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Page 8 of 15 Hu et al. J Mater Inf 2023;3:1 I http://dx.doi.org/10.20517/jmi.2022.28

2
10

]
2 B 3
k 10
A
2 A
m
/
A 4
3 A 10
[
c
R 5
10

6
10
1.0 1.2 1.4 1.6
2 3
(R = 10 ) [m/ ]
AA
Figure 4. The relationship between the critical cooling rate and the low temperature glass density . The samples with = 10 −6 do not
crystallize in the longest computational timescale. They are shown here for convenience.

These findings demonstrate that the GFA of an alloy is more complex than from some single parameters. We
need to figure out the high-order correlations between the GFA and the elemental and alloy properties. Nowa-
days, there is no explicit function that can be used for this purpose. To better define the function and get
the main factors, we should turn our attention to some advanced big data analysis techniques, for example,
supervised machine learning. This methodology will enable us to explore such a kind of relationship without
knowing the function in priori.

Machine learning has become an innovative tool to explore big datasets and make predictions based on the
known features [26–28] . It has been applied in enormous numbers of fields, including materials science [29–33] .
Meanwhile, many advanced theoretical models have been developed for different application cases. In this
study, we are trying to explore the simulation GFA datasets and gain physical insights into glass formation.
Usually, machine learning is likely a black box for users with high-dimensional inputs. The designed model
with a specific algorithm will take care of the mathematical relationships from the input features to the labels.
The nonlinearity involved is hard to explain in a physical manner. Here, we start with a simple model with a
small number of features so as to capture all the details.

Considering our simple model systems, there are several independent variables. Namely, / , / ,
/ , . Thus, we are trying to build a minimal number of basic features for the machine learning
model. Based on the previous understandings of the GFA, four fundamental features are thus considered:
1 = ( − )/( + ) and 2 = 2 /( + ), = ( − )/ , and . These features mainly
consider how different the two components are. Under the well-mixed condition, the more different the two
species are, the stronger frustration towards crystallization will be. Hence, the GFA will be elevated.

Withthecriticalcoolingrates(inlogscale, log c)asthelabel,ourmachinelearningproblemisintrinsicallya
10
regressionproblem. Weconstructedthemachinelearningmethodsbyemployingtheopen-sourceScikit-learn
package [34] . Before building the model, the input features need cleaning and preprocessing. As a first step, we
recall that about 25% of the samples cannot be crystallized in the simulation timescale. Therefore, they are not