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Chemical Physics Lettersjournal homepage: www.elsevier.com/locate/cplett

Research paper

Data analysis of multi-dimensional thermophysical properties of liquid
substances based on clustering approach of machine learning

7

Gota Kikugawaa,⁎, Yuta Nishimurab, Koji Shimoyamaa, Taku Oharaa, Tomonaga Okabec,d,Fumio S. OhuchidaInstitute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
School of Engineering, Tohoku Univ., 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japanc
Department of Aerospace Engineering, Tohoku University, 6-6-01, Aramaki Aza Aoba, Aoba-ku, Sendai, Miyagi, 980-8579, Japand
Department of Materials Science and Engineering, University of Washington, BOX 352120, Seattle, WA 98195, USAb

H IG HL IG HT S

map is performed on thermophysical properties of liquid substances.
• Self-organizing
learning-assisted screening protocol of liquid substances is proposed.
• Machine
substances are automatically categorized based on various properties.
• Liquid• Easy visualization technique of relative relationships among liquids is provided.
A R TIC L E INFOA B S TR A C T

Keywords:
Self-organizing map
Clustering analysis
Machine learning
Thermophysical properties
Heat medium

In order to develop an eﬃcient framework for global screening in the material exploration, we performed aclustering analysis of machine learning on the multi-dimensional thermophysical properties of the liquid substances. Data mining using a self-organizing map (SOM) based on the unsupervised learning was employed toproject high-dimensional thermophysical data onto a low-dimensional space. Here we adopted 98 liquid substances with eight thermo-physical properties for the SOM training in order to group the liquid substances. The
present SOM-clustering approach properly categorized liquid substances according to the chemical species
characterized by the functional groups.

1. Introduction
Technology to design and synthesize liquid substances having appropriate thermophysical properties for specific applications is an important subject in a wide variety of scientific and technological fields.
At the industrial level, eﬃcient development and exploration of heattransfer fluids or phase-change materials, which are used as a working
fluid of heat exchangers in refrigeration and air-conditioning equipment or used for thermal storage, are highly required these days. In
these areas, prior knowledge-based survey and/or conventional empirical laws for materials properties are utilized for the design guideline; however, when novel materials with superior properties are developed, a trial-and-error approach is needed since the required
specification is so multi-objective, or the empirical laws is not always
eﬀective due to the outside of application limit. For example, if required
thermophysical properties of the liquids has been realized by mixing⁎

multiple liquids, the number of mixing combinations and variation in
the composition of each liquid get enormous, which makes the materials exploration almost impossible. Therefore, an alternative approachis highly needed for design and discovery of novel liquid substances inmore eﬃcient manner.
One promising approach is a data-driven machine learning (ML)technique, which is known as materials informatics (MI) [1] recently.
Materials informatics has drawn considerable attentions in various
material design partly because application of ML rapidly prevails to awide spectrum of the scientific and technological field with the aid ofadvancement of computational performance for ML. So far, MI is intensively applied for accelerating search of inorganic materials likeshape memory alloys [2–4] and piezoelectrics [5,6], and for predicting
properties of perovskite crystal and finding one having optimal properties [7,8]. Other example is ML-assisted materials design and property
prediction of solid materials such as elpasolite [9,10], metallic alloys

Corresponding author.
E-mail address: kikugawa@tohoku.ac.jp (G. Kikugawa).

