MRI]Materials Research Institute, The Pennsylvania State University,
University Park, PA 16802 MTSE]Department of Materials Science and
Engineering, The Pennsylvania State University, University Park, PA 16802
[ICDS]Institute for Computational and Data Sciences, The Pennsylvania State
University, University Park, PA 16802

# Quantitative Analysis of MoS2 Thin Film Micrographs with Machine Learning

Isaiah A. Moses  [  Wesley F. Reinhart<EMAIL_ADDRESS>[

###### Abstract

Isolating the features associated with different materials growth conditions
is important to facilitate the tuning of these conditions for effective
materials growth and characterization. This study presents machine learning
models for classifying atomic force microscopy (AFM) images of thin film MoS2
based on their growth temperatures. By employing nine different algorithms and
leveraging transfer learning through a pretrained ResNet model, we identify an
effective approach for accurately discerning the characteristics related to
growth temperature within the AFM micrographs. Robust models with up to 70%
test accuracies were obtained, with the best performing algorithm being an
end-to-end ResNet fine-tuned on our image domain. Class activation maps and
occlusion attribution reveal that crystal quality and domain boundaries play
crucial roles in classification, with models exhibiting the ability to
identify latent features beyond human visual perception. Overall, the models
demonstrated high accuracy in identifying thin films grown at different
temperatures despite limited and imbalanced training data as well as variation
in growth parameters besides temperature, showing that our models and training
protocols are suitable for this and similar predictive tasks for accelerated
2D materials characterization.

#### Keywords:

MoS2 thin film, Morphological features, Machine learning, Transfer learning,
Explainable AI

##  1 Introduction

Material properties are significantly influenced by conditions experienced
during synthesis.1, 2, 3, 4, 5 A systematic way of isolating the properties
associated with different conditions is essential to enable growth of
materials with predefined properties on demand. We particularly seek
approaches that eliminate intuition-based experimentation with different
process variables, replacing them with data-driven approaches which are more
efficient with time, effort, and other resources.

Several studies on the thin film MoS2 have revealed a number of growth
parameters that determine the morphological features and properties of the
grown materials. Instances include the shape evolution of monolayer MoS2
crystals grown by chemical vapor deposition (CVD).6 Domain shape variation
from the triangular to hexagonal geometries has been shown to depend on the
Mo:S ratio of the precursors.6 Similarly, a MoS2 domain shapes of mainly
round, nearly round and hexagonal, truncated triangles, and triangles are
observed at the temperatures of the MoO3 precursor of 760∘C, 750∘C, 730∘C, and
710∘C, respectively.7

The domain density and size have also been shown to decrease with the
temperature,7, 8 with a random orientation of the MoS2 domain associated with
the growth temperature below 850∘C9 or at a much higher temperature.10 In the
former, the authors linked the phenomenon to inability to attain
thermodynamically stable state at the lower temperature, and in the latter,
the inferred culprit is the step edges and step edge meanderings of substrate
(sapphire) surface.

The grain size and crystal coverage of the the MoS2 have also been shown to be
tunable with the growth time.7 The authors showed that the grain size
increased when the growth time was increased from 20 minutes to 30 minutes.
With the materials grown for 45 minutes, the grains merged to form a
continuous MoS2.7 Similarly, an increased in growth temperature8 and O2 flow
rate11 were shown to result in larger thin film crystal coverage.

In designing high throughput on-demand materials, deployment of data-based
screening approaches have become more critical.12, 13, 14, 15, 16, 17 Data-
driven approaches are being explored for materials characterization18, 19, 20,
21, 22 and serve to provide greater clarity when searching the synthesis
condition space compared to intuition-based experimentation.23, 24, 25, 26, 27
With the use of the existing data consisting of the conditions and the
corresponding materials properties, models that predict what conditions are
necessary for a given properties can be developed. As observed, a number of
these conditions play similar and intertwined roles in the materials
properties. For instance, time, temperature, and O2 flow rate, all determine
the MoS2 thin film crystal coverage.7, 8, 11 It will be interesting to use
machine learning to isolate the distinct latent features associated with the
different growth parameters. Additionally, identifying distinct latent
features for these different growth parameters would result in the capability
to classify material samples based on their growth conditions.

