Interpretable deep learning for guided
structure-property explorations in photovoltaics
Balaji Sesha Sarath Pokuri
Department of Mechanical Engineering
Iowa State University
Ames, IA 50011
Sambuddha Ghosal
Department of Mechanical Engineering,
Department of Computer Science
Iowa State University
Ames, IA 50011
Apurva Kokate
Department of Computer Science,
Iowa State University
Ames, IA 50011
Baskar Ganapathysubramanian
Department of Mechanical Engineering
Iowa State University
Ames, IA 50011
Soumik Sarkar
Department of Mechanical Engineering
Iowa State University
Ames, IA 50011
Abstract
The performance of an organic photovoltaic device is intricately connected to its
active layer morphology. This connection between the active layer and device
performance is very expensive to evaluate, either experimentally or computationally.
Hence, designing morphologies to achieve higher performances is non-trivial and
often intractable. To solve this, we first introduce a deep convolutional neural
network (CNN) architecture that can serve as a fast and robust surrogate for
the complex structure-property map. Several tests were performed to gain trust
in this trained model. Then, we utilize this fast framework to perform robust
microstructural design to enhance device performance.
1 Introduction
Mapping microstructure to macro-scale property of materials and controlling such relationships has
been an important theme of modern materials research [
11
]. Despite the investment of millions of
research hours and dollars [
1
], this largely remains elusive to the research community. A major reason
is that the map from microstructure (domain) to property (co-domain) is inherently non-surjective
and highly non-linear, making incremental judgments based on incremental modifications infeasible.
Added to this is the infinite dimensionality of microstructure space, which makes the description of
the domain in-exhaustible. Hence, estimating the property of one morphology from another visually
similar morphology is not trivial – each morphology will require a full scale experiment/simulation
for reliable quantification. In this paper, we discuss one such problem and present a solution using
modern machine learning paradigms. More specifically, we look at solving the relationship between
active layer microstructure and performance of an Organic Solar Cell (OSC). OSCs utilize a bulk
heterojunction morphology in the active layer to efficiently convert incident solar radiation into
Workshop on Machine Learning for Molecules and Materials, (NIPS 2018), Montréal, Canada.
electrical energy [
19
]. The total power conversion efficiency is very intricately related to this material
distribution if acceptor and donor polymers in the active layer (See Sec. 2). This relationship has
several contradicting and competing factors. For example, larger interfacial area between acceptor
and donor regions enables higher production of charges, but simultaneously also increases the loss of
charges through recombination. While larger domains can help transport charges faster, they also
impede excitons from dissociating into charges. These contradictory features make this an exciting
area of research, finally culminating in the search for the most efficient microstructures for solar
energy conversion.
Traditionally, this structure-property map was computationally resolved either through a detailed
and tedious PDE simulation [
14
] or Kinetic Monte Carlo simulation [
4
,
16
,
15
,
21
] or through
identification of surrogate descriptors of performance [
22
]. While the first method is robust and
accurate, it is limited by the size of microstructure. Often it requires massive, robust, and well
established computational resources along with a perfectly scaling computational model to solve
for even simple representations of morphologies. Hence such analysis was often limited to 2D
microstructure quantification, although 3D quantification is not uncommon [
14
]. The second method
overcomes most of these computational challenges. Typically intuitive features of the microstructure
such as domain sizes and orientations, connectivities and islands are quantified (using graphs) instead
of performing a full scale PDE simulation. This technique is intuitive and requires substantially
less computational resources (although memory requirements are higher). Subsequently, it enables
simultaneous parallel analysis of multiple morphologies at once. Moreover, close to linear dependence
of several stage efficiencies on these microstructural descriptors was also shown [
23
]. However, since
the dimensionality of the domain is infinite, the intuitive metrics tend to be a limited description of
the bigger reality.
In this work, we take the approach called DLSP (Deep Learning based Structure-Property exploration)
involving machine learning to solve this complex map of microstructure to performance (depicted
in Fig. 1). Modern machine learning has been shown to be a powerful tool to learn complex
phenomena [
6
], especially image recognition [
24
,
2
]. This technique has the potential to identify
features in the microstructure that are not intuitive to the simple eye. By posing the task of enumerating
microstructure informed performance as an image recognition problem, we can easily and confidently
extend current implementations of neural networks to this problem. Furthermore, interpreting the
trained network can give both trust in training as well as insights into the most impactful features of a
microstructure, thereby enabling researchers to tailor processes to create such features.
