=Paper=
{{Paper
|id=Vol-2844/ainst1
|storemode=property
|title=Hybridizing AI and Domain Knowledge in Nanotechnology: the Example of Surface Roughness Effects on Wetting Behavior
|pdfUrl=https://ceur-ws.org/Vol-2844/ainst1.pdf
|volume=Vol-2844
|authors=Antonios Stellas,George Giannakopoulos,Vassilios Constantoudis
|dblpUrl=https://dblp.org/rec/conf/setn/StellasGC20
}}
==Hybridizing AI and Domain Knowledge in Nanotechnology: the Example of Surface Roughness Effects on Wetting Behavior==
https://ceur-ws.org/Vol-2844/ainst1.pdf
Hybridizing AI and Domain Knowledge in Nanotechnology: the
Example of Surface Roughness Effects on Wetting Behavior
Antonios Stellas George Giannakopoulos Vassilios Constantoudis
Department of Mathematics and Institute of Informatics and Institute of Nanoscience and
Computer Science, Telecommunications, Nanotechnology,
Technical University of Eindhoven NCSR Demokritos NCSR Demokritos
Netherlands and and
SciFY P.N.P.C. Nanometrisis P.C.
Greece Greece
ABSTRACT morphology. To this end, several parameters and metrics have been
In this paper, we propose a scheme for the hybridization of domain proposed for the quantitative characterization of nanostructure
modeling and theoretical knowledge in nanotechnology with Ar- morphology. Some of them are more closely linked to the fabrica-
tificial Intelligence(AI) techniques and evaluate the success of its tion process, while others more directly fit to the critical property
application to predict the relationship between nanosurface mor- of a targeted application. For example, surfaces with stochastic
phology and wettability. We utilize domain knowledge consisting morphologies (rough surfaces) are widely used in the strong modifi-
of two parts. The first part is a mathematical modeling based on the cation of the wetting behaviour of materials. According to the first
inverse Fourier transform for the generation of rough surfaces with scenario (Wenzel model) for the impact of surface roughness on
Gaussian or non-Gaussian height distributions, characterized by wetting and contact angle, the critical parameter of surface nanor-
their first moments (Rms, skewness, kurtosis) and the correlation oughness is the roughness ratio π [1], defined as the ratio of true
lengths along x and y-axes. The second part lies in the assump- (active) area of the solid surface to the apparent (projected) area
tion that the Wenzel scenario for wetting of rough surfaces holds [2]. On the other side, the fabrication of surfaces is more usually
where the critical parameter for contact angle determination is the related with the surface Rms, correlation length or other surface
roughness ratio π , defined as the ratio of true (active) area of the height parameters. Furthermore, the measurement of the latter is
solid surface to the apparent (projected) area. By creating different more straightforward and accurate with respect to the full active
types of surfaces with a variety of input parameters, we create a surface area [3]. Therefore, an estimated function connecting fabri-
database linking surface roughness parameters to the ratio π . This cation parameter of full active area) (and thus, the roughness ratio
database is used to train Machine Learning (ML) models and vali- π and contact angle) to roughness parameters (Rms, π and other mo-
date them appropriately. Specifically, we train deep, feed-forward ments), can significantly help the fabrication parameter selection
neural networks and random forest models and validate them on a process.
separate (held-out) test dataset. We investigate systematically the Up until now, theoretical modelling and experiments have been
amount of input data needed to get accurate predictions on the test used to quantify these links [3β6]. However, these methods are
data. We also evaluate the importance of different input roughness time-consuming and their results are limited to the specific cases
parameters with respect to their effects on surface wettability. To they investigate. Could integrating AI techniques improve the time-
this end, we study the weights that the learning AI models assigned efficiency of these methods, making them more applicable in an
to roughness parameters through training and discuss the findings industrial environment? If yes, how can we incorporate domain
with respect to experimental expectations. knowledge coming from both modeling and experimental results in
AI models to achieve a hybridization of both, improve the accuracy
KEYWORDS of results and the success of the AI predictions? By the term domain
knowledge, we refer to the specific scientific area of used data which,
Wetting roughness, mathematical modeling, Wenzel model, contact
in our case is nanoscience/nanotechnology.