The Lifetime Sample Tracking (LiST) is a database hosted by the Penn State’s
2D Crystal Consortium (2DCC) facility, consisting of experimentally grown thin
film transition metal chalcogenides materials, among others. Among the
characterization methods stored in LiST is the Atomic Force Microscopy (AFM).
AFM images of 2D MoS2 and their corresponding synthesis condition are a set of
data among other categories in LiST.10, 28, 29 To accelerate the synthesis of
MoS2 with the desired properties, we deploy different machine learning (ML)
models to classify AFM images of the material based on their growth
temperature. Despite the limited data available for the training, up to 71%
test accuracy was obtained on the image classification. Most importantly, this
study presents a simple approach that could help isolate underlying
morphological features associated with different growth conditions for a broad
range of materials, paving the way for rapid and cost effective materials
development.

##  2 Methods

###  2.1 Data Preparation

Raw spm files of MoS2 were retrieved from LiST.30These 262 AFM height maps
were processed into greyscale images and either resized or randomly cropped to
the common size of $224\times 224$, depending on the augmentation method
adopted, as discussed below. Training computer vision models on such a small
dataset requires transfer learning, a common approach that utilizes CNN models
pretrained on one image domain to extract features from a new image domain.31,
32, 33 Many popular pretrained CNNs, such as the VGG,34 ResNet,35 and
Inception model36, 37 architectures were trained on the ImageNet dataset.38
ImageNet contains millions of color images of natural objects from thousands
of categories. Using the size of the model architecture as the main basis for
our choice, because of the small data volume in our characterization problem,
ResNet18 architecture pretrained on the ImageNet is used for the transfer
learning.

However, our data distribution is very different than the ImageNet data. To
evaluate the effect of the pretraining domain, we consider pretraining on
micrographs contained in the MicroNet dataset39, which should be more similar
to our image domain. The MicroNet dataset has been shown to give better
performance on micrographs, indicating that the proximity of the two image
domains should enhance the model performance.39 We have therefore additionally
used ResNet18 pretrained on the MicroNet dataset. This will enable us to
compare how the same model architecture pretrained on different datasets
perform on our characterization task. Features were extracted from the
pretrained models for our shallow ML models. The pretrained convolutional
models were also fine-tuned for the CNN model in our study (1).

Figure 1:  An overview of the transfer learning approach. (top) A ResNet CNN
model is trained on a different image domain with a large number of images.
The task may be unrelated to the present task – all that matters is that
convolutional filters are learned that can extract information (e.g., texture,
color, shapes) from the images. (middle) The filters from the pretrained model
can be used directly to extract relevant image features, which are interpreted
in a supervised manner by a shallow model to predict a new label, such as the
growth temperature. (bottom) Alternatively, the filters from the pretrained
model can be fine-tuned on the new image domain to better capture relevant
information for the task at hand.

###  2.2 Data Augmentation

Figure 2: Sample images from MoS2 grown at 900, 950, and 1000∘C.

The dataset consists of 262 instances of AFM height maps across 3 growth
temperatures (Figure 2). In addition to the limited data, there is a
significant imbalance among the different classes with the 900∘C, 950∘C, and
1000∘C making up 11%, 50%, and 39% respectively (Table 1).

Table 1: Data augmentation policies and the corresponding data sets for the different classes, 900∘C, 950∘C, and 1000∘C. In Aug1, multiple random cropping of image size $224\times 224$ is used to obtain balanced instances among the different classes, Aug2 is augmentation policy learned on ImageNet40, and in Aug3 weighted random sampler and oversampling are used to correct the imbalance in train set for CNN and other models, respectively. Aug4 is without biased augmentation. In CNN models, random rotations between 0 to 180∘, horizontal and vertical flipping at 50% probability were additionally used on the train and validation set on the fly. | 900∘C | 950∘C | 1000∘C | Total
---|---|---|---|---
| train | validation | test | train | validation | test | train | validation | test |
Aug1 | 207 | 27 | 3 | 212 | 22 | 13 | 215 | 24 | 11 | 726
Aug2 | 207 | 27 | 3 | 208 | 24 | 13 | 210 | 23 | 11 | 734
Aug3 | 105 | 3 | 3 | 105 | 12 | 13 | 105 | 9 | 11 | 342
Aug4 | 23 | 3 | 3 | 105 | 12 | 13 | 83 | 9 | 11 | 262

