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ARTICLE OPEN
Predicting the synthesizability of crystalline inorganic
materials from the data of known material compositions
Evan R. Antoniuk
1,2
✉, Gowoon Cheon
3,4
, George Wang
5,6,7
, Daniel Bernstein
8
, William Cai
8
and Evan J. Reed
8
Reliably identifying synthesizable inorganic crystalline materials is an unsolved challenge required for realizing autonomous
materials discovery. In this work, we develop a deep learning synthesizability model (SynthNN) that leverages the entire space of
synthesized inorganic chemical compositions. By reformulating material discovery as a synthesizability classification task, SynthNN
identifies synthesizable materials with 7× higher precision than with DFT-calculated formation energies. In a head-to-head material
discovery comparison against 20 expert material scientists, SynthNN outperforms all experts, achieves 1.5× higher precision and
completes the task five orders of magnitude faster than the best human expert. Remarkably, without any prior chemical knowledge,
our experiments indicate that SynthNN learns the chemical principles of charge-balancing, chemical family relationships and
ionicity, and utilizes these principles to generate synthesizability predictions. The development of SynthNN will allow for
synthesizability constraints to be seamlessly integrated into computational material screening workflows to increase their reliability
for identifying synthetically accessible materials.
npj Computational Materials (2023) 9:155 ; https://doi.org/10.1038/s41524-023-01114-4
INTRODUCTION
Throughout the history of modern science, the discovery of novel
materials with technologically desirable properties has resulted in
rapid scientific innovation. The first step in the discovery of any
new material is to identify a novel chemical composition that is
synthesizable, which we here define to be a material that is
synthetically accessible through current synthetic capabilities, but
may or may not have been synthesized yet. Our ability to develop
new materials and technologies is therefore dependent on our
ability to efficiently search through the entirety of chemical space
to identify synthesizable materials for further investigation.
For the purposes of this work, we refer to synthesized materials
as the set of all materials that have had their synthesis details
reported in the literature or are naturally occurring. Predicting
synthesized materials is of little interest since this task can be
trivially accomplished by searching through existing materials
databases
1,2
. Instead, this work explores the question of whether it
is possible to develop a method for predicting the synthesizability
of inorganic crystalline materials, regardless of whether or not that
material has been synthesized yet.
Whereas organic molecules can often be synthesized through a
sequence of well-established chemical reactions
3
, the targeted
synthesis of crystalline inorganic materials is complicated by the
lack of well-understood reaction mechanisms
4
. Instead, specific
inorganic materials can be preferentially synthesized through
selecting reactants that provide thermodynamic or kinetic
stabilization of the product, choosing reaction pathways that
minimize unwanted side-products, and/or encouraging selective
nucleation of the target material
4–6
. However, the decision to
synthesize a material also depends on a wide range of non-
physical considerations including the cost of the reactants, the
availability of equipment required for the synthesis, and the
human-perceived importance of the final product. As a result,
synthesizability cannot be predicted based on thermodynamical
or kinetic constraints alone. The final decision to pursue the
synthesis of a target inorganic material has traditionally been the
responsibility of expert solid-state chemists who specialize in
specific synthetic techniques or classes of materials. The careful
consideration of these experts minimizes the chance of an
unsuccessful synthetic effort, but does not allow for rapid
exploration of inorganic material space.
Due to the lack of a generalizable synthesizability principle for
inorganic materials, the enforcement of a charge-balancing criteria
is a commonly employed proxy for synthesizability (Fig. 1a)
7–9
. This
computationally inexpensive approach filters out materials that do
not have a net neutral ionic charge for any of the elements’
common oxidation states. Despite the chemically motivated nature
of this approach, we find that charge-balancing cannot accurately
predict synthesizable inorganic materials. Among all inorganic
materials that have already been synthesized, only 37% can be
charge-balanced according to common oxidation states (Supple-
mentary Table 3) Remarkably, even among all ionic binary cesium
compounds which are typically considered to be governed by
highly ionic bonds, only 23% of known compounds are charge
balanced (Supplementary Table 5). The poor performance of this
charge-balancing approach is likely due to the inflexibility of the
charge neutrality constraint, which cannot account for the different
bonding environments that are present among different classes
of materials such as metallic alloys, covalent materials, or ionic
solids.
A wide array of ab-initio and machine learning methods have
been developed to aid in the discovery of synthesizable materials.
One commonly employed approach utilizes density-functional
theory (DFT) to calculate the formation energy of a material’s
crystal structure with respect to the most stable phase in the same
chemical space as the material of interest
2
. This approach assumes
1
Materials Science Division, Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA, USA.
2
Department of Chemistry, Stanford
University, Stanford, CA, USA.
3
Department of Applied Physics, Stanford University, Stanford, CA, USA.
4
Google Research, Mountain View, CA, USA.
5
Department of Physics,
Stanford University, Stanford, CA, USA.
6
Department of Mathematics, Stanford University, Stanford, CA, USA.
7
Department of Computer Science, Stanford University, Stanford, CA,
USA.
8
Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA. ✉email: antoniuk1@llnl.gov
www.nature.com/npjcompumats
Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences
1234567890():,;
Fig. 1 SynthNN architecture and usage in material discovery. a Depiction of predicting synthesizability with charge balancing (left),
thermodynamic stability (middle), and the SynthNN model developed in this work. bModel architecture of SynthNN. Each chemical formula is
represented by a learned vector embedding that is obtained by performing elementwise multiplication between the composition vector and
the learned atom embedding matrix. This embedded representation is then used as the input for a deep neural network architecture for
predicting synthesizability. cWorkflow for a conventional Materials Screening. Computational materials discovery efforts typically operate by
screening through a database of synthesized materials. The machine learning model developed in this work broadens the search space of
Materials Screenings to enable an exploration that encompasses all possible chemical compositions. dWorkflow for an Inverse Design
material discovery approach. Given a desired target property, a generative model can be used to generate candidate materials that are biased
toward the desired property. SynthNN can be naturally incorporated into this workflow to ensure that the generated inorganic materials are
synthesizable, as is commonly done for small organic molecules
54
.
E.R. Antoniuk et al.
2
npj Computational Materials (2023) 155 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences
1234567890():,;
that synthesizable materials will not have any thermodynamically
stable decomposition products. However, due to a failure to
account for kinetic stabilization, this approach has previously been
demonstrated to be unable to distinguish synthesizable materials
from those that have yet to be synthesized and only captures 50%
of synthesized inorganic crystalline materials
10–12
. A wide range of
machine learning-based composition models for predicting
thermodynamic stability have also been developed as a means
for assessing composition synthesizability (Fig. 1a)
13–17
. Formation
energy calculations have also been combined with the experi-
mental discovery timeline to generate a materials stability network
that can produce synthesizability predictions. More recently,
several machine-learning based methods have been developed
to predict the synthesizability of a material from its crystal
structure
11,18,19
. However, these methods requires the atomic
structure as an input, which is typically not known for materials
that have yet to be discovered. To enable predictions on materials
for which the crystal structure is not known, several composition-
based material representations have been developed, predomi-
nantly for the task of material property prediction
13,16,17
.