https://doi.org/10.1016/j.cplett.2019.04.075
Received 26 August 2018; Received in revised form 24 April 2019; Accepted 27 April 2019
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[11–13], transition metal complex [14], layered double hydroxide [15],high dielectric permittivity materials [16], and thermoelectric materials[17]. As such, these studies have already shown eﬀectiveness of materials informatics, i.e., a use of enormous data from experiments andnumerical simulations, in particular, first-principle calculations, gives
the accurate prediction of physical properties and development of improved materials.
Besides the inorganic materials, organic materials and organic-inorganic hybrid systems are getting targeted as an application of MI[18–25]. Discovery and design of polymeric materials, metal organic
frameworks (MOFs), and organic/inorganic perovskite are good candidates for MI subject and actually require the ML-assisted screening ordevelopment. For example, polymer dielectrics were studied by MLwith properties provided by DFT (density functional theory) calculations [18,19]. A Bayesian optimization technique was applied for proposing better experimental settings of polymer fiber synthesis [20]. A
couple of unsupervised and supervised ML techniques were applied todevelop the better prediction of CO2 absorption properties into amine
solutions [21]. For construction of a better quantitative structureproperty relationship (QSPR), a large dataset of polymeric materials has
been provided online [22,23]. ML-assisted materials development andproperty prediction for soft matters are also reviewed on Ref. [25].
Applications of MI protocols on the design and exploration of theliquid substances, on the other hand, have been very limited so far. As
mentioned earlier, the eﬃcient development and exploration of heattransfer fluids like a coolant is, however, getting required significantly.
When it comes to a coolant, the multi-objective design is needed since
the various requirement should be fulfilled as an industrial product,some of which are basic transport properties like thermal conductivity
and viscosity, non-flammability, and global warming potential (GWP).
Therefore, it is not an easy task to find the improved substances andoptimize the various properties at once.
In our study, we aim at building the overall platform for the eﬃcient
screening of materials candidates, which is constructed by a multi-stage
screening protocol. This platform involves “global screening” whichenables to roughly screen a lot of candidates by using data-mining
approach based on unsupervised learning, and precise exploration
which is realized by commonly adopted MI techniques based on the
structure/properties prediction model and/or structure optimization bydesired properties. The purpose of this study is to demonstrate that
unsupervised approach for grouping materials is eﬀective as the global
screening. Our vision regarding the multi-stage screening is mostly
motivated from the fact that large amount of dataset is not always
available for liquid substances. Therefore, in order to build an accurate
prediction model with relatively limited dataset, rough screening prior
to precise ML-driven materials finding is eﬀective.
In the present paper, we addressed the global screening stage for
exploration of the liquid substances assisted by ML techniques. To thisend, we propose to utilize one of the dimensionality reduction techniques called self-organizing map (SOM) to enable visual understandingof the diverse thermophysical properties from various liquid substances. Dimensionality reduction can be used when finding novel
materials with meeting a lot of requirements, which is the usual case in
the industrial process. SOM is one of the most appropriate techniques
for this purpose since we can keep proximity information on the low
dimensional mapping unlike the linear dimensionality reduction suchas the principal component analysis (PCA). Therefore, SOM has beendeveloped and progressively applied in a variety of engineering fields,such as optimal design of aircraft wings [26] and development ofthermosetting polymer resin [27]. Here, we present a combined approach of SOM and clustering applied to a wide variety of the liquid
substances, and a possibility of our framework for materials screening
to enable us to design and explore better liquid substances more easily.

2. Data analysis
2.1. Self-Organizing Map (SOM)
SOM provides a data-mining technique which helps to understandhigh dimensional data, such as various thermophysical properties of theliquid species in the present case, by reducing their dimensions of thedata to typically a two-dimensional space, so that the relative relationships among input data can be visualized intuitively [28,29]. In
this technique, the data are nonlinearly reduced to a low-dimensional
space with maintaining the neighborhood relationships among the
input data. This data mining technique is now utilized in various fields
to clarify relative relationships of complicated data.
In terms of machine learning, SOM is categorized into unsupervised
learning, which is based on a neural network (NN). Therefore, it isinterpreted as a feed-forward two-layer NN which is composed of an
input layer and an output layer. The input layer corresponds to all dimensions of the all input data (thermophysical properties in this study)
and all input-layer nodes are connected to all output-layer nodes.
Furthermore, each output-layer node has a vector composed of thethermophysical properties. This is called a weighted vector with thesame number of dimensions as that of input data, and is updated
through a competitive learning process. Each node of the output layer
holds the coordinate information at low dimensions (two dimensions inthis study) concurrently, and the neighborhood relationships amongnodes in the output layer are expressed by these coordinates, i.e.,
projection onto the low-dimensional map.
Detailed algorithm of the SOM is given in previous literatures, so weonly make a brief explanation below. Let total numbers of the inputlayer and output-layer nodes be I and J, respectively, and component
vectors of the input-layer nodes and the weighted vectors of the output
layer at the t-th learning cycle are expressed as x = [x1, x2, …, xI ] andm (t ) = [m1 (t ), m2 (t ), …, mJ (t )], respectively. As the first step of alearning process, a weighted vector from all the output-layer nodes,
which has the highest similarity to the input data, is chosen and that
node is defined as a winner node, mc (t ) , as follows.