angle, Machine learning, Artificial Intelligence, Nanotechnology,
During the last decade, several nanotechnology areas have started
Rough Surfaces
to benefit from AI techniques aiming for example, to predict the
properties of new nanomaterials, to enhance microscopy results,
1 INTRODUCTION to accelerate simulations, to link manufacturing conditions with
Nanostructuring plays a fundamental role in nanotechnology since nanostructure morphology and then with the properties and perfor-
it enables new properties and functionalities of material surfaces. mance of the nanostructured devices [7]. Due to the scientific and
In order to provide a quantitative link between the geometry of technological nature of data in these applications, there is an in-
nanostructure morphologies and the induced surface properties, we creasing need to devise ways to match AI methods with the domain
first need to find the proper mathematical tools to describe surface knowledge, as reported in the relevant theoretical and experimental
works.
AINST2020, September 02β04, 2020, Athens, Greece
Copyright Β© 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).
The overall aim of this paper is to propose a hybridization scheme scheme, using simulation data to train a ML algorithm to predict
to facilitate the synergy of data-centric methods with domain mod- faster solid-state properties. On the other hand, in the work of M
elling and theoretical knowledge concerning the link of the mor- Aziar Raissi and George Karniadakis et al. in 2019 [12], we find an
phology of nanostructured surfaces with their properties and func- elaborated methodology in which, physical modeling assists the
tionalities. The key ideas of this approach are: a) to use properly AI research by exploration of physics-informed neural network
designed modeling results to train and validate AI methods along algorithms.
with experimental data when they are available and b) to exploit Regarding the prediction of wetting behaviour, Amir Kordijazi
the ability of ML techniques to reverse input and output so that et al., (2020) used ML techniques to predict the water contact an-
the targeted design of a nanostructured product dictates the choice gle on surfaces of ductile iron. They used a set of experimental
of nanostructure geometry and manufacturing conditions. We will measurements with input parameters the material composition,
focus on the first idea and we will apply it to evaluate the success of droplet size, the surface grit size and roughness and the time of the
AI techniques hybridized with domain modeling results to predict exposure to the liquid. The authors also evaluated the importance
the relationship between nanosurface morphology and wettability. of each input parameter on the value of contact angle and they
More specifically, the contributions of the paper can be outlined as justified the primary role of surface roughness determined by the
follows: grit size. However, it was not specified which aspect of surface
β’ An implementation of domain modeling results in AI tech- roughness is more critical. Given that the roughness of surfaces is
niques is realized for training and validation. a complex multifaceted phenomenon characterized by a plethora
β’ A comparison of different AI models is performed based on of parameters, it is worth questioning the relative importance of
the physical modeling results. roughness parameters on surface wetting behavior. In literature,
β’ A study on the numerosity of required data (rough surfaces), one can find interesting results coming from both experimental and
to train sufficiently accurate AI methods. computational approaches exploring the impact of surface rough-
β’ An estimate of the relative importance of input roughness ness parameters on contact angle and hysteresis [4].
parameters on wetting behavior, supported by a discussion In our work, we follow the data-driven approach of the 4th
to feed domain decisions and evaluations. paradigm of science endowed by theoretical and computational
modelling knowledge of the 2nd and 3rd paradigms. The aim is to
The paper is structured as follows. We begin, in section 2, with investigate the prediction performance of these AI models on the
a presentation of the related recent work and the need to investi- effects of roughness parameters on the wetting behavior of solid
gate further the predictive capability of AI techniques in the nan- surfaces. We assume that the Wenzel model assumption holds: the
otechnology applications and specifically wetting behavior. The contact angle of droplets posed on rough surfaces is determined
mathematical modeling methodology for the generation of rough by the roughness ratio π and especially the full active surface area.
surfaces to train AI models as well as the AI techniques used in the A hybridization framework is implemented, in which simulated
paper is the subject of the section 3. Section 4 presents the results rough surfaces with a wide spectrum of parameters and appearances
of AI techniques and their comparison. The paper closes with the are used to train and evaluate the AI models and explore their
summary in the final section 5. performance versus the simulation cost. We also use the capability
of the developed AI models to reveal each roughness parameter
2 RELATED WORK importance on the observed wetting behavior.
The applications of AI to physical problems and especially materials
science have been studied in many contexts during the last decade,
creating a novel research framework termed βdata-driven materials 3 METHODOLOGY
scienceβ (Teng Zhou et al., 2019 [8] ). Teng Zhou highlighted the new 3.1 Mathematical modelling of rough surface
opportunities that a data-driven approach can provide in the study generation.
of materials and named it the 4th paradigm in materials science.