Composition-based representations enable material discovery
across the entirety of chemical composition space, but are unable
to differentiate between different crystal structures of the same
chemical composition. Finally, numerous works have utilized data-
mining to extract inorganic material synthesis recipes from the
literature
20,21
. These methods can prescribe a synthesis recipe for
a hypothetical material, but do not allow for an assessment of the
synthesizability of the hypothetical material
22,23
.
In this work, we develop a deep-learning classification model
(that we call SynthNN) to directly predict the synthesizability of
inorganic chemical formulas without requiring any structural
information. We accomplish this goal by training SynthNN on a
database of chemical formulas consisting of previously synthe-
sized crystalline inorganic materials that has been augmented
with artificially generated unsynthesized materials. SynthNN offers
numerous advantages over previous methods for identifying
synthesizable materials. Whereas expert synthetic chemists
typically specialize in a specific chemical domain of a few hundred
materials, this approach generates predictions that are informed
by the entire spectrum of previously synthesized materials.
Additionally, since this method trains directly on the database of
all synthesized materials (rather than employing proxy metrics
such as thermodynamic stability or charge-balancing), this
approach also eliminates questions of how well these metrics
can describe synthesizability. Rather, SynthNN learns the optimal
set of descriptors for predicting synthesizability directly from the
database of all synthesized materials, allowing it to better capture
the complex array of factors that influence synthesizability. Finally,
this method is computationally efficient enough to enable
screening through billions of candidate materials. Since SynthNN
can be seamlessly integrated with Materials Screening or Inverse
Design workflows (Fig. 1c, d), the development of SynthNN serves
to greatly improve the success rate and reliability of computa-
tional material discovery efforts by ensuring that the candidate
materials discovered through these efforts are synthetically
accessible.
RESULTS
Model development
One of the main challenges in predicting the synthesizability of
crystalline inorganic materials lies in the lack of a generalizable
understanding of what factors contribute to synthesizability.
Although charge-balancing and thermodynamic stability are likely
to play a role in the likelihood that a material has been
synthesized, these features alone are unlikely to serve as a
complete set of descriptors predicting synthesizability. To account
for this challenge, we adopt a framework called atom2vec, which
represents each chemical formula by a learned atom embedding
matrix that is optimized alongside all other parameters of the
neural network (Fig. 1b, Methods)
7,24
. In this manner, atom2vec
learns an optimal representation of chemical formulas directly
from the distribution of previously synthesized materials. The
dimensionality of this representation is treated as a hyperpara-
meter whose value is set prior to model training (see Methods,
Table 1). Notably, this approach does not require any assumptions
about what factors influence synthesizability or what metrics may
be used as proxies for synthesizability, such as charge balancing.
The chemistry of synthesizability is entirely learned from the data
of all experimentally realized materials.
The synthesizable inorganic materials that SynthNN is trained on
are extracted from the Inorganic Crystal Structure Database
(ICSD)
25
. This database represents a nearly complete history of
all crystalline inorganic materials that have been reported to be
synthesized in the scientific literature and have been structurally
characterized (see Methods). On the other hand, unsuccessful
syntheses are not typically reported in the scientific literature. We
treat this lack of recorded data on unsynthesizable materials by
creating a Synthesizability Dataset that is augmented with
artificially-generated unsynthesized materials. It is important to
note that some of these artificially-generated materials could be
synthesizable, but are absent from the ICSD database or have yet
to be synthesized. Definitively labeling a material as unsynthesiz-
able is potentially problematic since the ongoing development of
synthetic methodologies may enable the synthesis of previously
unsynthesizable materials. To account for this incomplete labeling
of the artificially generated examples, we develop a semi-
supervised learning approach that treats unsynthesized materials
as unlabeled data and probabilistically reweights these materials
according to the likelihood that they may be synthesizable (see
Methods)
26
. The ratio of artificially generated formulas to
synthesized formulas used in training is a model hyperparameter
that we refer to as Nsynth (see Supplementary Note 1).
SynthNN therefore fits into a broader category of positive-
unlabeled (PU) learning algorithms. Recently, PU learning
approaches have been adopted in materials science to handle
the large amount of unlabeled material data that exists because of
the tiny fraction of chemical space that has been experimentally
explored. A transductive bagging support vector machine
approach has been previously used for predicting the synthesiz-
ability of crystals and the discovery of synthesizable MXenes
11,27
.
However, the PU learning approach in the present work most
closely resembles the approach of Cheon et al., whereby
unlabeled examples are class-weighted according to their like-
lihood of synthesizability
26
.
Table 1. Model hyperparameters used in training SynthNN.
Hyperparameter Name Range of sampled values
Number of hidden units in hidden
layer #1:
[30,40,50,60,80]
Number of hidden units in hidden
layer #2:
[30,40,50,60,80]
Adam optimizer learning rate: [2´102,5´103,2´103,
5´104,2´104]
Number of initial supervised training
steps
[2´104,4´104,6´104,
8´104,1´105]
Batch size [512,1024]
Atomic Embedding Dimension (M) [2,6,10,15,20,25,30,35]
Ratio of Synthesized:Unsynthesized
Training Examples (Nsynth)
[5,10,15,20]
E.R. Antoniuk et al.
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Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences npj Computational Materials (2023) 155
Benchmarking against computational methods
The performance of SynthNN is shown in Fig. 2a alongside random
guessing and charge-balancing baselines. After model training, we
calculate standard performance metrics by treating synthesized
materials and artificially generated unsynthesized materials as
positive and negative examples, respectively. This choice results in
the positive class precision shown in Fig. 1a to be lower than the
true model precision since synthesizable, but unsynthesized
materials will be incorrectly treated as false positive predictions
(see Methods). The random guessing baseline corresponds to the
expected performance if one were to make random predictions
weighted by the class imbalance, whereas the charge balancing
approach simply predicts a material to be synthesizable only if it is
charge balanced according to the common oxidation states
listed in Supplementary Table 3. Although the performance
metrics in Fig. 2are intended to provide an intuitive comparison
of model performance, PU learning algorithms are most com-
monly evaluated based on the F1-score (shown in Supplementary
Table 4)
28
.