The effect of limited and imbalanced data on the model performance can be
partially mitigated with data augmentation approaches. Different data
augmentation policies were therefore deployed to determine which method works
best for our small, imbalanced dataset. The first was to randomly crop a
common size of $224\times 224$ from each of the original images. Multiple
croppings were carried out, depending on the class of the image, in order to
obtain a balanced representation of the different classes. This augmentation
policy is termed Aug1 (Table 1). Another augmentation policy examined is that
developed by Cubuk, et al,40 which we referred to as Aug2 hereafter. The
authors used a search algorithm to find the best policy, which is a
combination of many sub-policies consisting of functions such as the
translation, rotation, or shearing, and the probabilities and magnitudes with
which the functions are applied, that give the best validation accuracy on a
target dataset. Interestingly, they observed that the learned policy in a
given dataset is transferable to another. We therefore examined how
transferable the policy learned on ImageNet is to our present data domain. The
third augmentation method used is a weighted random sampler or oversampling to
correct the imbalance in the training set (Aug3). For Aug4, there is no biased
augmentation applied to the data and only in CNN models do we have random
rotations between 0 to 180∘, horizontal and vertical flipping at 50%
probability applied to the train and validation set on the fly.

###  2.3 Machine learning

A 10-fold cross-validation training scheme was used to train and evaluate the
models. The data were shuffled into train and validation sets 10 times using
different random states to ensure a different split each time. In each
instance, the training set was used to train the model parameters while the
validation set was used to determine the performance for hyperparameter tuning
using grid search. A held-out test set (not involved in the shuffle-split
procedure) was then used to evaluate the model performance in general.

Nine different ML models were considered: support vector classifier (SVC)41,
42, kernel ridge classifier (KRC)43, radius neighbors classifier (RNN)44,
Gaussian process classifier (GPC)45, k-nearest-neighbors classifier (KNN)44,
decision tree classifier (DTC)46, gradient boost classifier (GBC)47,
multilayer perceptron (MLP)48, and convolutional neural network (CNN)49, 50.
The shallow models were developed using the scikit-learn library51 and the MLP
and CNN were implemented in pytorch52.

Using AFM images of 2D MoS2 grown with MOCVD, we developed models to predict
the growth temperature (one of 900∘C, 950∘C, or 1000∘C). We considered framing
the task in several different ways to evaluate the efficacy of each: nominal
classification, ordinal classification, and regression. Here nominal
classification means the three growth temperatures were considered as distinct
classes with no ordering. Unless otherwise specified, results are for nominal
classifiers.

For ordinal classification, we implement NNRank53 to account for ordering
within the classes; the targets 900, 950, and 1000∘C are transformed into the
vectors $[1,0,0]$, $[1,1,0]$, and $[1,1,1]$, respectively. At inference time,
a threshold of $>0.5$ is applied to the prediction and the values are counted
from left to right, which provides the class label. Note that this scheme is
only applied to the NN models (MLP and CNN). Finally, we perform regression by
simply using the growth temperatures as continuous labels and evaluating the
MSE. The class labels are obtained by binning the predicted growth temperature
(e.g., $925-975^{\circ}$C belongs to the $950^{\circ}$C class).

