzik
,
A.
,
2018
, “
Automatic Chemical Design Using a Data-Driven Continuous Representation of Molecules
,”
ACS Central Sci.
,
4
(
2
), pp.
268
276
. 10.1021/acscentsci.7b00572
You do not currently have access to this content.