Separating the model performance into class-specific precision
provides interesting insights into each of these approaches for
predicting synthesizability. Both SynthNN and the charge-
balancing model perform similarly well at detecting the
artificially-generated unsynthesized materials in our dataset. The
ability of the charge-balancing model to predict these unsynthe-
sized materials with a high precision is likely a direct consequence
of our choice to use randomly generated atomic coefficients to
generate the unsynthesized formulas. Generating chemical
formulas with random coefficients is unlikely to yield a formula
with a net neutral oxidation state, which allows the charge-
balancing method to consistently identify these unsynthesized
formulas. However, we observe considerable differences for the
case of synthesizable formulas. We find that our SynthNN model is
able to detect synthesized materials with a precision that is 2.6x
higher than charge-balancing and 12x better than random
guessing (Fig. 2a). It is interesting to note that the predictive
accuracy of charge-balancing has significantly decreased over
time (Fig. 2b). This likely reflects that our ability to synthesize
complex stoichiometries has vastly outpaced the predictive ability
of a simple charge-balancing approach, which further highlights
the need for a more complex synthesizability predictor that
accounts for a broader range of synthesizability considerations.
Predicting the thermodynamic stability of a material with DFT
has been widely adopted as a standard approach for computa-
tionally discovering synthesizable materials
14,16,17,29
. As a means
of further benchmarking SynthNN, we compare the synthesiz-
ability predictions of SynthNN to approaches based on DFT
calculated formation energies (Fig. 2c). In a real-world material
discovery problem, the general task is to search across broad
regions of chemical space to accurately identify synthesizable
materials. An ideal direct comparison of material discovery based
on SynthNN and DFT would therefore involve identifying the
synthesized materials from a random sample of chemical
composition space. However, DFT requires a material’s crystal
Fig. 2 Benchmarking SynthNN against other computational methods. Additional performance metric comparisons between SynthNN,
charge-balancing and Roost are provided in Supplementary Table 4. aPerformance of the SynthNN model on a test set with a 20:1 ratio of
unsynthesized:synthesized materials (Nsynth ¼20), containing 2410 synthesized materials and 48,199 unsynthesized materials. We benchmark
the performance of this model against a random guessing baseline and a charge balancing baseline (predicting a material to be synthesizable
if it is charge balanced). The performance shown for the SynthNN model and charge-balancing is evaluated only on the test set. The random
guessing baseline is taken to be the expected performance if randomly predicting 1/21 of all materials to be synthesizable in the full
synthesizability dataset with Nsynth ¼20.bFraction of all unique binary, ternary, and quaternary ICSD compounds that are charge-balanced,
plotted for the decade that the materials were first synthesized. The number above the bar indicates the total number of materials that are
listed in the ICSD as having been synthesized in that decade. Duplicate formulas are removed when calculating the fraction of materials and
the listed total number of materials. Charge-balancing is determined according to the oxidation states listed in Supplementary Table 3.
cPrecision-recall curve comparison between SynthNN and Roost
17
for predicting the synthesizability of materials in the entire Synthesizability
Dataset with Nsynth ¼20.
E.R. Antoniuk et al.
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npj Computational Materials (2023) 155 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences
structure as input. Although the crystal structure of a given
composition can be computationally predicted through methods
such as ab-initio random structure searching (AIRSS), it is
computationally infeasible to predict the crystal structure for
even hundreds of unsynthesized chemical compositions
30–32
.
Existing materials databases are also not a suitable testbed for
such a material discovery task since they contain an unrealistically
high fraction of synthesized materials and do not uniformly
sample chemical composition space. The high proportion of
synthesized materials in these materials databases are expected to
greatly underestimate the false positive rate compared to a
realistic material discovery setting.
We account for these challenges by instead benchmarking
SynthNN against a composition-based machine learning model,
Roost
17
, to act as a surrogate model for DFT calculations of energy
above the convex hull. Notably, Roost was recently shown to
outperform previous machine learned models for predicting
formation energies and achieved an accuracy that approaches
the DFT error, relative to experiment
29
.Wefirst train Roost on DFT-
calculated energy above the convex hull values from the Materials
Project database, where the value is taken from the lowest energy
polymorph of each composition
2
. Notably, 37,538 out of 79,533 of
the compositions in this dataset of energy above the convex hull
values are present in the ICSD, and thus overlap with the
synthesized examples in our Synthesizability dataset. This re-
trained Roost model achieves a mean absolute error of 0.063 eV
across the entire dataset, which is nearly identical to 0.06 eV mean
absolute error of a previously reported Roost model trained on the
Materials Project
29
. Following training, we use Roost to predict the
energy above the convex hull values for all entries in the
Synthesizability Dataset. A material is predicted to be synthesiz-
able by Roost if the predicted energy above the hull is below a
cutoff value, Ehull;cutoff , where Ehull;cutoff is evaluated at
0eV;0:05eV;0:1eV;0:2eV;0:3eV; :::; 1eV
fg
. We construct a
precision-recall curve for Roost by evaluating its precision and
recall across these various Ehull;cutoff values (Fig. 2c).
Roost achieves a maximum F1-score of 0.12 when using
Ehull;cutoff ¼0:05eV. At this Ehull;cutoff , Roost achieves a recall of
69% and a precision of 6.8%. At the same recall of 69%, SynthNN
achieves a precision of 46.6%, nearly 7× higher than that of Roost.
Although both SynthNN and Roost are composition-based ML
models, the main difference between these approaches is that
Roost is trained on DFT-calculated energy above the convex hull
values, whereas SynthNN is trained as a synthesizability classifier.
Based on the 7× higher precision achieved by SynthNN,we
conclude that reformulating the material discovery problem as a
synthesizability classification task, rather than an energy above the
convex hull regression task, can be a powerful strategy towards
improving the accuracy for discovering novel materials. The
performance of Roost could likely be improved by training on a
hypothetical dataset of DFT calculated formation energies with
greater chemical diversity and a larger fraction of unstable
structures than is available in the Materials Project. However,
creating such a dataset is hindered by the computationally
expensive challenge of finding the most stable crystal structure for
any given chemical formula. On the other hand, simply training
SynthNN on the growing list of synthesized chemical compositions
allows for greater chemical diversity to be incorporated into the
training data without incurring additional computational expense.
Finally, it is interesting to note that increasing the number of
artificially generated unsynthesized materials in the training set of
SynthNN significantly improves model performance (Supplemen-
tary Tables 1–2). Generating these unsynthesized materials works
analogously to data generation techniques that have been
employed for the task of image classification
33–35
. For the task
of classifying images, generating new artificial images to increase
the amount of training data has been shown to be effective in
improving image recognition accuracy
34
. In an analogous fashion,
including artificially generated unsynthesized materials in training
may help to better inform our model about how synthesizability is
impacted by the atom types, atomic coefficients, and the number
of different atom types in the chemical formula. Including
artificially generated formulas also exposes our model to a much
broader chemical space beyond what is represented if we only
trained our model on synthesized materials. The results in
Supplementary Tables 1–2 suggest that this data augmentation
strategy improves SynthNN’sprecision at identifying promising
regions of chemical space for future material discovery efforts.