##  3 Results and Discussion

###  3.1 Depth of Image Features

Table 2:  Validation accuracy (in %) based on the features extracted from the different layers of the pretrained model (ResNet18 pretrained on ImageNet). Channels is the total size of raw feature vectors extracted from each block of the ResNet. PCA was applied to these channels, and then cumulative explained variance (CEV) of the components from PCA was used to determine the size of the input features for the listed shallow models. Separately, the dense layers of the pretrained model were replaced with fewer neurons and fine-tuned (last column).  | Block 2 | Block 3 | Block 4 | Pooling | Fine-Tuned
---|---|---|---|---|---
Channels | 100352 | 50176 | 25088 | 512 | 100
CEV | 85% | 99% | 85% | 99% | 85% | 99% | 85% | 99% | -
Features | 190 | 235 | 156 | 235 | 94 | 219 | 28 | 142 | 100
SVC | 66$\pm$6 | 59$\pm$7 | 64$\pm$5 | 62$\pm$8 | 77$\pm$6 | 58$\pm$5 | 78$\pm$5 | 71$\pm$6 | 80$\pm$7
KRC | 45$\pm$5 | 57$\pm$4 | 48$\pm$11 | 55$\pm$5 | 58$\pm$11 | 52$\pm$5 | 57$\pm$7 | 58$\pm$12 | 71$\pm$7
RNN | 21$\pm$4 | 15$\pm$2 | 35$\pm$11 | 15$\pm$3 | 42$\pm$9 | 20$\pm$5 | 57$\pm$7 | 39$\pm$7 | 70$\pm$9

We first determined the best location in the pretrained model from which to
extract image features for our models. Different portions (“blocks”) of the
ResNet were considered, providing filters with different levels of
abstraction. Due to the large number of channels in the pretrained model (see
Table 2), Principal Component Analysis (PCA) was applied to reduce the
dimension of input features to the shallow models, ideally reducing
overfitting and thus improving predictive performance.54, 55, 14 Cumulative
explained variance thresholds of 85% and 99% were used to determine the number
of features to keep for inference. We found that within a block, using fewer
features gave better performance in 9 of 12 cases despite lower explained
variance, likely because we had few training data compared to the size of the
feature vectors. Depending on the model architecture and number of features
used, minimal or significant deviations in model performance could be obtained
from any of the ResNet blocks (e.g., 66%, 64%, 77%, and 78% accuracy from
subsequent blocks, with typical standard deviation $\pm 6\%$).

Separately, the dense layers of the pretrained model was replaced with new
ones with fewer neurons and then fine-tuned on our training data. Finally, 100
features were extracted from the first dense layer. The performance of the
selected classifiers on the different features shows that the features
extracted from the fine-tuned dense layer gives the best performance overall,
with 80%, 71%, and 70% accuracy using SVC, KRC, and RNN, respectively.
Training the dense layer on a pretrained convolutional backbone might
therefore be a better approach for extracting a low-dimensional image feature
vector compared to PCA. These tuned features are therefore used in all of the
following analysis.

###  3.2 Data Augmentation

Figure 3: Accuracy obtained from different augmentation policies across three
different model types. Bars report averages over 10 folds, while error bars
indicate standard deviation. Some models were trained with increased data size
to have a balanced classes using different augmentation approaches, as
indicated in Table 1.

We then evaluated the effect of different data augmentation policies using the
SVC, KNN, and CNN models (Table 1 and Figure 3). Significantly worse
performances are obtained with Aug1 and Aug2, especially in the shallow
models, compared to Aug3 and Aug4. Meanwhile, the performance observed between
Aug3 and Aug4 is statistically indistinguishable.

The poor performance observed in the Aug1 and Aug2 might be related to the
properties of the images learned by the models. While in the case of the
natural images, activation of different classes are typically associated with
unique features of the classes,56, 57, 58 the class activation in the models
for the different synthesis conditions will be more likely due to differences
in magnitude of the same feature, such as the domain size and thickness.3, 4
These relevant features of the AFM images may be disrupted by shearing,
zooming, and resizing associated with Aug1, and the features location in the
image might be omitted due to the cropping in Aug2.

Although Aug3 and Aug4 present about the same accuracy, Aug3 has the desirable
property of oversampling less represented classes. This should help mitigate
systematic error related to class imbalance, a feature which is typical of
distributions in materials synthesis, especially when exploring different
growth conditions (e.g., poorly performing conditions will probably be
undersampled). Therefore, the Aug3 augmentation policy is selected for the
rest of this study.