xk

m c (t ) = minj x k

mj (t ) .

(1)

The weighted vector on the winner node is updated in such a waythat the vector gets closer to the input data; at the same time, theoutput-layer nodes near the winner node also become closer to the
input data, depending on their proximity to the winner node. By repeating this learning process, similarities among the weighted vectors
on the output-layer nodes near the winner node increase. This updateprocess is repeated until the weighted vectors converge to obtain the
final SOM. Liquid species with similar thermophysical properties are
finally distributed closer on the SOM. The learning algorithm of SOM
can be roughly categorized into two types: online-learning SOM andbatch-learning SOM (BLSOM). This study adopted a batch type, inwhich the learning result is not aﬀected by an input order of thelearning data.
For the input data to be used in the present analysis, we have chosen
98 liquid substances which are categorized into alkane, alcohol, aromatic series, carboxylic acid, amine, ketone, ester, and halide. Under
standard temperature and pressure conditions, these substances are in aliquid phase. Since the SOM learning does not allow missing data, i.e.,
SOM cannot be applied if a part of thermophysical properties is not
given in databases for a certain liquid substance, only 98 liquids, forwhich thermophysical properties are fully available in the literatures
without any missing data, were examined. In the analysis, the following
eight thermophysical properties were chosen; they are mass density,
specific heat at constant pressure, melting point, boiling point, saturated vapor pressure, surface tension, viscosity, and thermal

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conductivity, each of which was taken from the handbook and databaseof liquid properties [30–35]. All the datasets are available as
Supplementary Material. Note that these thermophysical properties do
not have the same averaged value and variance over the tested 98 liquids, i.e., each property has a diﬀerent data range. Therefore, they
were normalized into those with an average of 0 and a variance of 1
before they were used as the input data for learning. All the data analysis codes were implemented using python language (python 3.5) with
the SOMPY package [36].

2.3. U-Matrix method
A U-Matrix (unified distance matrix) method [38] is used to visualize the similarity between the adjacent nodes based on the distanceinformation between nearest neighbor output-layer nodes. Here, the UMatrix is given as

Ui =

1
Ni

Ni
j

mi

mj ,

(2)

where the output-layer node and the nearest neighbor output-layer
node are denoted as i and j, respectively, and Ni is the number of nodes
adjacent to node i. The U-Matrix gives local distance relationships between the nodes, and a large U-Matrix value would be regarded as aboundary of the clusters where separation between the nodes are large.
In this study, the U-Matrix is used for examining “quality” of the clustering result by using the k-means method.

2.2. Clustering approach
The output-layer nodes after the SOM learning have weighted vectors whose components are multi-dimensional thermophysical properties, and the nodes, which are mutually close in distance in a high dimensional space, are placed at mutually near locations in the twodimensional SOM. Furthermore, in order to easily visualize the nodes
with similar thermophysical properties, a clustering technique using a
k-means method [37] was performed. This unsupervised learning
method is one of non-hierarchical clustering techniques, which is used
to classify input data having multi-dimensional quantities into preliminarily defined K clusters. In this method, K clusters’ gravity center,i.e., centroid, are first given so as to be as far apart as possible eachother (the k-means++ method), and then all data points are engaged
in a cluster associated with the centroid to which the Euclidian distanceis closest. Next, the centroid is calculated from the data points belonging to each cluster again, and the data points belonging to eachcluster are updated. This process is repeated until the positions ofcentroids and the data points belonging to each cluster converge. The
overall procedure of SOM-clustering approach described throughSections 2.1 and 2.2 is summarized in Fig. 1.