Benchmarking against human experts
Although the model performance shown in Fig. 2establishes
SynthNN to outperform prior computational methods for predict-
ing synthesizability, realizing an acceleration in the rate of material
discovery is dependent on the ability of SynthNN to outperform
human experts. Since pursuing material synthesis requires
considerable resources, we anticipate that SynthNN will only see
adoption if it can offer higher precision synthesizability predic-
tions than human expert chemists. To compare the performance
of SynthNN against expert chemists, we create a Synthesizability
Quiz of 100 formulas by randomly sampling 91 unsynthesized
formulas and 9 synthesized formulas from the Synthesizability
Dataset (Supplementary Fig. 7). The high proportion of unsynthe-
sized formulas was chosen to simulate a realistic materials
discovery setting where synthesizable materials are expected to
be rare (Supplementary Note 3). A total of 20 human participants
were instructed to select the 9 materials that they think have been
synthesized, whereas SynthNN’s predictions were taken to be the 9
materials that were predicted to be most likely to be synthesiz-
able. Comparing the model performance of SynthNN to human
experts in this manner provides quantification for the magnitude
of improvement that artificial intelligence can provide for
discovering new materials, while also providing a more relatable
understanding of how well the SynthNN model performs.
Remarkably, SynthNN correctly predicts 6/9 synthesizable
materials, whereas the best human expert only recovered 4/
9 synthesizable materials. Although the Synthesizability Quiz
contains only 100 examples, we note that SynthNN’s precision on
this quiz (0.667) is comparable to the precision achieved on a
validation set with the same proportion of synthesizable materials
(precision of 0.665 for a recall of 0.600, shown in Supplementary
Fig. 4). Furthermore, the average number of correct guesses
achieved by SynthNN across 267 unique quizzes drawn without
replacement from the test set was 5.84, which is significantly
higher than the best human performance of 4.00. As has been
observed in a wide variety of contexts
36–39
, it is interesting to
note that the aggregate response of all human experts yields
predictions that are considerably more accurate than the average
individual human response. Since chemists tend to specialize in
specific domains of chemistry, this finding may highlight the
significant improvement in the ability to predict synthesizability
when the diverse domain expertize from multiple experts are
independently aggregated.
To further probe the performance of SynthNN and the human
experts, we explore how their predictions are affected by the
complexity of the chemical formula (number of unique atoms,
Fig. 3b) and the chemical family that the formula belongs to (Fig. 3c).
Interestingly, we find that the performance of human experts
significantly decreases for chemical formulas that contain d-block
and f-block elements, whereas the performance of SynthNN is
relatively constant across all chemical families (Fig. 3c). Chemical
formulas from the f-block of the periodic table are commonly
avoided due to their scarcity, radioactivity, and/or high cost
40,41
.We
speculate that this aversion to utilizing d- and f-block materials
decreases the familiarity of human experts with these elements,
which results in a decreased ability of human experts to identify
E.R. Antoniuk et al.
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Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences npj Computational Materials (2023) 155
synthesizable chemical formulas that contain them. It is also
interesting to note that human experts vastly overestimate the
likelihood that binary materials are synthesizable. Although binary
materials only comprise 15% of all synthesized inorganic materials,
binary materials accounted for 31% of the materials predicted by the
human experts to be synthesizable. In comparison, since SynthNN
has been trained on the distribution of all previously synthesized
materials, it is able to generate synthesizability predictions that are
well calibrated to match the distribution of formulas seen in known,
synthesized materials (Fig. 3b). Finally, we note that the self-reported
completion time for the Synthesizability Quiz was on the order of
30 min for the human experts, whereas SynthNN generates its
predictions in a few milliseconds- corresponding to a 105
acceleration in prediction rate.
Predicting future materials
One of the most important and challenging tasks for any machine
learning model is to make accurate predictions on examples that are
drawn from a different distribution than the training set. This is
particularly important for predicting synthesizability since new,
innovative materials are expected to follow a significantly different
distribution than the materials that have been previously synthe-
sized. As a notable example, NaCl
3
has recently been shown to be
synthesizable, in opposition to what would be predicted through
charge-balancing, a DFT-calculated phase diagram, or traditional
chemical intuition
42
. With the continued development of synthetic
technologies, we expect that future material discovery efforts will
increasingly move towards materials that do not obey simple
charge-balancing or thermodynamic stability criteria, such as meta-
Fig. 3 Benchmarking SynthNN against human experts. a Number of the 9 synthesizable formulas in the Synthesizability Quiz that are
correctly identified by a random guessing baseline (on average), the average human expert, the aggregate human response, the best
performing human expert, and SynthNN.bFraction of the human expert predictions on the Synthesizability Quiz that consist of binary,
ternary, and quaternary compounds (blue). Fraction of SynthNN predictions on the Synthesizability Dataset test set that consist of binary,
ternary, and quaternary compounds (orange) The true fraction of each compound type among the synthesized materials in the
Synthesizability Quiz and the Synthesizability Dataset test set are shown for comparison. cAverage F1-score of SynthNN and human experts
on the Synthesizability Quiz, decomposed by periodic table blocks. A chemical formula is included in a block if any of its constituent elements
belong to that block of the periodic table. The error bars of the SynthNN line provide the mean and standard deviation of the F1-score
achieved by SynthNN across all quizzes (with 9 synthesized formulas and 91 unsynthesized formulas) generated from sampling without
replacement from the test set of the Synthesizability Dataset.
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npj Computational Materials (2023) 155 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences
stable materials
43,44
. Indeed, as illustrated in Fig. 2b, 84% of materials
discovered between 1920 and 1930 were charge-balanced,
compared to only 38% of materials discovered between 2010 and
2020. In particular, since DFT approaches to material discovery are
designed for targeting ground-state structures, there is a growing
need to develop more sophisticated computational methodologies
that can capture a broad range of synthesizability factors.
To quantify the performance of SynthNN at predicting
synthesizable materials for future material discovery efforts, we
train SynthNN on training sets where the positive examples are
materials that were synthesized before a given decade and the
negative examples are artificially generated as before. We then
evaluate the performance of SynthNN on a test set that consists of
materials that were synthesized in the decades after the materials
in the training set. Since these test sets consist of only synthesized
materials, we quantify the model performance by calculating the
fraction of future synthesized materials that are predicted by our
model to be synthesizable (i.e., recall). We evaluate this test recall
at a decision threshold that corresponds to a precision that is 5×
better than random guessing on a validation set that is drawn
from the same distribution as the training data (Fig. 4).