###  3.3 Pretraining Domain

Table 3: Validation accuracy (in %) over 10 folds obtained for the feature extraction (shallow and MLP models) or end-to-end learning (CNN) with ResNet18 pretrained on ImageNet and MicroNet. Values are reported as mean $\pm$ standard deviation. Difference is the fractional change in the average score between MicroNet and ImageNet. Best model performance in each row is shown in bold.  Models | SVC | KRC | RNN | GPC | KNN | DTC | GBC | MLP | CNN
---|---|---|---|---|---|---|---|---|---
MicroNet | 73$\pm$6 | 65$\pm$10 | 63$\pm$9 | 52$\pm$12 | 59$\pm$10 | 71$\pm$9 | 71$\pm$9 | 65$\pm$8 | 63$\pm$8
ImageNet | 80$\pm$7 | 71$\pm$7 | 70$\pm$9 | 59$\pm$10 | 67$\pm$12 | 78$\pm$4 | 78$\pm$11 | 86$\pm$6 | 70$\pm$6
Difference | +10% | +9% | +11% | +13% | +14% | +10% | +10% | +32% | +11%

We next seek to quantify how transfer learning from the ResNet18 model
pretrained on the ImageNet data domain compares with the same model
architecture pretrained on the seemingly more relevant MicroNet data domain.
We therefore compared the performance of each pretrained model on the same
nominal classification task across a wide range of predictive model types. In
these experiments, we used the fine-tuned features from Table 2 in all cases
except CNN, which was simply fine-tuned in an end-to-end manner using the
original ResNet18 architecture (i.e., with a three-way classification layer
attached to the end in place of the original classification layer). Based on
the results shown in Table 3, the ImageNet model gives conclusively better
performance than MicroNet, with at least 9% improvement and up to 32%
improvement in the case of MLP (compared to a typical uncertainty of about
6%).

While standard deviations for individual observations are high, the fact that
none of the nine model types shows a negative difference is compelling,
especially because MicroNet was trained on greyscale micrographs of materials
while ImageNet was trained on color images of macroscale objects. Previous
work has suggested that ImageNet relies more heavily on texture rather than
shape59, while MicroNet was designed primarily for segmentation tasks. We
speculate that this focus on texture gives ImageNet filters that can be used
for identifying distinguishing textures in the AFM height maps. The results
presented here suggest that ImageNet may be surprisingly well suited for out-
of-domain materials characterization data whose information content is
primarily texture. All following results are based on transfer learning from
the ImageNet pretraining since its features are strictly superior to MicroNet.

###  3.4 Model Performance

Figure 4: The average train, validation (val), and test accuracy over 10
models for the different algorithms. The data were shuffled 10 times with
different random seeds to obtain 10 different train and validation splits.
Hyperparameters were tuned to obtain a trained model for each of the 10
splits. The trained models were tested with the test set.

We next investigate the performance of different algorithms in greater detail.
As before, we rely on the features extracted from the fine-tuning procedure
above, with additional shallow models trained on these static feature vectors
of each image. The CNN model is the one exception to this, as it uses the
original ResNet18 architecture and is fine-tuned on this task without
modification to feature size. The classification accuracy across 10 different
model instances of each type is shown in Figure 4. Overfitting is observed
across all model types, with training performance over 90% being typical,
while validation typically only reaches around 60-85%. The greatest
overfitting, in terms of the gap between train and validation performance, is
seen in KRC and GPC, while SVC, DTC, and MLP exhibit the least. The best
performing models in terms of validation performance is the MLP, with SVC
coming in second but exhibiting training and validation scores one standard
deviation below the MLP.

To understand how well the models can generalize to classifying images outside
of the training data, we additionally examine their performance on a held-out
test set (i.e., not used for training or hyperparameter selection). In this
regard, MLP again showed the highest accuracy, with GBC and GPC appearing
within one standard deviation. It is reassuring to see that MLP gave the
highest scores in both validaiton and testing, inspiring confidence in its
performance overall.

Figure 5: The average confusion matrix for the test set predictions of
production models trained on the 10 folds train data. Values indicate the
number of samples in each bin. This is based on nominal classification.

To understand the model performance on the different growth temperatures in
greater detail, and particularly to check if the underrepresented classes have
comparable accuracy, average confusion matrices of the held-out test set on 10
models are reported in Figure 5. To focus the discussion, only the highly
performant GBC and MLP models and the end-to-end CNN are examined in this
regard. It is notable that the performance within each class does not vary
substantially between different model types, as the overall accuracy are
similar. For instance, the GBC, MLP, and CNN predict about the same number of
samples grown at 950∘C and 1000∘C correctly (about 70% and 75% respectively).
The samples grown at 900∘C are found to have the lowest in-class accuracy.
This seems to be partially an artifact of under-representation in the test
set; as shown in Table 1, classes are significantly imbalanced in the data,
with the 900∘C classes having the least number of samples.