Figure 1: DLSP framework: We construct a forward map from morphology to performance. Upon
building trust in this trained model, it was further used for performing manual and automated design.
2
The rest of the paper is organised as follows: In Sec. 2, we discuss the physics behind the problem of
morphology design. Subsequently, a short discussion on the methods for data generation and labelling
is discussed. The details of network architecture and other machine learning parameters are discussed
in Sec. 3. In Sec. 4, the results of training, validation and testing on in-sample and out-of-sample
morphologies and performance interpretations are presented. The benefits of such fast interpretable
forward surrogate model are demonstrated through the design of property-maximized-microstructure
in Sec. 5. Finally in Sec. 6, key takeaways from this work and future directions are discussed.
2 Physics of structure-property explorations in photovoltaics
2.1 Organic Photovoltaics
Organic photovoltaic devices are energy harvesting devices which employ organic materials for
solar energy conversion. These provide multiple advantages over traditional silicon based cells, like
flexibility, transparency and ease of manufacturability. They however are limited by their efficiency
of operation. Although major breakthroughs in processing and materials have improved the efficiency
drastically, they still lag behind the traditional photovoltaics.
The efficiency of these devices is intricately dependant on the material distribution/morphology in the
active layer. The active layer generally is a bulk hetero-junction, enabling multiple sites for charge
generation. Several features of the morphology have different roles in the process of converting solar
energy. The ability to change these morphological features by changing the processing protocol is a
major source of control in these devices.
There are several stages during the solar power conversion in an OPV. Firstly, the incident solar
energy generates excitons in the donor phase. These excitons are highly unstable and need to diffuse
to a nearest interface with the acceptor material to separate into positive and negative charges. This
diffusion to the interface is critical to evaluate the efficiency of absorption of incident light. The
dissociation of excitons to form charges depends on the nature of interface and the materials in the
interface. For example, interfaces with non-aligned crystal boundaries show lower dissociation than
those with aligned crystals . In the next stage, these charges (positive charge in the donor and negative
charge in the acceptor) need to be drifted to the respective electrode to produce electricity. Usually,
this drift is provided by the potential difference between the two electrodes. However, these charges
also encounter other interfaces which have pairs of positive and negative charges, leading to potential
recombination. In summary, the total efficiency of the active layer involves exciton production, charge
separation and charge transportation efficiencies.
In this context, quantifying the dependence of the device as well as stage efficiencies becomes a
critical part in developing strategies to design processing conditions. It can already be seen that the
role of morphology cannot be over-estimated in the power conversion efficiency. Hence strategies
were developed to quantify the efficiencies these morphologies. While these techniques are robust
and rigorous, they are expensive and time intensive. This makes them infeasible for further designing
morphologies, which often requires several quantifications. So, we turn to modern fast methods of
quantifying data, especially images. We represent the morphologies as images and take advantage of
the deep convolutional neural networks to do performance based classification.
2.2 Data generation and quantification
In order to train the network (to be described in Sec. 3), we generate a dataset of microstructural
images using the Cahn-Hilliard equation. This process generates time series of images that can be
treated as independent images for the sake of training. This method helps to quickly produce several
thousands of images within a very short amount of time. Previous analysis using these images can
be found in [
23
]. A characteristic of this procedure for generating morphologies through simulation
is their similarity to morphologies in real active layers produced during thermal annealing. In the
morphology, the domains are similar in size and have smooth interface contours. These characteristics
will also help us to build trust in the training process by manually create morphologies breaking these
characteristics and testing the performance of the trained network. More implications of this will
be in discussed in Sec. 4. Using data augmentation techniques over the originally simulated data,
we finally produce a dataset of nearly
65, 000
(2D) morphologies. Each morphology is a gray-scale
image of size 101px × 101px.
