Identifying the key microstructure representations is crucial for computational materials design (CMD). However, existing microstructure characterization and reconstruction (MCR) techniques have limitations to be applied for microstructural materials design. Some MCR approaches are not applicable for microstructural materials design because no parameters are available to serve as design variables, while others introduce significant information loss in either microstructure representation and/or dimensionality reduction. In this work, we present a deep adversarial learning methodology that overcomes the limitations of existing MCR techniques. In the proposed methodology, generative adversarial networks (GAN) are trained to learn the mapping between latent variables and microstructures. Thereafter, the low-dimensional latent variables serve as design variables, and a Bayesian optimization framework is applied to obtain microstructures with desired material property. Due to the special design of the network architecture, the proposed methodology is able to identify the latent (design) variables with desired dimensionality, as well as capturing complex material microstructural characteristics. The validity of the proposed methodology is tested numerically on a synthetic microstructure dataset and its effectiveness for microstructural materials design is evaluated through a case study of optimizing optical performance for energy absorption. Additional features, such as scalability and transferability, are also demonstrated in this work. In essence, the proposed methodology provides an end-to-end solution for microstructural materials design, in which GAN reduces information loss and preserves more microstructural characteristics, and the GP-Hedge optimization improves the efficiency of design exploration.

References

1.
Thornton
,
K.
,
Nola
,
S.
,
Garcia
,
R. E.
,
Asta
,
M.
, and
Olson
,
G.
,
2009
, “
Computational Materials Science and Engineering Education: A Survey of Trends and Needs
,”
JOM
,
61
(
10
), p.
12
.
2.
Olson
,
G. B.
,
1997
, “
Computational Design of Hierarchically Structured Materials
,”
Science
,
277
(
5330
), pp.
1237
1242
.
3.
Saito
,
T.
,
2013
,
Computational Materials Design
, Vol.
34
,
Springer Science & Business Media
, Berlin, Germany.
4.
Kuehmann
,
C.
, and
Olson
,
G.
,
2009
, “
Computational Materials Design and Engineering
,”
Mater. Sci. Technol.
,
25
(
4
), pp.
472
478
.
5.
Vickers
,
J.
, 2015, “
Materials Genome Initiative
,” Energy Efficiency & Renewable Energy, Washington, DC.
6.
Agrawal
,
A.
, and
Choudhary
,
A.
,
2016
, “
Perspective: Materials Informatics and Big Data: Realization of the “Fourth Paradigm” of Science in Materials Science
,”
APL Mater.
,
4
(
5
), p.
053208
.
7.
Zhao
,
H.
,
Li
,
X.
,
Zhang
,
Y.
,
Schadler
,
L. S.
,
Chen
,
W.
, and
Brinson
,
L. C.
,
2016
, “
Perspective: Nanomine: A Material Genome Approach for Polymer Nanocomposites Analysis and Design
,”
APL Mater.
,
4
(
5
), p.
053204
.
8.
Wang
,
Y.
,
Zhang
,
Y.
,
Zhao
,
H.
,
Li
,
X.
,
Huang
,
Y.
,
Schadler
,
L. S.
,
Chen
,
W.
, and
Brinson
,
L. C.
,
2018
, “
Identifying Interphase Properties in Polymer Nanocomposites Using Adaptive Optimization
,”
Compos. Sci. Technol.
,
162
(7), pp. 146–155.
9.
Paul
,
D.
, and
Robeson
,
L. M.
,
2008
, “
Polymer Nanotechnology: Nanocomposites
,”
Polymers
,
49
(
15
), pp.
3187
3204
.
10.
Natarajan
,
B.
,
Li
,
Y.
,
Deng
,
H.
,
Brinson
,
L. C.
, and
Schadler
,
L. S.
,
2013
, “
Effect of Interfacial Energetics on Dispersion and Glass Transition Temperature in Polymer Nanocomposites
,”
Macromolecules
,
46
(
7
), pp.
2833
2841
.
11.
Hassinger
,
I.
,
Li
,
X.
,
Zhao
,
H.
,
Xu
,
H.
,
Huang
,
Y.
,
Prasad
,
A.
,
Schadler
,
L.
,
Chen
,
W.
, and
Brinson
,
L. C.
,
2016
, “
Toward the Development of a Quantitative Tool for Predicting Dispersion of Nanocomposites Under Non-Equilibrium Processing Conditions
,”
J. Mater. Sci.
,
51
(
9
), pp.