There is also some consistency among the models in misclassifying the 900∘C as
950∘C and not as 1000∘C. Similarly, 1000∘C is rarely misclassified as 900∘C.
On the contrary, 950∘C is about equally likely to be misclassified as 900∘C as
it is as 1000∘C by the MLP and CNN. This seems to suggest that the proximity
of the growth temperature, which is expected to be reflected in the image
features, makes it more likely for the model to group them together. Recall
that this is for nominal classification, so this proximity is not reflected in
the loss function. This could imply a fundamental bias in the data where the
image feature learned by the models for a given temperature are more similar
to that for the adjacent temperatures.

Figure 6: Samples grown at 900∘C (1-3), 950∘C (4-16), and 1000∘C (17-27) in
the test set. The predicted class by end-to-end CNN is shown at the bottom
(yellow) for each image. (b) and (c) are the samples with their growth time
and substrate orientation, respectively. The AFM # in (a) corresponds to the
sample # in (b) and (c).

To further understand the classification fidelity of our models, we examine
images that are correctly and incorrectly classified by the CNN in Figure 6.
Visual inspection suggests significantly different image features among the
same growth temperature, demonstrating how difficult this classification task
is. Some images grown at 950∘C show larger crystal domains typically
associated with 1000∘C. Conversely, some images grown at 1000∘C show poor
crystal formation and very small domain sizes exhibited mostly by the 900∘C
growth temperature. Therefore, these wrongly classified images may be
exceptional among the target class and would likely confuse even a human
expert. However, they offer some preliminary insight into which features the
classifier attributes to each growth temperature.

More fundamentally, other growth variables are not entirely fixed across the
samples. For instance, the growth time varies significantly among the
different samples (Figure 6(b)). While the least growth time in the test set
is as low as about 100 s, some samples are grown at much longer time, with up
to 1650 s. Also, while most of the samples are grown on c-plane sapphire
substrate, we also have some that are grown on A- and M-plane sapphire (Figure
6(c)). These inconsistent growth parameters might have accounted for the
significant differences observed among the samples grown at the same
temperature and might have also resulted in some classification errors (e.g
images 2, 5, 15, and 18). However, we do not observe any obvious trend in
these growth parameters that leads to consistent misclassification, once again
demonstrating how challenging this classification task is.

###  3.5 Ordinality

The preceding results were all based on nominal classification, without any
notion of ordering. However, the classes consisting of the growth temperatures
would appear to be ordered due to their continuous nature (i.e., ranging from
900 to 1000∘C). We therefore further quantify the effect of ordinal treatment
of the class labels on model accuracy. In accounting for ordinality in shallow
(i.e., non-NN-based) models, we adopted a simple approach based on training a
regressor and then binning the results into classes. For the NN-based models,
we further implemented the NNrank ordinal classification scheme. The results
of this study are given in Table 4.

Table 4: Performance of nominal and ordinal treatment of class labels, expressed as accuracy on held-out test data in % for classification and ∘C for regression. Best model performance in each row is shown in bold.  Models | SVM | KR | RNN | GP | KNN | DT | GB | MLP | CNN
---|---|---|---|---|---|---|---|---|---
Classification (%) | 62$\pm$4 | 54$\pm$4 | 64$\pm$3 | 66$\pm$2 | 64$\pm$3 | 57$\pm$8 | 66$\pm$4 | 69$\pm$5 | 64$\pm$10
NNRank (%) | - | - | - | - | - | - | - | 71$\pm$4 | 68$\pm$3
Regression (%) | 50$\pm$8 | 60$\pm$5 | 64$\pm$4 | 48$\pm$0 | 58$\pm$6 | 54$\pm$6 | 64$\pm$7 | 42$\pm$8 | 61$\pm$7
RMSE (∘C) | 31$\pm$2 | 26$\pm$1 | - | 36$\pm$9 | 32$\pm$3 | 38$\pm$5 | 28$\pm$3 | 62$\pm$8 | 34$\pm$4

While results vary for each model type, some general trends emerge. Accounting
for ordinality in model training leads to improvement in the test accuracy in
only one of the shallow models (KR), but matches or degrades the performance
for all others. Most of these are statistically indistinguishable, with only
SVM, GP, and MLP exhibiting significant decreases. Overall, nominal
classification gave superior performance over regression, with the top
performing shallow models GP and GB giving 66% accuracy.