3
Figure 2: Proposed CNN architecture. Note that this is much shallower and has less trainable
parameters compared to VGG-16 and ResNet-50.
These morphologies were then characterized using an in-house physics based simulator [
14
]. This
simulator uses steady state excitonic drift diffusion equation to model the processes of exciton
dissociation and charge transport. We use the short circuit current
J
sc
as a means of labelling the
data. The whole data was divided into
10
classes which are equally spaced between the best(
J
sc
=
7mA/cm
2
) and worst performing(J
sc
= 0.2mA/cm
2
) in the data.
3 Proposed Deep Learning framework
Convolutional Neural Networks (CNN) are well-established architectures for classification of images.
They have proved to perform outstandingly well in terms of efficiently extracting complex features
from images and function as a classification technique when provided with sufficient data [
6
,
24
,
2
,
17, 20, 8, 7]. Hence, to address the task above, we develop a CNN based architecture to classify the
morphologies. The data label, originally a continuous value, is discretized into
10
bins. The network
architecture is depicted in Fig. 2, with
1.2
million learning parameters. This architecture was taken
from [
3
], where the original aim was to determine steering angles for a car from the dash camera
image. The task is similar here also – both use images from time series data with predefined label
to train. Our network is slightly shallower, to enable better training, enhanced with better feature
visualization. This is also to prevent problems that can arise with deeper networks – vanishing (or
exploding) gradients [
9
], which provide a hindrance to convergence, and the accuracy saturation with
increasing depth. Shallower networks also provide better feature visualizations – in this case, we use
saliency maps [
12
] to visualize learnt features(Sec. 4). The network was trained for approximately
70
epochs (with
18s
per epoch) with a learning rate of
0.0001
, on the
45, 000
-image training set to
reach the desired accuracy (
95.41%
). The crossentropy (categorical) loss (or cost) function along
with the Adam optimizer [13] was used to minimize the error.
Apart from this, we also tested two standard architectures with our dataset:
•
VGG-16 (learning parameters
50
million) , with learning rate of
0.0001
, batch size of
128
initialized with random weights was also trained on the training dataset, achieving a test
accuracy of 96.61% at epoch 70 (with 180s per epoch).
•
ResNet-
50
(learning parameters
23
million) , with learning rate of
0.0001
, batch size of
128
initialized with random weights was also trained on the training dataset, achieving a test
accuracy of 96.45% at epoch 70 (with 580s per epoch).
We can see that our custom (shallower) CNN, while with lower training parameters, performs very
similar to the established deep CNNs. Therefore, we defer the choice of selecting a "good" network
to be based on the learnt features and out-of-sample performance and not just the accuracy/f1-score
of the testing dataset.
4
4 Results
Figure 3 shows the confusion matrices for in-sample test data classification. It had an accuracy of
95.41%
and F1-score of
94.45%
. From the confusion matrix, it can clearly be seen that most of the
classification is correct, and those which are wrongly predicted are only off by one class. This wrong
prediction is not unexpected, as we are binning a continuous variable into non-overlapping classes.
The edge cases have the potential to be misclassified. It is also to be noted that other two standard
architectures show similar confusion matrices, with similar prediction accuracies.
Figure 3: Confusion matrix for insample test predictions. Notice the heavily diagonally dominant
matrix, indicating a very good classification accuracy.
4.1 Out-of-sample testing
While it is a known fact in the machine learning community that neural networks in their training
phase can possibly overfit (depending on the model capacity, amount of training data and training
hyperparameters), we resort to two methods of checking the robustness of our trained network(s).
As noted earlier, the morphology data used for training is generated by solving a PDE. This inherits
certain properties to the data such as smooth contours and uniform domain sizes. Hence we try to
systematically break these assumptions about the dataset and see the performance of the network.
Firstly, we test the network on a columnar structure (Fig. 4b). This is a widely studied structure, often
considered as a high performing morphology. This is a completely out-of-sample data. This columnar
morphology also has several sharp interface contours, which are completely absent in the training
dataset. The results are in Fig. 4b. The actual
J
sc
values from a full scale drift-diffusion simulation
(along with the corresponding true label) are also presented. We can see how the network is able to
predict the correct label corresponding to each of the columnar microstructures.