4238
4249
.
12.
Brough
,
D. B.
,
Wheeler
,
D.
,
Warren
,
J. A.
, and
Kalidindi
,
S. R.
,
2017
, “
Microstructure-Based Knowledge Systems for Capturing Process-Structure Evolution Linkages
,”
Curr. Opin. Solid State Mater. Sci.
,
21
(
3
), pp.
129
140
.
13.
Liu
,
R.
,
Yabansu
,
Y. C.
,
Yang
,
Z.
,
Choudhary
,
A. N.
,
Kalidindi
,
S. R.
, and
Agrawal
,
A.
,
2017
, “
Context Aware Machine Learning Approaches for Modeling Elastic Localization in Three-Dimensional Composite Microstructures
,”
Integr. Mater. Manuf. Innov.
,
6
, p. 160.
14.
Yang
,
Z.
,
Yabansu
,
Y. C.
,
Al-Bahrani
,
R.
,
Liao
,
W-K.
,
Choudhary
,
A. N.
,
Kalidindi
,
S. R.
, and
Agrawal
,
A.
,
2018
, “
Deep Learning Approaches for Mining Structure-Property Linkages in High Contrast Composites From Simulation Datasets
,”
Comput. Mater. Sci.
,
151
, pp.
278
287
.
15.
Yu
,
S.
,
Zhang
,
Y.
,
Wang
,
C.
,
Lee
,
W-K.
,
Dong
,
B.
,
Odom
,
T. W.
,
Sun
,
C.
, and
Chen
,
W.
,
2017
, “
Characterization and Design of Functional Quasi-Random Nanostructured Materials Using Spectral Density Function
,”
ASME J. Mech. Des.
,
139
(
7
), p.
071401
.
16.
Fullwood
,
D. T.
,
Niezgoda
,
S. R.
,
Adams
,
B. L.
, and
Kalidindi
,
S. R.
,
2010
, “
Microstructure Sensitive Design for Performance Optimization
,”
Prog. Mater. Sci.
,
55
(
6
), pp.
477
562
.
17.
Bostanabad
,
R.
,
Zhang
,
Y.
,
Li
,
X.
,
Kearney
,
T.
,
Brinson
,
L. C.
,
Apley
,
D. W.
,
Liu
,
W. K.
, and
Chen
,
W.
, “
Computational Microstructure Characterization and Reconstruction: Review of the State-of-the-Art Techniques
,”
Prog. Mater. Sci.
,
95
, pp. 1–41.
18.
Jiao
,
Y.
,
Stillinger
,
F.
, and
Torquato
,
S.
,
2007
, “
Modeling Heterogeneous Materials Via Two-Point Correlation Functions: Basic Principles
,”
Phys. Rev. E
,
76
(
3
), p.
031110
.
19.
Xu
,
H.
,
Dikin
,
D.
,
Burkhart
,
C.
, and
Chen
,
W.
,
2014
, “
Descriptor-Based Methodology for Statistical Characterization and 3d Reconstruction of Microstructural Materials
,”
Comput. Mater. Sci.
,
85
, pp.
206
216
.
20.
Jiang
,
Z.
,
Chen
,
W.
, and
Burkhart
,
C.
,
2013
, “
Efficient 3d Porous Microstructure Reconstruction Via Gaussian Random Field and Hybrid Optimization
,”
J. Microsc.
,
252
(
2
), pp.
135
148
.
21.
Bostanabad
,
R.
,
Bui
,
A. T.
,
Xie
,
W.
,
Apley
,
D. W.
, and
Chen
,
W.
,
2016
, “
Stochastic Microstructure Characterization and Reconstruction Via Supervised Learning
,”
Acta Mater.
,
103
, pp.
89
102
.
22.
Cang
,
R.
,
Xu
,
Y.
,
Chen
,
S.
,
Liu
,
Y.
,
Jiao
,
Y.
, and
Ren
,
M. Y.
,
2017
, “
Microstructure Representation and Reconstruction of Heterogeneous Materials Via Deep Belief Network for Computational Material Design
,”
ASME J. Mech. Des.
,
139
(
7
), p.
071404
.
23.
Li
,
X.
,
Zhang
,
Y.
,
Zhao
,
H.
,
Burkhart
,
C.
,
Brinson
,
L. C.
, and
Chen
,
W.