For the NN models, MLP outperformed CNN overall, with statistically
indistinguishable accuracy using nominal classification and ordinal
classification. While the end-to-end CNN performed significantly better than
the MLP on the regression task, the performance on regression was the worst of
the three schemes for each model, making it somewhat irrelevant. Somewhat
counterintuitively, slightly higher accuracy could be obtained by binning the
output of the GB regressor (64%) which had a higher RMSE compared to the KR
regressor ($28\pm 3^{\circ}$C versus $26\pm 1^{\circ}$C). This suggests that
least-squares regression may be placing too much weight on outliers, which are
less influential in the case of ordinal classification. It is even possible
that the growth temperatures are not really ordinal after all, perhaps with
950∘C representing a value close to optimal while 900∘C and 1000∘C could be a
similar distance away from optimal.

The best-performing model across any type or scheme was the MLP NNrank ordinal
classifier with an accuracy of 71%. For the NNRank applied to the MLP and CNN,
the average test accuracy of the CNN and MLP improved minimally with +2% and
+4%, repectively, over the nominal classification. This improvement is
accounted for mainly in reduced classification errors of the 1000∘C images
from 75% to 82% accuracy (Figure 7).

Figure 7: The average confusion matrix of the 3 classes of temperature (900,
950, and 100∘C) on the test set for the 9 different model architectures. This
is based on ordinal classification with regression used for the GBR and NNrank
for the MLP and CNN.

In an effort to explain the surprising trend observed in the ordinal treatment
of the data, we obtained the first 2 principal components of the data using
principal component analysis (PCA)60. The image classes are embedded in the 2
components shown in Figure 8. The figure shows overlap of all three classes
and more significantly between neighboring classes, with very poor separation
visible in the first two components. We visualize the micrographs in the PCA
space in Figure 9, indicating variations in the domain size (PC1) and density
(PC2). Because these features vary significantly even within the same
temperature class (e.g., see Figure 8), the image feature vectors likely do
not show consistent trends from 900∘C to 950∘C to 1000∘C, leading to no
advantage in the ordinal treatment of growth temperature.

Figure 8: The first two principal components of the image features showing the
temperature class distribution in the reduced dimensional representation from
the principal component analysis. Significant overlap is observed among the
different classes in the embedding space. Figure 9: The first two principal
components of the image features showing the sample images, in the reduced
dimensional representation from the principal component analysis. The
embedding shows that the first dimension (PC1) is associated with the domain
size, while the second dimension (PC2) seems to indicate the domain density.

###  3.6 Model Explanations

Beyond the capacity of the ML models to isolate the morphological features
associated with the different growth temperature of the thin film MoS2 based
on their AFM images, we want to understand what features of the images the
models used in the classification. Class activation maps (CAM) of the
different classes are therefore obtained following the implementation by Zhou,
et al.61 The feature maps of the last convolutional layer are summed and then
normalized by dividing by the maximum value to obtain a heatmap with the same
dimensions as the layer. The bright yellow spot on the class activation maps
represent the region with the highest activation which the model used for the
classification.

Figure 10: Class activation maps (CAM) and occlusion attribution showing
different regions of the images the model used for the classification. (a),
(b), and (c) are for samples of images grown at 900∘C, 950∘C and 1000∘C,
respectively. (i), (ii), and (iii) are the original AFM images, CAM, and AFM
images overlaid with CAM, respectively.

Additionally, we obtained the occlusion attribution; the probability of a
class of image as a function of an occluder object,62 using the implementation
in Captum library.63 To achieve this, we iteratively set a patch of the image
to be zero-pixel values and then obtain the probability of the class. Stride
size of $5\times 5$ and the patch size of $15\times 15$ were used. The
probability is visualized as a 2D heat map. Both positive and negative
attributions, indicating that the presence and absence of the area,
respectively, increases the prediction scores are shown on the heat map. The
occlusion attribution is applied to four sample images, for each class,
correctly predicted by the CNN model. Green regions on the image have positive
attributions while red regions have negative attribution.