Each line of Fig. 4illustrates how SynthNN’sability to predict
synthesizability changes as more materials are used in model
training. As SynthNN is exposed to more materials and more
diverse chemistries, we observe a considerable improvement in
SynthNN’sability to predict materials that will be synthesized in
both the current decade and future decades. In the most recent
example, training SynthNN on all materials synthesized before
2010 results in a model that can correctly identify 80% of all
materials that were synthesized between 2010 and 2019. On the
basis of the observed trend that model performance increases
with the number of materials used in training, we anticipate that
the continued discovery of new materials will further improve the
ability of SynthNN to predict future materials. Nevertheless, it is
important to recognize that we observe a notable reduction in
recall when predicting the synthesizability of materials in future
decades, compared to the current decade. This result suggests
that SynthNN performs better at identifying synthesizable
materials that are similar to the materials seen in training than
for materials that are significantly different from any materials that
have been previously synthesized.
Model interpretability
Now that we have explored the performance of our model and its
potential applications, we now turn our focus to obtaining a better
understanding of the inner workings of our model. Although deep
neutral networks often outperform simpler models (such as random
forests or linear models), obtaining interpretable predictions from
neural networks is notoriously challenging
45–48
. Interpretable predic-
tions are particularly important for the task of identifying synthesiz-
able materials since unsuccessful syntheses are extremely costly.
Understanding the physically motivated principles that guide the
model’s decisions can therefore alleviate concerns that the predic-
tions may be the result of an unphysical computational artifact.
Towards this goal, we obtain model interpretability through
analyzing both the atomic embeddings that are used to represent
the chemical formulas, the hidden layer embeddings of the neural
network, and the model outputs. We gain insight into the role of
the atomic coefficients by plotting the synthesizability predictions
of SynthNN for four representative chemical families with varying
atomic ratios (Fig. 5a). First, there is a notable distinction between
the ionic compounds (Li
x
Cl
y
,Li
x
O
y
,Fe
x
Cl
y
) and the covalent
compound (Li
x
Ge
y
). The Li
x
Cl
y
and Li
x
O
y
synthesizability predic-
tions exhibit a single sharp peak centered at the compositions that
correspond to the most stable oxidation states, indicating the
enforcement of learned charge-balancing criteria. By comparison,
the Li
x
Ge
y
predictions display a much broader range of
synthesizable oxidation states, consistent with the covalent nature
of this chemical family. Interestingly, the synthesizability predic-
tions of the Fe
x
Cl
y
family not only capture both stable oxidation
states (Fe
3+
and Fe
2+
), but the higher synthesizability prediction
output for FeCl
3
is also consistent with the greater stability of the
Fe
3+
oxidation state
49
. Whereas the results in Fig. 5a are intended
to be an instructive example of how charge-balancing influences
SynthNN synthesizability predictions, we generalize this result (see
Supplementary Note 5 and Supplementary Fig. 11) to show that
SynthNN applies charge-balancing constraints more frequently to
ionic materials than non-ionic materials. Taken together, these
results suggest that SynthNN learns charge-balanced as a rule for
predicting synthesizability. However, rather than indiscriminately
applying charge-balancing criteria to all predictions, SynthNN
learns that charge-balancing is most appropriate for ionic
compounds. The charge-balancing criteria is relaxed for non-
ionic compounds, leading to better generalization across the
whole chemical composition space.
Next, we utilize t-distributed stochastic neighbor embedding (t-
SNE) to visualize the hidden layer embeddings of the neural
network (Fig. 5b). We find that atom types are clustered in a
manner that closely resembles traditional periodic table classifica-
tions, despite the fact that no periodic table information is
provided to our model in training. Whereas the periodic table was
originally formulated from an understanding of atomic structure,
SynthNN is able to derive chemical characteristics of elements
through a statistical comparison of the types of formulas that each
element can form. Based on these embeddings, we can infer that
the predictions of SynthNN are partially based on chemical
analogy. For example, Fig. 5b shows a clustering of Li
2
S with
Li
2
Se and Li
3
S with Li
3
Se. This clustering suggests that the
synthesizability predictions are partially informed by the synthe-
sizability of chemically analogous materials. A similar clustering of
periodic table classifications is observed by visualizing the learned
atomic embeddings (Supplementary Fig. 10). This approach bears
some similarity to the common material discovery strategy of
substituting chemically analogous elements
50
, but we emphasize
that SynthNN is considerably more flexible since this principle is
not strictly enforced for all materials and SynthNN is utilizing
additional learned criteria for generating synthesizability predic-
tions (Fig. 5a, b).
Fig. 4 Performance of SynthNN model at discovering future
materials. The performance of SynthNN for recalling the materials
synthesized in a decade, when trained on all the materials synthesized
in earlier decades. For example, the ‘<1980 Training Data’and ‘1990s
Test Data’entry gives the recall of a model trained on all materials
synthesized before 1980, when tested on all materials synthesized
between 1990 and 1999. The first entry in each row therefore
corresponds to the in-distribution test recall, whereas all other entries
are the out-of-distribution test recall. In all cases, Nsynth ¼20 is used in
training. To allow comparison between models trained on different
datasets, the recall values are reported for a precision of 5/21 (5× the
random guessing baseline). For each data point, the hyperparameters
used are taken from the best-performing model trained on materials
from all decades (as shown in Supplementary Table 1).
E.R. Antoniuk et al.
7
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Although it is not possible to fully capture all of the factors that
SynthNN utilizes to generate synthesizability predictions, we have
shown that the predictions are influenced by the chemical
formula’s number of unique atom types, thermodynamic stability,
charge balance, similarity to chemically analogous formulas and
atomic composition (Figs. 3b, 5a, b, and Supplementary Figs.
8–10). Although previous material discovery efforts have
employed these metrics, it is notable that the current approach
allows for all of these relevant factors to be seamlessly combined
in a manner that does not require a manual weighting of these
important considerations. Furthermore, criteria such as charge-
balancing are flexibly accounted for- only being applied to the
materials where it is deemed to be relevant (Fig. 5a).
DISCUSSION
Recent estimates have postulated that approximately 10
10
−10
100
total unique inorganic materials may exist, which is prohibitively
large for discovering materials through an iterative search
8,51
.