,
2018
, “
A Transfer Learning Approach for Microstructure Reconstruction and Structure-Property Predictions
,” preprint
arXiv: 02784
.https://arxiv.org/abs/1805.02784
24.
Lubbers
,
N.
,
Lookman
,
T.
, and
Barros
,
K.
,
2017
, “
Inferring Low-Dimensional Microstructure Representations Using Convolutional Neural Networks
,”
Phys. Rev. E
,
96
(
5
), p.
052111
.
25.
Paulson
,
N. H.
,
Priddy
,
M. W.
,
McDowell
,
D. L.
, and
Kalidindi
,
S. R.
,
2017
, “
Reduced-Order Structure-Property Linkages for Polycrystalline Microstructures Based on 2-Point Statistics
,”
Acta Mater.
,
129
, pp.
428
438
.
26.
Xu
,
H.
,
Liu
,
R.
,
Choudhary
,
A.
, and
Chen
,
W.
,
2015
, “
A Machine Learning-Based Design Representation Method for Designing Heterogeneous Microstructures
,”
ASME J. Mech. Des.
,
137
(
5
), p.
051403
.
27.
Kingma
,
D. P.
, and
Welling
,
M.
,
2014
, “
Auto-Encoding Variational Bayes
,” preprint
arXiv: 1312.6114
.https://arxiv.org/abs/1312.6114
28.
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
, Neural Information Processing Systems, Montreal, Canada, pp.
2672
2680
.
29.
Makhzani
,
A.
,
Shlens
,
J.
,
Jaitly
,
N.
,
Goodfellow
,
I.
, and
Frey
,
B.
,
2016
, “
Adversarial Autoencoders
,” preprint
arXiv:1511.05644
.https://arxiv.org/abs/1511.05644
30.
Dumoulin
,
V.
,
Belghazi
,
I.
,
Poole
,
B.
,
Lamb
,
A.
,
Arjovsky
,
M.
,
Mastropietro
,
O.
, and
Courville
,
A.
,
2017
, “
Adversarially Learned Inference
,” preprint
arXiv:1606.00704
.https://arxiv.org/abs/1606.00704
31.
Cang
,
R.
,
Li
,
H.
,
Yao
,
H.
,
Jiao
,
Y.
, and
Ren
,
Y.
,
2018
, “
Improving Direct Physical Properties Prediction of Heterogeneous Materials From Imaging Data Via Convolutional Neural Network and a Morphology-Aware Generative Model
,” preprint
arxiv:1712.03811
.https://arxiv.org/abs/1712.03811
32.
Guo
,
T.
,
Lohan
,
D. J.
,
Cang
,
R.
,
Ren
,
M. Y.
, and
Allison
,
J. T.
,
2018
, “
An Indirect Design Representation for Topology Optimization Using Variational Autoencoder and Style Transfer
,”
AIAA
Paper No. AIAA 2018-0804.
33.
Mosser
,
L.
,
Dubrule
,
O.
, and
Blunt
,
M. J.
,
2017
, “
Reconstruction of Three-Dimensional Porous Media Using Generative Adversarial Neural Networks
,”
Phys. Rev. E
,
96
(
4
), p.
043309
.
34.
Mosser
,
L.
,
Dubrule
,
O.
, and
Blunt
,
M. J.
,
2017
, “
Stochastic Reconstruction of an Oolitic Limestone by Generative Adversarial Networks
,” preprint
arXiv:1712.02854
.https://arxiv.org/abs/1712.02854
35.
Osborne
,
M. J.
, and
Rubinstein
,
A.
,
1994
,
A Course in Game Theory
,
MIT Press
, Cambridge, MA.
36.
Radford
,
A.
,
Metz
,
L.
, and
Chintala
,
S.
,
2016
, “
Unsupervised Representation Learning With Deep Convolutional Generative Adversarial Networks
,” preprint
arXiv:1511.06434
.https://arxiv.org/abs/1511.06434
37.
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
.
38.
Nair
,
V.
, and
Hinton
,
G. E.
,
2010
, “
Rectified Linear Units Improve Restricted Boltzmann Machines
,”
27th International Conference on Machine Learning (ICML-10)
, Haifa, Israel, June 21–24, pp.
807
814
.
39.
Maas
,
A. L.
,
Hannun
,
A. Y.
, and
Ng
,
A. Y.
,
2013
, “
Rectifier Nonlinearities Improve Neural Network Acoustic Models
,” 30th International Conference on Machine Learning (
ICML
), Atlanta, Georgia, June 16–21.https://ai.stanford.edu/~amaas/papers/relu_hybrid_icml2013_final.pdf
40.