The previous three paradigms are assumed to be the empirical, In this section, we describe the methodology we used for generating
theoretical and computational ones respectively. In the framework simulated rough surfaces with similar characteristics with a large
of this data-driven materials science, several studies have achieved variety of experimental ones. These surfaces will be used to enrich
to make significant contributions to the design and development of the dataset for training and validating the ML models. We begin
new materials (Sutton, C. et al., 2019 [9]), the prediction of material by describing the methodology for generating Gaussian and non-
properties (electronic, mechanic, thermal,. . . ) (SchΓΌtt, K. T. et al., Gaussian surfaces with controlled spatial correlations.
2014 [10]) or the evaluation of the importance of manufacturing
and structure parameters on material surface functionalities such Gaussian surfaces: We produce three-dimensional Gaussian sur-
as wetting behavior (Amir Kordijazi et al., 2020 [11]). Furthermore, faces by inputting the Rms of the height distribution and the cor-
a critical question in this framework has been the incorporation of relation lengths along the x and y axes (ππ₯ and π π¦ ) of the surface
the domain knowledge of materials science (theoretical concepts (Table 1). (Figure 1a and 1b). The heights of the generated surfaces
and laws, modeling and simulation results) coming from previous are calculated on a square lattice π Γ π points and area ππΏ Γ ππΏ.
paradigms in the data-driven algorithms, to avoid significant errors Therefore, the spacing in x and y direction corresponds the ratio:
in the provided predictions. To this end, Sutton, C. et al., (2019) and π β1 . The methodology for simulating the Gaussian surfaces is
ππΏ
SchΓΌtt, K. T. et al., (2014) applied the data-driven science paradigm based on the work of Garcia et.al. [13]. First, we produce a white
Surface Type Input Parameters Output Parameter
Gaussian Rms, ππ₯ , π π¦ active area
Non-Gaussian Rms, ππ₯ , π π¦ , skewness, kurtosis active area
Table 1: Input parameters used for generating the active
area of Gaussian and non-Gaussian surfaces. The input
(roughness) parameters for the Gaussian consist of the Rms
heights and the correlation lengths (π) in x and y directions.
For the Non-Gaussian surfaces the inputs include addition-
ally the skewness and kurtosis.
noise ππ πΊ distribution with mean value zero and standard devia-
tion equal to the input Rms value. By applying the Gaussian filter
πΉπΊ , described in the following equation (Eq. 1) to the distribution
we add the desired correlations along x and y axis.
Figure 1: Examples of simulated rough nano-surfaces
π₯2 π¦2
πΉπΊ = ππ₯π (β(2 2 + 2 2 )) (1) a) Isotropic Gaussian surface N= 600 points, rL=4 πm, ππ₯ =0.5
ππ₯ ππ¦ πm, π π¦ =0.5 πm, Rms=0.1 πm
Then, we take the Inverse Fourier Transform of the product of b) Anisotropic Gaussian surface N= 600 points, rL=6 πm,
Fourier transforms of ππ πΊ and πΉπΊ and multiply with normalization ππ₯ =0. πm, π π¦ =0.6 πm, Rms=0.1 πm
factors to generate correlated isotropic and anisotropic Gaussian c) Isotropic non-Gaussian surface N= 600 points, rL=6 πm,
surfaces After producing the surface, their Rms, ππ₯ and π π¦ are com- ππ₯ =0.5 πm, π π¦ =0.5 πm, Rms=0.05 πm Sk=2, Ku=6
pared with the inputs to check possible divergence. The divergence d) Anisotropic non-Gaussian surface N= 600 points, rL=6 πm,
is related with limitations imposed by the discrete sampling and ππ₯ =0.2 πm, π π¦ =0.6 πm, Rms=0.05 πm Sk=-0.4, Ku=2
finite range of surfaces. In such case, the algorithm of the surface
generation is repeated until the input parameters are converged.
