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Page 22 of 45 Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41

and time, it is crucial for researchers to understand which method is most useful for their individual
applications. This section offers a direct comparison between their individual strengths and weaknesses
based on the previously discussed studies.

ML techniques have numerous advantages that researchers can use to explore many compositions at once.
5
Firstly, the computational efficiency of most ML methods allows some studies to screen up to 10
[90,137]
compositions in a reasonable time frame . The faster computation speed of ML than other
computational techniques makes it particularly suited to exploring large composition spaces. Additionally,
the ability to select various combinations of features as input variables, such as composition, atomic radius,
valence electron concentration etc., gives ML a significant advantage in versatility allowing for pattern
[82,138,139]
recognition between features that would normally not be possible with the human mind . Despite the
impressive capabilities, ML techniques rely heavily on large robust datasets to generate useful models [81,90,139] .
Unfortunately, the relatively young age of the field of HEAs and the vast composition space means that the
[48]
relative size of the currently available datasets is still quite small . The small datasets limit the
compositional regions where accurate ML models can be trained and applied [81,82] . The other common
criticism of ML models is their lack of interpretability. ML models essentially act as a computational black
box, meaning that even when they provide accurate predictions, the underlying physics is obscured by the
complicated statistical calculations that are performed, making it difficult to build useful intuition from such
models [78,79,87,140] .

In contrast to the ML models, both first-principles and MD simulation methods rely primarily on well-
known quantum mechanical and classical laws instead of statistical models [114,117,138] . This ensures that a
strong fundamental understanding of the predicted properties can be extracted from such models. The
reliance on fundamental physics also reduces the need for large training datasets as the required datasets are
often already contained in readily available databases [125,141] . MD simulations also have the added benefit of
illustrating the dynamic evolution of microstructures during an experiment, thereby providing atomic scale
information on the phase transformation and deformation of materials during usage, which cannot be
[127,142]
achieved using any other computational technique . However, both first-principles and MD simulation
[138]
methods are much more computationally expensive than ML and CALPHAD methods . Thus, first-
principles and MD techniques cannot explore as many compositions as ML and CALPHAD methods as
4
3
seen in Table 1, where first-principles and MD can screen up to 10 and 10 compositions, respectively.
Recent studies have attempted to overcome this flaw by combining first-principles calculations with ML to
produce models that are computationally efficient and highly accurate and provide physical insight into
chemical segregation and phase formation [143-145] . Leong et al. used a cluster expansion (CE) model, which
[144]
expands the configurational energy of an alloy structure in terms of various atomic clusters . This model
was trained using data obtained through first-principles calculations. Once the configurational energy is
calculated for the clusters in the test set, the authors calculate the probability of the nearest neighbor (NN)
atomic pairing between the different atomic species in a Mo-V-Nb-Ti-Zr alloy system to predict the
[144,146]
Warren-Cowley short-range order (SRO) parameters . This SRO allows the authors to highlight the
tendency of Zr to segregate and cluster leading to the formation of intermetallic phases below 1,400 K and
single-phase solutions above 1,400 K.

Finally, CALPHAD methods are both computationally efficient and have sufficiently large databases to
produce accurate predictions for many HEA compositions [147,148] . In fact, CALPHAD methods are able to
6
screen more compositions than any of the other computational methods (up to 10 compositions) in a
[135]
reasonable time span . Despite this large computational efficiency, CALPHAD methods can only provide