Salimans
,
T.
,
Goodfellow
,
I.
,
Zaremba
,
W.
,
Cheung
,
V.
,
Radford
,
A.
, and
Chen
,
X.
,
2016
, “
Improved Techniques for Training Gans
,” 30th Conference on Neural Information Processing Systems (NIPS), Barcelona, Spain, Dec. 5–8, pp.
2234
2242
.
41.
Gatys
,
L.
,
Ecker
,
A. S.
, and
Bethge
,
M.
,
2015
, “
Texture Synthesis Using Convolutional Neural Networks
,” 28th International Conference on Neural Information Processing Systems, Montreal, QC, Canada, Dec. 7–12, pp.
262
270
.
42.
Simonyan
,
K.
, and
Zisserman
,
A.
,
2015
, “
Very Deep Convolutional Networks for Large-Scale Image Recognition
,” preprint arXiv:1409.1556.
43.
Zhao
,
J.
,
Mathieu
,
M.
, and
LeCun
,
Y.
,
2017
, “
Energy-Based Generative Adversarial Network
,” preprint arXiv:1609.03126.
44.
Kingma
,
D. P.
, and
Ba
,
J.
,
2017
, “
Adam: A Method for Stochastic Optimization
,” preprint arXiv:1412.6980.
45.
Lu
,
B.
, and
Torquato
,
S.
,
1992
, “
Lineal-Path Function for Random Heterogeneous Materials
,”
Phys. Rev. A
,
45
(
2
), p.
922
.
46.
McKay
,
M. D.
,
Beckman
,
R. J.
, and
Conover
,
W. J.
,
2000
, “
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code
,”
Technometrics
,
42
(
1
), pp.
55
61
.
47.
Rasmussen
,
C. E.
,
2004
, “
Gaussian Processes in Machine Learning
,”
Advanced Lectures on Machine Learning
,
Springer
, Berlin, pp.
63
71
.
48.
Hoffman
,
M. D.
,
Brochu
,
E.
, and
de Freitas
,
N.
,
2011
, “
Portfolio Allocation for Bayesian Optimization
,” Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, Barcelona, Spain, July 14–17, pp.
327
336
.
49.
Jones
,
D. R.
,
Schonlau
,
M.
, and
Welch
,
W. J.
,
1998
, “
Efficient Global Optimization of Expensive Black-Box Functions
,”
J. Global Optim.
,
13
(
4
), pp.
455
492
.
50.
Kushner
,
H. J.
,
1964
, “
A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise
,”
J. Basic Eng.
,
86
(
1
), pp.
97
106
.
51.
Auer
,
P.
,
2002
, “
Using Confidence Bounds for Exploitation-Exploration Trade-Offs
,”
J. Mach. Learn. Res.
,
3
, pp.
397
422
.
52.
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, pp.
2172
2180
.
53.
Yosinski
,
J.
,
Clune
,
J.
,
Bengio
,
Y.
, and
Lipson
,
H.
,
2014
, “
How Transferable Are Features in Deep Neural Networks?
,” 27th International Conference on Neural Information Processing Systems, Montreal, QC, Canada, Dec. 8–13, pp.
3320
3328
.
54.
Lee
,
W.-K.
,
Yu
,
S.
,
Engel
,
C. J.
,
Reese
,
T.
,
Rhee
,
D.
,
Chen
,
W.
, and
Odom
,
T. W.
,
2017
, “
Concurrent Design of Quasi-Random Photonic Nanostructures
,”
Proc. Natl. Acad. Sci.
,
114
(
33
), pp.
8734
8739
.
55.
He
,
K.
,
Zhang
,
X.
,
Ren
,
S.
, and
Sun
,
J.
,
2016
, “
Deep Residual Learning for Image Recognition
,”
IEEE Conference on Computer Vision and Pattern Recognition
(
CVPR
), Las Vegas, NV, June 27–30, pp.
770
778
.
56.
Mnih
,
V.
,
Heess
,
N.
,
Graves
,
A.
, et al.
2014
, “
Recurrent Models of Visual Attention
,” 27th International Conference on Neural Information Processing Systems, Montreal, QC, Canada, Dec. 8–13, pp.
2204
2212
.
You do not currently have access to this content.