Non-Gaussian surfaces: The method we used to model non-Gaussian 3.2 AI techniques
surfaces is based on the work of Yang et al. [14] where, the John-
In this section, we outline the AI methods we utilized in this work.
son and Pearson transformations systems are used to transform
We begin by overviewing the main points describing the methods
random Gaussian noise with specified average height and Rms into
and then we align these descriptions with our work.
non-Gaussian noise with user-defined skewness, and kurtosis (Ta-
A physical model is a domain-driven model that is created through
ble 1). The steps of the method are as follows: First, we generate
functions that follow underlying physical laws to predict a property.
a random two-dimensional non-Gaussian noise via Johnson trans-
When using those models, the relation between the input parame-
form system giving as input parameters the first four statistical
ters and the output value is already known and used for predictions.
moments (mean, Rms, skewness and kurtosis). If the distribution
A ML model is a data-driven model that is used to find an appropri-
parameters cannot converge, we use the Pearson transformation
ate (originally unknown) function that reflects the connection of
system. Then, we measure the skewness and kurtosis of the surface
an input (given) property to an output property that we want to
to satisfy the chosen precision conditions. If the conditions are not
predict. Even though the actual relation is unknown, given suffi-
met, we repeat the generation of the surface and validation. Finally,
cient values for input and output values from experiments, we can
the surface becomes correlated by reconstructing and rearranging
create a ML (statistical) model that approximates the relation. Along
the height sequence in the x and y directions imitating a known
with pre-existing human expertise, the approximations could add
Gaussian correlated surface with correlation lengths ππ₯ and π π¦
value to the manufacturer that aims to predict physical properties,
along axes x and y respectively. Yangβs method is characterized by
without the need to exhaustively perform experiments, given the
its efficiency as different internal fitting methods are used for con-
cost of such experiments in time and money.
vergence. Thus, we can create surfaces with skewness and kurtosis
In this work, we are using three ML models: 1) Linear Regres-
inputs that can successfully (with low error) cover every point in
sion 2) Random Forests 3) Neural Networks. We try these different
the skewness-kurtosis plane πΎπ’ β ππ 2 β 1 β₯ 0.
families of learning, since this problem has no prior indication of
Subsequently, the active area was measured by integrating the
the underlying input-output relation, which may affect the method
secant of the angle πΎ between the surface normal and its z-direction
selection. For example, linear regression models will assume a lin-
normal.
β« β« β« β« ear relationship between the input and the output. On the other
ππ΄ = π ππ (πΎ)ππ₯ππ¦ (2) hand, Random forests and Neural network models use different
methodologies to approximate/learn non-linear relationships be-
Where, πΎ is defined as the angle that the z-axis makes with the tween (even high dimensional) input parameters and a predicted
normal vector of the differential surface dA. output property. We stress that there is no single, overall better
method for all estimation problems. This statement is better known Linear regression models are faster that both Neural networks
as the "no-free-lunch theorem" [15]. and Random Forests but have less accuracy in cases where non-
Linear regression models [16] (or in our case a multiple linear linear inner dependencies appear in data. Both, Neural Networks
regression model) approximate the relationship between the input (NN) and Random Forests offer good levels of performance in dif-
space and the output variable by fitting a linear equation. Those ferent application areas. However, different methods offer different
models are characterized by their simplicity and speed and are potential for learning and approximating, coupled with different
oftentimes used as a benchmark, to allow comparison to other, processing requirements (in time and memory). Random forests
more complex models. training costs less time (when compared to NNs in a generic setting)
Random Forests [17] are ensemble methods that use multiple and after training, they can be more interpretable than the average
decision trees. A decision tree partitions the input space into sub- NN. On the other hand, the accuracy a neural network can reach
spaces and maps each subspace to a predicted output value. The is higher, if we have access to the required volume and diversity
division of the space is done using training (example) data from of data (more data is usually needed to tune more parameters).