The CAM and occlusion attribution in Figure 10 show substantial agreement in
identifying the activation region, with the latter giving more specific
spatial attribution. The activation features are easier to perceive in images
with bigger domain sizes, especially those grown at higher temperature. For
some of the images from samples grown at higher temperature and which show
clearly defined domains, some domain boundaries are highlighted, indicating
the model’s reliance on the boundaries in identifying such images. Also,
regions with clean multi-steps crystals are shown to be important for the
model in the classification (Figure 10c), while the messy crystals post
adverse effect to class attribution, as shown in the occlusion attribution.

From the experimental observations, the samples grown at higher temperatures
are expected to exhibit greater domain sizes.3, 4 However, in the data used in
training our models, there is significant variation in the quality of the
samples, such that most images grown at higher temperature do not necessarily
have greater domain sizes (Figures 2 and 6). Additionally, if the model
depends on domain size in identifying the images, it will be difficult to
visually identify such features in images with less defined domains, and the
only difference among the classes would only be the magnitude of the same
feature. This is unlike the natural images where activation of different
classes are typically associated with unique features of the classes that can
be visually identified.56, 57, 58 The models have therefore shown to be
capable of identifying image features even beyond human visual capability.

##  4 Conclusion

This study focuses on the development of ML models for the classification of
AFM images of thin film MoS2 based on the growth temperatures of their
samples. Many different strategies were explored for feature extraction,
including use of features from different depths in a pretrained ResNet,
different pretraining image domains, and the use of different transfer
learning approaches including feature extraction, fine-tuning of convolutional
filters followed by shallow learning, and end-to-end fine-tuning. Different
augmentation strategies from the literature were evaluated to determine their
effect on overall model performance. Beyond these pretraining schemes, nine
different ML algorithms were evaluated to determine the most suitable approach
for identifying morphological features associated with different growth
temperatures.

The study also examined the impact of considering the ordinality of the
classes on the accuracy of the models in identifying AFM images grown at
different temperatures. We found that accounting for ordinality (i.e., by
switching from classification to regression loss functions) improved the
accuracy of some algorithms while decreasing performance for others. For
instance, the best model overall was obtained using an NNrank ordinal
classifier, but some nominal classifier were nearly as accurate. Furthermore,
some algorithms had equivalent accuracy regardless of whether the data was
treated as nominal classes or ordinal. Thus, there seems to be no clear
advantage to using least-squares regression here, despite the data appearing
in the form of continuous, ordered growth temperatures, which is a
counterintuitive result.

To address class imbalance, weighted random sampling and oversampling
techniques were employed, and robust ML models that generalize well to out-of-
sample data were developed using model ensembles. The best-performing
algorithms, MLP and end-to-end CNN, achieved classification accuracy of about
70% on held-out test data. The high accuracy obtained demonstrates the
effectiveness of ML in accurately identifying thin films grown at different
temperatures, despite the limitations of other inconsistent growth parameters
and imbalances in the training data.

This study also sought to understand the features utilized by the ML models
for classification by obtaining class activation maps and occlusion
attribution. These strategies revealed that images from samples grown at
higher temperatures, exhibiting well-defined domains, had the highest
activation at the domain boundaries, aligning with experimental observations.
Moreover, the models demonstrated the capability to identify latent features
beyond human visual perception, accurately classifying images with varying
domain sizes that would be challenging for human experts. Future work may
explore the relationship between these image features and additional
attributes of the samples; the robustness of these features across growth
chambers, characterization instruments, and even repeatability over time may
be interesting ways to utilize the quantitative capability of deep learning to
unlock new insights into challenging materials synthesis problems.

## Acknowledgments

This study is based upon research conducted at The Pennsylvania State
University Two-Dimensional Crystal Consortium – Materials Innovation Platform
(2DCC-MIP) which is supported by NSF cooperative agreement DMR-2039351.

## Data Availability

The raw data required to reproduce these findings are available to download
from.30 The processed data required to reproduce these findings are available
to download from.64

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