3. Results of SOM-clustering approach
The SOM learning was performed on aforementioned 98 liquid
substances with eight thermophysical properties. A positioning map
where each substance is assigned to the output-layer node that has theweight vector closest to each substance is presented using a 30 × 30
map in Fig. 2. The clustering result obtained using the k-means method
as described in Section 2.2 is represented by the individual color designating each cluster. Originally, an attempt was made to determine thenumber of clusters through the Elbow method and Silhouette analysis[37]; the number adopted in the present study was 10, selected among
those which have relatively good (not best) results of the Silhouette
analysis (details not shown here). The liquid substances classified into
clusters are outlined as follows.
(1) Water (yellow-green, lower right) and glycerol (red, middle rightside) belong to independent clusters.
(2) Liquid species having small molecular weights and likely to formhydrogen bonding, such as ethylene glycol and ethanolamine(yellow, lower right)(3) Alcohol and alkane liquids with relatively large molecular weights(blue, right)(4) Alcohol and alkane liquids with relatively small molecular weights(light blue, bottom)(5) Aromatic series and cycloalkane (purple, top center)(6) Alkane smaller than 4), unsaturated alkane, and ketone (pink,
lower left)(7) Halogen compounds with relatively small molecular weights (orange, upper left)(8) Halogen compounds with relatively large molecular weights (green,
upper left)(9) Heavy halogen compounds substituted for two bromine and/or iodine molecules (light purple, top center)
As a whole, the SOM indicates that the liquid substances characterized by each functional group are properly classified into groups. It
is found that the liquid species with special thermophysical properties
such as water or glycerol are automatically distinguished as an individual cluster and that halogen compounds are clearly separated asother clusters. In addition, cyclohexane and benzene are placed inmutually near positions in SOM, although their electronic structures are
diﬀerent with each other.
Fig. 3 depicts results from the U-Matrix analysis. Red and blue regions of the figure represent higher and lower values of the U-Matrix,
respectively. Therefore, liquid substances in a blue valley separated by
the red ridge have the larger deviation in thermophysical properties.
The result indicates that some liquid substances, which are classified
into the same cluster by the k-means method as shown in Fig. 2, have a

Fig. 1. Flowchart of overall SOM-clustering analysis.
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Fig. 2. SOM positioning map obtained from thermophysical properties of various liquids. The output nodes are classified via the k-means method and colored
separately by each cluster.

large distance in terms of thermophysical properties. This is because
relatively small numbers of the input data are used for learning as
compared to the defined number of clusters employed here. It will benecessary to enlarge the number of liquid species for better examinationof SOM-clustering approach.