the dataset. The algorithm searches for an appropriate partitioning, Essentially, the selection of training data is a defining factor for ML,
which reduces the error of the predicted value across all training beyond the algorithms and the corresponding architecture. These
examples. Normally, each decision tree is fed by all the available data should satisfy three basic requirements in order to make a good
training data. However, in the Random forest approach, the learning approximation through a ML model. Those requirement are related
creates several trees, each applied on a randomly selected subset of to the: 1) quantity 2) diversity 3) quality of data. Regarding our
the full training data. The model predicts the output by considering work, we aimed to satisfy these three requirements while creating
all of the predictions of each decision tree. This approach has been the training and testing datasets before using the models.
shown to be more effective and also generalize better with respect
to unseen examples [18]. 4 RESULTS
Neural Networks (NNs) are models that learn complex functions,
combined in a non-linear manner over several layers. As such, NNs 4.1 Database Characteristics
have been shown to be excellent approximators of many families By applying the methodology described in section 3.1, we gener-
of functions [19], meaning that they can mimic many underlying ated two databases for the training and the validation of the ML
functions very efficiently, when given enough training data. NNs models respectively. The databases consist of surfaces with diverse
include neurons (or layers of nodes) that are combined to solve combinations of roughness parameters (Rms, correlation lengths,
complex problems. A NN consists of an input layer, one or more Skewness and Kurtosis) and the corresponding functional param-
hidden layers and an output layer. The input layer is fed a repre- eter (active area). The distribution of the training and validation
sentation of the independent variables that (we expect) define the datasets are shown in Figure 2 a) and b):
output. The output layer is expected to deliver the estimation of The total volume of training data-surfaces has been 3000 surfaces
the output, dependent variable. Intermediate layers of nodes take while for validating reached 15000. We trained each model with
as input the output of previous layers and transform it (i.e. apply a different percentages of surfaces from the train dataset to examine
function on it). In essence, each node of a NN is a linear function of the effects of the training data size on model success. Also, for every
its input, passed through a non-linear operator. The intermediate percentage of the training set, we applied the training procedure
layers end up forming a (sometimes very complex) function that 10 times with randomly selected surfaces from the database.
connects input to output.
NN models with many layers are called Deep Neural Networks. 4.2 Model evaluation metric
Such a network may contain millions of parameters, identifying For the validation of the predictability of models, we evaluated
the function the network represents. No matter whether we have a the RMSRE (Root Mean Square Relative Error). While the RMSE
deep network or not, these parameters are optimized to minimize (Root Mean Square Error) can indicate successfully the appearance
the estimation error. In other words, we take each training example, of outliers, the relative value of RMSE has no units. RMSE is the
provide it as input to the network and get its output prediction. squared root error of the average predicted active area π΄π from the
Based on the real value it should have output, we change (i.e. op- average actual active area π΄π .
timize) the parameters of the network to minimize the prediction
error. A number of optimization methods can be used to infer these βοΈ
parameters from the training data, the most well-known being
Γπ
π=1 (π΄π β π΄π )
back-propagation. π
πππΈ = (3)
π
There is no a-priori best way to create a NN. However, standard
practices can be applied to create such an architecture [20]. Gener- To produce the RMSRE, the RMSE is normalized by the projected
ally, a Neural Network can be made deeper by adding more hidden area of our surfaces. In our case, the projected area is π΄πππ ππππ‘ππ =
layers or more nodes, that however may lead the function to over- ππΏ 2 = 64ππ 2 .Thus, for N surfaces the RMSRE would take the
fitting, i.e. reducing generalization ability to unseen input, which following formation:
in turns increases the error when using the network for prediction.
Thus, the definition of an architecture can be a challenge in itself.
However, techniques such as dropout [21] have been proved to be π
πππΈ
π
πππ
πΈ = 100 (4)
effective. π΄πππ ππππ‘ππ
Figure 3: RMSRE vs the volume of the training data for Lin-
ear Regression, Random Forests, Neural Networks and Deep
Neural Networks
Figure 2: a) Database of the surface roughness parameters
used to train the models. b) Database of the roughness pa-
rameters used to validate the models. Each box represents a
histogram for the specific parameters (Rms, ππ₯ ,π π¦ , skewness,
kurtosis) and the functional parameter of active area.