5
(a) Saliency map for in-sample
testing morphologies
(b) Saliency maps for out-of-sample morpholo-
gies
(c) Saliency maps for ’opti-
mized’ structures from [5]
Figure 4: Saliency maps and performance of our custom trained CNN. Note how the saliency maps
closely follow the interface regions in the microstructure. It should also be noted that the networks
shows good performance even on samples outside the training dataset.
Next, we also test our framework with the "high" performing morphologies described in [
5
]. These
morphologies were obtained through optimization strategies using graph based surrogate performance
descriptors. We can also see how our network has rightly identified (Fig. 4c) all these as high
performing class label 9.
4.2 Interpretability
We next query the network to understand the learnt features. For this, we use saliency maps [
12
,
18
] to
identify important features of the image input. Saliency map visualization is a visualization technique
that generates heat maps on test images that bring out (highlight) the regions (microstructure regions,
for our case) the trained CNN model focuses on to generate it’s classification output. The heat-map
signifies the aspect that regions highlighted more than the others carry a greater significance towards
the model’s classification output. Fig. 4 shows the saliency maps for morphologies in the data,
columnar structures and the "high" performing morphologies identified in [5].
We can see, in all Figs. 4a, 4b & 4c, how the network highlights interface between the acceptor and
donor regions. This is a vital test of the learning capabilities of the network. In terms of the underlying
physics, the interface is the most critical feature of performance. Properly configured interface enables
charge separation and hence better conversion. Poorly configured interface enables poor dissociation
and higher recombination, which depreciates conversion efficiency. Finally, interface further away
from the top and bottom electrodes are more critical, as the charges produced at these locations have
a higher chance of recombination. We can see from Fig. 4 how the network is able to find the right
type of interface as critical to device performance.
Furthermore, we also observe from Fig. 5 that the saliency maps from the standard deep networks
(VGG-
16
and ResNet-
50
) are unable to locate these above features. Although, the test accuracy is
slightly higher than our custom network, we see that the saliency outputs do not provide us with
any understandable information. This observation is in line with [
10
], where it was shown that
deeper models are harder to explain than their shallower counterparts even though they may achieve
a higher classification accuracy. These results signify the importance of tailoring architectures to the
application. Thus, for performing morphology design, we use the custom architecture as a surrogate
map from the microstructure space to the performance space.
6
Figure 5: Comparison of Saliency map outputs for our Custom Model (second column), VGG-net
shows an example image for class 0, bottom row shows an example image from omega morphologies
(correctly predicted as class 9 by our custom model)
5 Morphology design
Having developed a fast and trust-worthy surrogate map from the microstructures to the performance,
we can use it enable microstructural design. In this section, we show two separate techniques,
manual and automated, for designing microstructures. The goal of both these techniques is to explore
(uncanny) morphologies that demonstrate superior performance. Traditionally, this was generally
achieved through a conventional optimization strategy, like simulated annealing, where an initial
morphology is tweaked repeatedly to achieve superior performance. At every stage, the current
morphology is evaluated for its performance. Subsequently, the whole process requires several
computationally expensive evaluations and hence becomes time consuming. But, with the above
demonstrated framework, evaluating the morphology becomes significantly faster and easier. Hence
it provides an very powerful way to quickly ’evolve’ morphologies to optimize performance.
5.1 Manual design
In order to enable manual exploration, we created a browser interface (Fig. 6) that enables the user to
interactively modify morphologies to both visualize and improve morphology performance. Using
this interface, the user can incrementally add changes to the initial morphology that can improve the
predicted performance. Since the performance assessment is done by the trained CNN, the whole
process happens real-time. Fig. 7 shows how one can modify images to include several features of
varying sizes, with the aim of improving performance. This tool can in turn help identify features of
morphology that affect the performance.
Figure 6: Browser interface for performing manual exploration and design.
7
(a) Class 1
(b) Class 2
(c) Class 3
(d) Class 9
(e) Class 3
(f) Class 9
(g) Class 2/3
Figure 7: Exploration by manual design: Notice how the trained network captures the underlying
physics – addition of non-interfering features improves performance. When a ‘blocking’ layer
was added in (e), the performance drops. Also note that increasing domain size (in (g)) leads
to performance drop, in conjunction with reduced exciton dissociation efficiency and increased
recombination.