Considerable efforts have focused on identifying new materials in
this vast search space by performing millions of high-throughput
density functional theory (DFT) calculations. Despite considerable
advances in the accuracy of DFT calculations, this approach to
materials discovery will always be hindered by the extent to which
DFT can provide a reliable model of real material systems, as well
as the inability of DFT to capture relevant, but incalculable
synthesizability criteria. In this work, we have developed an
alternative route towards materials discovery that is based on the
idea that a meaningful synthesizability classifier can be learned
directly from the distribution of previously synthesized chemical
compositions. By augmenting this dataset with unsynthesized
compositions, we develop a neural network-based synthesizability
classifier that utilizes learned compositional features to extract an
optimal set of descriptors for the task of predicting synthesiz-
ability. In this way, SynthNN learns a holistic array of factors that
influence synthesizability, beyond what can be captured by DFT.
Fig. 5 Extracting interpretability from SynthNN predictions. a Normalized synthesizability predictions produced by SynthNN for a series of
chemical compositions from 4 chemical families (Li
x
Cl
y
,Li
x
O
y
,Li
x
Ge
y
,Fe
x
Cl
y
). All synthesizability predictions are normalized within each
chemical family. bTwo-dimensional representations of the second hidden layer embeddings for representative binary Li chemical
compositions obtained with t-SNE.
E.R. Antoniuk et al.
8
npj Computational Materials (2023) 155 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences
Our results have shown that this methodology affords signifi-
cantly more accurate synthesizability predictions than computa-
tional approaches based on charge-balancing and DFT calculated
formation energies, as well as the predictions of expert human
chemists. Importantly, SynthNN is also several orders of magnitude
faster than predicting synthesizability by calculating formation
energies with DFT. We anticipate that SynthNN can therefore be
used to rapidly search across unexplored regions of chemical space
to target fruitful regions of chemical composition space much
faster and more accurately than was previously possible. The
predictive capabilities of SynthNN also have far-reaching implica-
tions for realizing an improvement in the reliability and success of
computational and experimental materials discovery efforts. Based
on the results shown in Fig. 2, utilizing SynthNN in computational
discovery efforts instead of charge balancing would be expected to
yield a 2.6× increase in the precision of identifying synthesizable
novel materials. In turn, this is expected to directly translate into a
2.6× reduction in the rate of unsuccessful synthesis attempts,
thereby saving years of wasted experimental effort.
METHODS
Synthesizability dataset
The Inorganic Crystal Structure Database (ICSD) is a materials
repository that contains inorganic materials that have been both
synthesized and structurally characterized. The positive examples
that our model is trained on is the set of 53,594 unique binary,
ternary, and quaternary compositions in the ICSD database that do
not contain fractional stoichiometric coefficients. These positive
examples are comprised of 8,194 binary compounds, 26,218
ternary compounds, and 19,182 quaternary compounds. This data
was pulled from the ICSD database in October 2020. Due to
continuous discovery of new materials, we note that the materials
available in the ICSD database are subject to change over time.
Unsynthesized formulas are sampled such that the relative
proportion of binary, ternary, and quaternary formulas is the same
as in the synthesized materials in our dataset. After the number of
unique elements in the unsynthesized formula is selected, the
elemental composition is sampled according to the same atomic
abundance as the set of positive examples. For example, if 4% of
synthesized formulas contain Li, then unsynthesized formulas are
generated with a 4% chance of containing Li. Finally, we generate
coefficients for each atom in the formula by uniformly sampling
between 1 and 20. After generating each formula, we check to
ensure the formula, or any multiple of the formula (up to a factor of
20), is not present in the list of synthesized formulas or the set of
previously generated unsynthesized formulas. We emphasize that
some of these artificially generated materials could be synthesizable,
but are absent from the ICSD database or have yet to be synthesized.
Atom2Vec
The methodology for obtaining learned atomic embeddings is
derived from the approach developed by Cubuk et al and Zhou
et al.
7,24
. Each chemical formula in the Synthesizability Dataset is
represented by a normalized (94 ´1) composition vector, where the
rows correspond to relative atomic fraction of each element type. As
an example, the composition vector for Na
2
O would have 2/3 in the
11
th
row, 1/3 in the 8
th
row, and zeroes elsewhere. Then, this
composition vector is embedded by performing element-wise
multiplication against the (94 ´M)-dimensional learned atom embed-
ding matrix, where Mis a hyperparameter (Table 1). This yields a (
94 ´M)-dimensional embedding of the material which is then
reduced by averaging across each column of the matrix. This reduced
embedding is then used as the input to the deep neural network,
described below. The learned atom embedding matrix is randomly
initialized and trained alongside all other model parameters.
Neural network model architecture
The SynthNN model used in this work is a 3-layer deep neural
network originally implemented in TensorFlow 1.12.0. The first two
layers utilize hyperbolic tangent (tanh) activation functions,
whereas the final layer uses a softmax activation function. The
number of hidden units in the first two layers are hyperparameters
that are sampled from [30,40,50,60,80]. SynthNN is trained with an
Adam optimizer
52
with the learning rate as a hyperparameter that
is sampled from [2 ´102,5´103,2´103,5´104,2´104]
and a cross-entropy loss function.
We train SynthNN on a 90:5:5 split of the Synthesizability Dataset,
for a predetermined ratio of synthesized:unsynthesized chemical
formulas (Nsynth in Table 1). To perform semi-supervised learning, we
first train SynthNN for Ninit initial iterations by treating the
unsynthesized materials as negative examples, where Ninit is a
hyperparameter sampled from [2 ´104,4´104,6´104,8´104,
1´105]. After this initial training stage, we reweight all of the
unsynthesized materials according to the procedure specified by
Elkan and Noto
53
. With this approach, all unsynthesized formulas are
duplicated to give one positively labeled example and one negatively
labeled example. The positive and negative duplicates are then
weighted according to the probability that they belong to their
respective classes. This approach therefore helps to overcome the
incomplete labeling of unsynthesized examples by allowing
unsynthesized materials to be treated as positive examples if there
is a high probability that they are synthesizable. The model is then
trained on this reweighted dataset for an additional 8 ´105steps (see
Supplementary Fig. 6). The final model parameters of each training
run are then taken from the step in training that achieves the highest
validation accuracy. All hyperparameters are tuned by performing a
grid-search and choosing optimal values according to the area under
a precision-recall curve (AUC) for a Nsynth ¼20 validation set (see
Supplementary Note 1). The hyperparameters used in this model and
their range of sampled values are given in Table 1below. For each
value of Mand Nsynth , at least 20 training runs were performed with all
other hyperparameters randomly sampled. The training run that
achieved the best performance on the validation set for each value of
Mand Nsynth is given in Supplementary Tables 1–2.