are less correlated, for example, between vapor pressure and density.
This weak correlation suggests that thermophysical properties are notmutually in a trade-oﬀ relationship, which implies a possibility in designing the liquid substances with a higher degree of freedom.
Fig. 5 shows various thermophysical properties represented as “heatmaps” after the SOM learning. In each figure, the positions of liquid
substances and the cluster boundaries are identical to those shown in
the SOM positioning map (see Fig. 2). Therefore, one can get a grasp of
a whole distribution of various thermophysical properties and correlations of various liquid substances at a glance. For example, these heatmaps immediately give a strong negative correlation between density
and heat capacity, and specifically this correlation gets stronger near at
the cluster of halogen compounds (upper left). The result implies that
halogenation of the liquid molecule greatly influences specific thermophysical properties and transport properties. In terms of searchingheat-transfer fluids, liquid substances having low viscosity and highthermal conductivity are ideal, i.e., the high heat transfer coeﬃcient
can be obtained with low pumping power. Such materials can bereadily found in Fig. 5 like methanol and allyl alcohol at the bottom
center and formic acid at the lower right as examples. In fact, methanol
has thermal conductivity of 0.202 W/(m·K) and viscosity of
0.544 mPa·s, whereas the 2-methyl-2-propanol, which is greatly separated from methanol with large U-matrix ridge (see also Fig. 2 and4. Consideration based on each thermophysical property
While the SOM itself can provide information concerning distance
relationships of the input data, more detailed information can be extracted by visualizing distributions of each thermophysical properties
projected onto the two-dimensional SOM, i.e., each component of theweighted vectors, as discussed later. To briefly visualize the correlations between various thermophysical properties, a correlation matrix
for all the thermophysical properties just obtained from the input data
is presented in Fig. 4. In this figure, we can find obvious strong correlations, some of which are the positive correlation between boilingpoint and melting point and negative correlation between boiling point
and saturated vapor pressure as expected. Meanwhile, interesting but
not straightforward correlations are also found between the specificheat and thermal conductivity, the surface tension and thermal conductivity, and density and specific heat for the tested liquids. In contrast
to the strongly correlated properties, several thermophysical properties

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Fig. 3. U-Matrix values on output nodes obtained
from the weighted vectors. Red and blue regions of
the figure represent higher and lower values of the
U-Matrix, respectively. Each liquid species is placedat the same location as in Fig. 2. (For interpretationof the references to color in this figure legend, thereader is referred to the web version of this article.)latent heat of vaporization is actively utilized to remove emitted
thermal energy eﬀectively. In this case, the boiling temperature should
be within an appropriate range, taking into account operating conditions. Assuming a HP is operated under the atmospheric pressure andfor cooling of electronic devices, liquid substances having high thermal
conductivity and low boiling point (in a temperature range shown in
Fig. 5) are desirable like methyl formate or methanol. Although manyother restricting conditions, e.g., inflammability, toxicity, and environmental impact, must be considered in actual industrial applications, a highly practicable data mining technique can be achieved byinvolving such conditions into the framework of SOM.
5. Conclusions
We applied unsupervised machine learning protocols to multi-dimensional thermophysical data of liquid substances, and the liquid
substances were mapped in two-dimensional space using the SOM andclustering techniques to visualize the proximity relationship. It wasdemonstrated that this framework enabled us to easily understand relative relationships of the thermophysical properties among liquid
substances. Grouping of the liquid substances was successfully achieved
via the clustering approach using the k-means method which was applied to the weighted vectors on output-layer nodes in the SOM. Various
thermophysical properties of the tested liquid substances were represented as “heat maps” in the SOM. This visualization gives precise
correlations among thermophysical properties of a lot of liquid substances at a glance. Thus, the presented framework is useful for quick
design and exploration of the candidates of liquid materials for specificapplications.

Fig. 4. Correlation matrix for all the thermophysical properties. Each value
depicted in the boxes indicates the correlation coeﬃcient between two thermophysical properties.

Fig. 3), has lower thermal conductivity of 0.112 W/(m·K) and higher
viscosity of 4.31 mPa·s. Thus, we can easily separate superior substances among inferior ones in a certain practical use. In addition, if
heat-transfer fluids are used as a working fluid in a heat pipe (HP),

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Fig. 5. Heat maps of thermophysical properties projected on the SOM. The cluster boundaries using k-means clustering, which are identical to those in Fig. 2, are also
drawn in the figure.

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The authors declared that there is no conflict of interest.
Acknowledgments
We thank Dr. Yutaka Oya for a fruitful discussion. GK and TO thanks
the support of the Cross-ministerial Strategic Innovation Promotion
Program. We also would like to acknowledge the vitally importantencouragement and support made through the University ofWashington-Tohoku University: Academic Open Space (UW-TU:AOS).
Appendix A. Supplementary material
Supplementary data to this article can be found online at https://doi.org/10.1016/j.cplett.2019.04.075.
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