Figure 4: True actual active versus predicted active area for
the linear regression model. This model was trained with
4.3 Machine Learning Results 610 random data-surfaces
Linear Regression.
We trained a set of Linear Regression models as a basis com-
parison with the rest of models. Figure 3 shows the RMSRE of the
trained models within a volume range of training data (surfaces).
The linear models reached a plateau of RMSRE 9.6% using the vali-
dation dataset after approximately 100 training data points-surfaces.
The model predictions diverge from the true values for high and
low active area values, as seen in Figure 4.
Random Forests.
We used random forest estimators fitting 25 regression decision
trees each. Each tree averages the results to improve the predictive
accuracy and control over-fitting. The decision trees used for train-
ing had a maximum depth of 25 branches with a minimum number
of internal node splits of two and a mean squared error criterion Figure 5: True actual active versus predicted active area from
for splitting. Random Forest models outperforms the Linear Regres- a random forest model that was trained with 2137 random
sion models after approximately 120 data-surfaces (Figure 3) and data-surfaces
achieved less than 4.0% RMSRE after 2100 training data-surfaces.
The standard deviation of the RMSRE decreases as the training
dataset becomes larger. Figure 5 shows that the models were able Neural Networks and Deep neural networks.
to predict the high and low active areas of the surfaces with less
error as compared to the the linear regression models. However, We used a set of neural network (NN) and a deep neural network
there is still a significant amount of error for high active areas. (DNN) models for the prediction of active areas. NN models were
trained using the adam [22] solver with a five-layer architecture
consisting of 15,25,40,25,15 nodes respectively. The DNN models
were trained through rmsprop optimizer with a two-layer archi-
tecture consisting of 200 nodes each. To overcome any overfitting
tendency, a 50% dropout was established between the two layers
and an additive zero-centered Gaussian noise of π π‘π = 1 was added
to the last layer. Both models had activation function the Rectified
Linear unit (ReLu).
For training datasets with a size of less than 300 surfaces, the NNs
performed worse as compared to the linear regression models (Fig-
ure 3). After 300 surfaces, they outperformed the linear regression
models reaching a π
πππ
πΈ = 6%. It is noted that in this case as
well, the standard deviation increases with the size of the training Figure 7: Absolute value of the weights between the input
data. The performance of DNNs is comparable to the Random forest and the first layer of a Deep Neural Network that was trained
model. For 2700 surfaces of training data, the DNN models show with 2700 random data-surfaces
an average error of π
πππ
πΈ = 2% (Figure 6). Therefore, the DNNs
generally show a significantly lower error compared to the NNs.
By taking the average of the absolute value of the weights between 5 SUMMARY
the input layer and the first layer of the DNN, we can identify the In our work, we proposed a hybridization scheme that combines
most important features of the model. Figure 7 shows that Rms has data-driven methodologies (4th paradigm [8]) with domain the-
the highest weight intensity, followed by the correlation lengths in oretical and modeling knowledge as an alternative (2nd and 3rd
x and y axis (ππ₯ and π π¦ resp). This results is in harmony with pre- paradigm) link between the configuration of nanosurface rough
vious findings based on computational analysis and experimental morphology and prediction of wetting behaviour.
measurements [4] [3] In particular, we trained Linear Regression, Random Forest, Neu-
ral Network and Deep Neural Network models with simulated
nanosurfaces in order to predict the true (active) area of the surface,
a critical parameter for wetting when Wenzel model is assumed. We
then compared their performances in relation to the required data
(simulation cost to produce rough surfaces). Random Forests and
Deep Neural Networks showed the highest performance reaching
4 % of RMSRE after 1000 training data-surfaces. The models and
particularly the Deep Neural Networks indicate that Rms has the
highest importance in wetting behavior. The correlation lengths in
the x and y axis showed lower but significant importance as well
whereas skewness and kurtosis play a minor though detectable
role.
REFERENCES
[1] Y.-P. Zhao, Characterization of Amorphous and Crystalline Rough Surface: Princi-
ples and Applications. San Diego, CA: Elsevier, 2000.