Model performance evaluations
The model performance evaluations shown in Fig. 2are all
calculated by treating the artificially generated unsynthesized
materials as negative examples. Specifically, true positives are
synthesized materials predicted to be synthesizable, false positives
are unsynthesized materials predicted to be synthesizable, true
negatives are unsynthesized materials predicted to be unsynthe-
sizable, and false negatives are synthesized materials predicted to
be unsynthesizable. Following from these definitions, the perfor-
mance evaluations shown throughout this paper take on the
definitions used in standard classification tasks.
Synthesized Material Precision ¼True positives
True positives þFalse positivesðÞ
(1)
Unsynthesized Material Precision ¼True negatives
ðTrue negatives þFalse negativesÞ(2)
Recall ¼True positives
ðTrue positives þFalse negativesÞ(3)
Accuracy ¼True positives þTrue negatives
ðTrue positives þFalse negatives þTrue negatives þFalse positivesÞ
(4)
F1 score ¼2Synthesized Material PrecisionðÞðRecallÞ
Synthesized Material PrecisionðÞþðRecallÞ(5)
In the context of predicting the synthesizability of materials,
synthesized material precision therefore corresponds to the
E.R. Antoniuk et al.
9
Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences npj Computational Materials (2023) 155
fraction of materials predicted to be synthesizable that can be
successfully experimentally synthesized. A high precision model
therefore minimizes the likelihood that materials predicted to be
synthesizable will not be able to be experimentally synthesized in
the lab. On the other hand, recall corresponds to the fraction of all
synthesizable materials that are successfully predicted to be
synthesizable by the model. Achieving a model with high recall is
therefore desirable to ensure that a high proportion of all
synthesizable materials in the chemical space of interest are
captured by the model.
Importantly, the incomplete labeling of the unsynthesized
materials results in an overestimation of false positive predictions
and an underestimation of true positive predictions since
materials that are synthesizable, but have yet to be synthesized
will be incorrectly treated as false positives instead of true
positives. In terms of these performance metrics, this results in an
underestimation of the synthesized material precision and
accuracy relative to the true model performance. However, the
recall is unaffected since recall only depends on the set of
synthesized materials, for which we have correct class labels. Since
the F1-score is harmonic mean of precision and recall, it will also
be underestimated due to the underestimation of precision.
Finally, the area under the curve of a precision-recall curve (i.e.,
Supplementary Figs. 1–5) will be underestimated due to the
underestimation of precision.
DATA AVAILABILITY
The Synthesizability Dataset used during the current study can be obtained from the
Inorganic Crystal Structure Database
25
. The formation energy dataset used for
training Roost (Fig. 2c) is included at https://github.com/antoniuk1/SynthNN.
CODE AVAILABILITY
Code used for training SynthNN and generating synthesizability predictions is
available at https://github.com/antoniuk1/SynthNN. The code for Roost is available at
https://github.com/CompRhys/roost.
Received: 10 February 2023; Accepted: 8 August 2023;
REFERENCES
1. Choudhary, K. et al. The joint automated repository for various integrated
simulations (JARVIS) for data-driven materials design. Npj Comput. Mater. 6,1–13
(2020).
2. Jain, A. et al. Commentary: The Materials Project: a materials genome approach to
accelerating materials innovation. APL Mater. 1, 011002 (2013).
3. Corey, E. J., Cramer, R. D. I. & Howe, W. J. Computer-ass isted synthetic analysis for
complex molecules. Methods and procedures for machine generation of syn-
thetic intermediates. J. Am. Chem. Soc. 94, 440–459 (1972).
4. Aykol, M., Montoya, J. H. & Hummelshøj, J. Rational solid-state synthesis routes for
inorganic materials. J. Am. Chem. Soc. 143, 9244–9259 (2021).
5. Chamorro, J. R. & McQueen, T. M. Progress toward solid state synthesis by design.
Acc. Chem. Res. 51, 2918–2925 (2018).
6. Turnbull, D. & Vonnegut, B. Nucleation catalysis. Ind. Eng. Chem. 44, 1292–1298
(1952).
7. Cubuk, E. D., Sendek, A. D. & Reed, E. J. Screening billions of candidates for solid
lithium-ion conductors: a transfer learning approach for small data. J. Chem. Phys.
150, 214701 (2019).
8. Davies, D. W. et al. Computational screening of all stoichiometric inorganic
materials. Chemistry 1, 617–627 (2016).
9. Dan, Y. et al. Generative adversarial networks (GAN) based efficient sampling of
chemical space for inverse design of inorganic materials. Npj Comput. Mater. 6,84
(2020).
10. Sun, W. et al. The thermodynamic scale of inorganic crystalline metastability. Sci.
Adv. 2, e1600225 (2016).
11. Jang, J., Gu, G. H., Noh, J., Kim, J. & Jung, Y. Structure-based synthesizability
prediction of crystals using partially supervised learning. J. Am. Chem. Soc. 142,
18836–18843 (2020).
12. Aykol, M., Dwaraknath, S. S., Sun, W. & Persson, K. A. Thermodynamic limit for
synthesis of metastable inorganic materials. Sci. Adv. 4, eaaq0148 (2018).
13. Meredig, B. et al. Combinatorial screening for new materials in unconstrained
composition space with machine learning. Phys. Rev. B 89, 094104 (2014).
14. Ward, L., Agrawal, A., Choudhary, A. & Wolverton, C. A general-purpose machine
learning framework for predicting properties of inorganic materials. Npj Comput.
Mater. 2,1–7 (2016).
15. Dunn, A., Wang, Q., Ganose, A., Dopp, D. & Jain, A. Benchmarking materials
property prediction methods: the matbench test set and automatminer reference
algorithm. Npj Comput. Mater. 6, 138 (2020).
16. Jha, D. et al. ElemNet: deep learning the chemistry of materials from only ele-
mental composition. Sci. Rep. 8, 17593 (2018).
17. Goodall, R. E. A. & Lee, A. A. Predicting materials properties without crystal
structure: deep representation learning from stoichiometry. Nat. Commun. 11,
6280 (2020).
18. Davariashtiyani, A., Kadkhodaie, Z. & Kadkhodaei, S. Predicting synthesizability of
crystalline materials via deep learning. Commun. Mater. 2,1–11 (2021).
19. Aykol, M. et al. Network analysis of synthesizable materials discovery. Nat.
Commun. 10, 2018 (2019).
20. Swain, M. C. & Cole, J. M. ChemDataExtractor: a toolkit for automated extraction
of chemical information from the scientific literature. J. Chem. Inf. Model. 56,
1894–1904 (2016).
21. Kononova, O. et al. Text-mined dataset of inorganic materials synthesis recipes.
Sci. Data 6, 203 (2019).
22. Kim, E. et al. Materials synthesis insights from scientific literature via text
extraction and machine learning. Chem. Mater. 29, 9436–9444 (2017).