(a) Iteration 10 (b) Iteration 30 (c) Iteration 50
Figure 8: Exploration by automated design: The optimization started with a bilayer structure. Notice
how the framework directs the formation of finer features
5.2 Automated design
While the above interface may serve very well to understand the influence of morphological features
on performance, it is not feasible to perform a full scale morphology design. Manual exploration
space, we link this fast surrogate with a probabilistic optimization algorithm to find those optimal
structures. More specifically we use a population based incremental learning (PBIL) approach to
model morphologies and evolve them to achieve optimum performance. PBIL estimates the explicit
probability distribution of the optimal morphology. The multi variate probability distribution is stored
as a probability matrix
P
of the 2D morphology, i.e., each pixel is associated with a probability. This
matrix
P
is updated as follows: the optimization starts with a given probability matrix, generally
based on the intuition of the researcher. Subsequently,
n
morphology instances are sampled around
this matrix
P
. For each realization, the DLSP is deployed to evaluate the performance,
f
j
, j ∈ [1, n]
.
Then
n
b
best samples (
n
b
< n
) are used to calculate,
P
u
, the probabilistic update matrix. Next,
the probability vector is updated according to
P = P · (1 − l
r
) + P
b
· l
r
, where
l
r
is the learning
rate. Intuitively, the update step reinforces features present in the best performing morphologies,
and dampens those missing. The algorithm terminates by standard criteria (iteration limits and
improvement bounds). Only the probability matrix is stored and multiple realizations’ evaluations
can embarrassingly parallel.
The results of PBIL optimization are very promising. Fig. 8 indicates structure at different scales,
mimicking finger-like fractal structures. These are very similar to the results presented in [5].
6 Conclusion
In this work, we address the issue of designing active layer morphologies to enhance device perfor-
mance, especially in OPV applications. The usual methods to quantify morphology are either too
costly or too simplistic. Hence we take a data-driven approach (DLSP) to create a morphology quan-
tifier that can perform fast evaluations. We train a custom designed CNN that reads the morphology
and classifies it into
10
bins of increasing performance metric
J
sc
. Using out-of-sample datasets, we
confirm that there is no severe over-fitting issues during the training process. Two other standard
8
networks (VGG-16 and ResNet-50) were trained end-to-end independently. It was observed that
the custom network, although shallower, gave very similar accuracy. However, our custom network
performed much better when visualized using saliency maps as well as when tested on out-of-sample
datasets. It identified critical features of the interface in the morphology, which both VGG-16 and
ResNet-50 failed to identify consistently. The custom designed network is then used to perform
morphology design for achieving enhanced performance. Two approaches were taken to do this –
the first one aims to inform the user about the effect of morphology on performance. The second
approach uses the trust-worthy network as a fast cost function and performs morphology optimization
using PBIL algorithm. It should be noted that this work serves as a proof of concept of using deep
neural networks for material morphology quantification. It raises several other interesting questions
of how to integrate physical phenomena into the training process. Can these physics based intuitions
can be exploited to reduce the demand on the size of data for training? Can a most effective dataset
be created to reduce the training data? Can we make the training process more robust to adversarial
attacks? All these questions form the scope of future study.
References
[1]
Designing materials to revolutionize and engineer our future.
https://www.nsf.gov/
funding/pgm_summ.jsp?pims_id=505073. Accessed: 2018-11-01.
[2]
B. Alipanahi A. Delong, M.T. Weirauch and B.J. Frey. Predicting the sequence specificities of
dna-and rna-binding proteins by deep learning. Nature Biotechnology, 33(8):831–838.
[3]
M. Bojarski, D. Del Testa, D. Dworakowski, B. Firner, B. Flepp, P. Goyal, L. D. Jackel,
M. Monfort, U. Muller, J. Zhang, et al. End to end learning for self-driving cars. arXiv preprint
arXiv:1604.07316, 2016.