[2] R. N. Wenzel, βResistance of solid surfaces to wetting by water,β Industrial &
Engineering Chemistry, vol. 28, no. 8, pp. 988β994, 1936.
[3] L. Lai and E. A. Irene, βArea evaluation of microscopically rough surfaces,β Journal
of Vacuum Science & Technology B: Microelectronics and Nanometer Structures
Processing, Measurement, and Phenomena, vol. 17, no. 1, pp. 33β39, 1999.
[4] F. Foadi, G. H. ten Brink, M. R. Mohammadizadeh, and G. Palasantzas, βRoughness
dependent wettability of sputtered copper thin films: The effect of the local surface
slope,β Journal of Applied Physics, vol. 125, no. 24, p. 244307, 2019.
[5] M. B. Stearns, βMagnetization and structure of mn-ni and mn-co layered magnetic
thin films,β Journal of Applied Physics, vol. 53, no. 3, pp. 2436β2438, 1982.
Figure 6: True actual active versus predicted active area from [6] Y. Zhang, The effect of surface roughness parameters on contact and wettability of
a Deep Neural Network model that was trained with 2700 solid surfaces. PhD thesis, Iowa State University, 2007.
[7] G. M. Sacha and P. Varona, βArtificial intelligence in nanotechnology,β Nanotech-
random data-surfaces nology, vol. 24, p. 452002, oct 2013.
[8] T. Zhou, Z. Song, and K. Sundmacher, βBig data creates new opportunities for
materials research: A review on methods and applications of machine learning
for materials design,β Engineering, vol. 5, no. 6, pp. 1017 β 1026, 2019.
[9] C. Sutton, βCrowd-sourcing materials-science challenges with the nomad 2018
kaggle competition,β npj Computational Materials, vol. 5, 2019.
[10] K. T. SchΓΌtt, H. Glawe, F. Brockherde, A. Sanna, K. R. MΓΌller, and E. K. U. Gross,
βHow to represent crystal structures for machine learning: Towards fast prediction
of electronic properties,β Physical Review B, vol. 89, May 2014.
[11] A. Kordijazi, H. M. Roshan, A. Dhingra, M. Povolo, P. K. Rohatgi, and
M. Nosonovsky, βMachine-learning methods to predict the wetting properties of
iron-based composites,β Surface Innovations, pp. 1β9, 2020. [17] Tin Kam Ho, βRandom decision forests,β in Proceedings of 3rd International Con-
[12] M. Raissi, P. Perdikaris, and G. E. Karniadakis, βPhysics informed deep learning ference on Document Analysis and Recognition, vol. 1, pp. 278β282 vol.1, 1995.
(part i): Data-driven solutions of nonlinear partial differential equations,β 2017. [18] Tin Kam Ho, βThe random subspace method for constructing decision forests,β
[13] N. Garcia and E. Stoll, βMonte carlo calculation for electromagnetic-wave scat- IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 8,
tering from random rough surfaces,β Phys. Rev. Lett., vol. 52, pp. 1798β1801, May pp. 832β844, 1998.
1984. [19] M. A. Nielsen, βNeural networks and deep learning,β 2018.
[14] G. Yang, B. Li, Y. Wang, and J. Hong, βNumerical simulation of 3d rough surfaces [20] P. Benardos and G.-C. Vosniakos, βOptimizing feedforward artificial neural net-
and analysis of interfacial contact characteristics,β CMES - Computer Modeling in work architecture,β Engineering Applications of Artificial Intelligence, vol. 20, no. 3,
Engineering and Sciences, vol. 103, pp. 251β279, 12 2014. pp. 365 β 382, 2007.
[15] D. H. Wolpert, βThe lack of a priori distinctions between learning algorithms,β [21] N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov,
Neural Computation, vol. 8, no. 7, pp. 1341β1390, 1996. βDropout: A simple way to prevent neural networks from overfitting,β J. Mach.
[16] D. W. Gareth James and H. Tibshirani, An Introduction to Statistical Learning pp Learn. Res., vol. 15, p. 1929β1958, Jan. 2014.
59-126 and pp. New York, NY: Springer, 2013. [22] D. P. Kingma and J. Ba, βAdam: A method for stochastic optimization,β 2014.