23. Kim, E. et al. Inorganic materials synthesis planning with literature-trained neural
networks. J. Chem. Inf. Model. 60, 1194–1201 (2020).
24. Zhou, Q. et al. Atom2Vec: learning atoms for materials discovery. Proc. Natl Acad.
Sci. USA 115, E6411–E6417 (2018).
25. Levin, I. NIST Inorganic Crystal Structure Database (ICSD). (2020) https://doi.org/
10.18434/M32147.
26. Cheon, G. et al. Revealing the spectrum of unknown layered materials with
superhuman predictive abilities. J. Phys. Chem. Lett. 9, 6967–6972 (2018).
27. Frey, N. C. et al. Prediction of synthesis of 2D metal carbides and nitrides
(MXenes) and their precursors with positive and unlabeled machine learning. ACS
Nano 13, 3031–3041 (2019).
28. Bekker, J. & Davis, J. Learning from positive and unlabeled data: a survey. Mach.
Learn. 109, 719–760 (2020).
29. Bartel, C. J. et al. A critical examination of compound stability predictions from
machine-learned formation energies. Npj Comput. Mater. 6,1–11 (2020).
30. Oganov, A. R., Lyakhov, A. O. & Valle, M. How evolutionary crystal structure
prediction works—and why. Acc. Chem. Res. 44, 227–237 (2011).
31. Pickard, C. J. & Needs, R. J. Ab initio random structure searching. J. Phys. Condens.
Matter 23, 053201 (2011).
32. Cheon, G., Yang, L., McCloskey, K., Reed, E. J. & Cubuk, E. D. Crystal Structure
Search with Random Relaxations Using Graph Networks. ArXiv201202920 (2020).
33. Frid-Adar, M., Klang, E., Amitai, M., Goldberger, J. & Greenspan, H. Synthetic Data
Augmentation using GAN for Improved Liver Lesion Classification.
ArXiv180102385 Cs (2018).
34. Wang, X., Man, Z., You, M. & Shen, C. Adversarial Generation of Training Examples:
Applications to Moving Vehicle License Plate Recognition. ArXiv170703124 Cs
(2017).
35. Marmanis, D. et al. Artificial Generation of Big Data for Improving Image Classi-
fication: A Generative Adversarial Network Approach on SAR Data.
ArXiv171102010 Cs (2017).
36. Moore, T. & Clayton, R. Evaluating the Wisdom of Crowds in Assessing Phishing
Websites. In Financial Cryptography and Data Security (ed. Tsudik, G.) 16–30
(Springer, 2008). https://doi.org/10.1007/978-3-540-85230-8_2.
37. Budescu, D. V. & Chen, E. Identifying expertise to extract the wisdom of crowds.
Manag. Sci. 61, 267–280 (2015).
38. Steyvers, M., Miller, B., Hemmer, P. & Lee, M. The Wisdom of Crowds in the
Recollection of Order Information. In Advances in Neural Information Processing
Systems vol. 22 (Curran Associates, Inc., 2009).
39. Hertwig, R. Tapping into the Wisdom of the Crowd—with Confidence. Science
336, 303–304 (2012).
40. Kostelnik, T. I. & Orvig, C. Radioactive main group and rare earth metals for
imaging and therapy. Chem. Rev. 119, 902–956 (2019).
41. Martinez-Gomez, N. C., Vu, H. N. & Skovran, E. Lanthanide chemistry: from
coordination in chemical complexes shaping our technology to coordination in
enzymes shaping bacterial metabolism. Inorg. Chem. 55, 10083–10089 (2016).
42. Zhang, W. et al. Unexpected stable stoichiom etries of sodium chlorides. Science
342, 1502–1505 (2013).
43. Hong, J. et al. Metastable hexagonal close-packed palladium hydride in liquid cell
TEM. Nature 603, 631–636 (2022).
E.R. Antoniuk et al.
10
npj Computational Materials (2023) 155 Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences
44. Gopalakrishnan, J. Chimie Douce approaches to the synthesis of metastable
oxide materials. Chem. Mater. 7, 1265–1275 (1995).
45. Ziletti, A., Kumar, D., Scheffler, M. & Ghiringhelli, L. M. Insightful classification of
crystal structures using deep learning. Nat. Commun. 9, 2775 (2018).
46. Schmidt, J., Marques, M. R. G., Botti, S. & Marques, M. A. L. Recent advances and
applications of machine learning in solid-state materials science. Npj Comput.
Mater. 5,1–36 (2019).
47. Zhang, P., Shen, H. & Zhai, H. Machine learning topological invariants with neural
networks. Phys. Rev. Lett. 120, 066401 (2018).
48. Xie, T. & Grossman, J. C. Hierarchical visualization of materials space with graph
convolutional neural networks. J. Chem. Phys. 149, 174111 (2018).
49. Tomyn, S. et al. Indefinitely stable iron(IV) cage complexes formed in water by air
oxidation. Nat. Commun. 8, 14099 (2017).
50. Davies, D. W., Butler, K. T., Isayev, O. & Walsh, A. Materials discovery by chemical
analogy: role of oxidation states in structure prediction. Faraday Discuss 211,
553–568 (2018).
51. Walsh, A. The quest for new functionality. Nat. Chem. 7, 274–275 (2015).
52. Kingma, D. P. & Ba, J. Adam: A Method for Stochastic Optimization. ArXiv14126980
Cs (2014).
53. Elkan, C. & Noto, K. Learning classifiers from only positive and unlabeled data. In
Proceeding of the 14th ACM SIGKDD international conference on Knowledge dis-
covery and data mining - KDD 08 213–220 (ACM Press, 2008). https://doi.org/
10.1145/1401890.1401920.
54. Gao, W. & Coley, C. W. The synthesizability of molecules proposed by generative
models. J. Chem. Inf. Model. 60, 5714–5723 (2020).
ACKNOWLEDGEMENTS
This work was performed under the auspices of the U.S. Department of Energy by
Lawrence Livermore National Laboratory under Contract DE-AC52–07NA27344. We
would like to thank Prof. Tony Heinz for the original project inspiration and the
human participants of the Synthesizability Quiz.
AUTHOR CONTRIBUTIONS
The project was conceived by E.R.A., G.C., and E.J.R. E.R.A., G.W., D.B., G.C., and W.C.
contributed to the development of the machine learning models. E.R.A. performed
the machine learning experiments and wrote the initial manuscript. All authors
contributed to editing the manuscript.
COMPETING INTERESTS
All authors declare no competing interests.
ADDITIONAL INFORMATION
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41524-023-01114-4.
Correspondence and requests for materials should be addressed to Evan R. Antoniuk.
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