[4]
M. Casalegno, G. Raos, and R. Po. Methodological assessment of kinetic monte carlo simula-
tions of organic photovoltaic devices: The treatment of electrostatic interactions. The Journal of
chemical physics, 132(9):094705, 2010.
[5]
P. Du, A. Zebrowski, J. Zola, B. Ganapathysubramanian, and O. Wodo. Microstructure design
using graphs. npj Computational Materials, 4(1):50, 2018.
[6]
A. Esteva. Dermatologist-level classification of skin cancer with deep neural networks. Nature,
542(7639):115–118, 2017.
[7]
S. Ghosal, A. Akintayo, P. Boor, and S. Sarkar. High speed video-based health monitoring using
3d deep learning. Dynamic Data-Driven Application Systems (DDDAS), 2017.
[8]
S. Ghosal, D. Blystone, A. K. Singh, B. Ganapathysubramanian, A. Singh, and S. Sarkar. An
explainable deep machine vision framework for plant stress phenotyping. Proceedings of the
National Academy of Sciences, 115(18):4613–4618, 2018.
[9]
X. Glorot and Y. Bengio. Understanding the difficulty of training deep feedforward neural
networks. AISTATS, 2010.
[10]
A. Nguyen T. Fuchs J. Yosinski, J. Clune and H. Lipson. Understanding neural networks
through deep visualization. arXiv preprint, 1506.06579, 2015.
[11]
S. Ju, T. Shiga, L. Feng, Z. Hou, K. Tsuda, and J. Shiomi. Designing nanostructures for phonon
transport via bayesian optimization. Physical Review X, 7(2):021024, 2017.
[12]
A. Vedaldi K. Simonyan and A. Zisserman. Deep inside convolutional networks: Visualising
image classification models and saliency maps. arXiv preprint, 1312.6034, 2013.
[13]
D. Kingma and J. Ba. Adam: A method for stochastic optimization. arXiv preprint, 1412.6980,
2014.
[14]
H. K. Kodali and B. Ganapathysubramanian. Computer simulation of heterogeneous poly-
mer photovoltaic devices. Modelling and Simulation in Materials Science and Engineering,
20(3):035015, 2012.
9
[15]
R.A Marsh, C. Groves, and N. C. Greenham. A microscopic model for the behavior of
nanostructured organic photovoltaic devices. Journal of applied physics, 101(8):083509, 2007.
[16]
L. Meng, Y. Shang, Q. Li, Y. Li, X. Zhan, Z. Shuai, R. GE. Kimber, and A. B Walker. Dynamic
monte carlo simulation for highly efficient polymer blend photovoltaics. The Journal of Physical
Chemistry B, 114(1):36–41, 2009.
[17]
V. Mnih. Human-level control through deep reinforcement learning. Nature, 518(7540):529–533,
2015.
[18]
G. Montavon, W. Samek, and K. Müller. Methods for interpreting and understanding deep
neural networks. Digital Signal Processing, 2017.
[19]
B. Ray, M. S. Lundstrom, and M. A. Alam. Can morphology tailoring improve the open circuit
voltage of organic solar cells? Applied Physics Letters, 100(1):7, 2012.
[20]
D. Silver. Mastering the game of go with deep neural networks and tree search. Nature,
529(7587):484–489, 2016.
[21]
P. K. Watkins, A. B. Walker, and G. LB Verschoor. Dynamical monte carlo modelling of
organic solar cells: The dependence of internal quantum efficiency on morphology. Nano letters,
5(9):1814–1818, 2005.
[22]
O. Wodo, S. Tirthapura, S. Chaudhary, and B. Ganapathysubramanian. A graph-based formula-
tion for computational characterization of bulk heterojunction morphology. Organic Electronics,
13(6):1105–1113, 2012.
[23]
O. Wodo, J. Zola, B. S. S. Pokuri, P. Du, and B. Ganapathysubramanian. Automated,
high throughput exploration of process–structure–property relationships using the mapreduce
paradigm. Materials discovery, 1:21–28, 2015.
[24]
D.L. Yamins and J.J. DiCarlo. Using goal-driven deep learning models to understand sensory
cortex. Nature Neuroscience, 19(3):356, 2016.
10
