Inorganic Synthesis Reaction Condition Prediction
with Generative Machine Learning

Christopher Karpovich, Zach Jensen, Vineeth Venugopal, Elsa Olivetti
Dept. of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139{ckarp, zjensen, vineethv, elsao}@mit.edu

Abstract
Data-driven synthesis planning with machine learning is a key step in the designand discovery of novel inorganic compounds with desirable properties. Inorganic
materials synthesis is often guided by chemists’ prior knowledge and experience,
built upon experimental trial-and-error that is both time and resource consuming. Recent developments in natural language processing (NLP) have enabledlarge-scale text mining of scientific literature, providing open source databases ofsynthesis information of synthesized compounds, material precursors, and reaction
conditions (temperatures, times). In this work, we employ a conditional variational
autoencoder (CVAE) to predict suitable inorganic reaction conditions for the crucial
inorganic synthesis steps of calcination and sintering. We find that the CVAE modelis capable of learning subtle differences in target material composition, precursor
compound identities, and choice of synthesis route (solid-state, sol-gel) that arepresent in the inorganic synthesis space. Moreover, the CVAE can generalize wellto unseen chemical entities and shows promise for predicting reaction conditions
for previously unsynthesized compounds of interest.

1

Introduction

Virtual materials screening and physics-based simulations have in recent years greatly accelerated
the design and discovery of novel inorganic compounds with applications in chemical catalysis [1],thermoelectrics [2], and metal-organic frameworks [3]. However, while existing tools have largely
focused on the inverse design of inorganic materials, one major remaining challenge is the development of inverse synthesis planning, where, given a target material, appropriate synthesis parameters
are suggested as a means to synthesize the compound. In comparison to widely available organic
chemistry reaction databases, the vast majority of openly accessible inorganic synthesis informationis contained within the text of scientific journal articles [4]. Recent efforts have leveraged advancesin Natural Language Processing (NLP) to extract and convert inorganic synthesis information in
unstructured scientific text into machine readable databases [5, 6, 7]. In the organic chemistry space,previous works have investigated synthesis temperature prediction using feedforward neural network
based models [8]; however, they utilize a dataset on the order of 107 points with a small range ofreported temperatures (-100 to 300 ◦ C), while inorganic synthesis datasets typically consist of 104 to
105 points and report temperatures ranging from 200 to 2000 ◦ C. The dearth of available inorganic
synthesis data and wide range of reported reaction conditions makes the inorganic prediction problem
challenging. In the inorganic space, other works have developed methods for condition generation
for specific materials families such as TiO2, MnO2, and SrTiO3 [9], inverse prediction of precursor
materials and synthesis operation sequences [10], forward prediction of target compositions [11], andprecursor selection based on kinetic factors [12]; however, to the best of our knowledge, no studies
have explored the prediction of synthesis conditions for novel inorganic compounds.
Fourth Workshop on Machine Learning and the Physical Sciences (NeurIPS 2021).

Generative machine learning models have already proven to be powerful tools in the chemical andmaterials spaces for materials discovery. Autoencoder models have been leveraged to optimize
molecules with desirable properties over a learned latent space [13] and predict crystal structures
for new inorganic compounds [14]. Generative adversarial networks have also been explored for
drug discovery [15] and to screen inorganic material compositions [16]. In the case of experimental
synthesis, reaction conditions present several important variables in the validation of computeraided synthesis planning. Broadly, in solid-state synthesis, two or more non-volatile solid precursor
materials are ground and heated in multiple consecutive steps to temperatures below their melting
points to react and form the desired product [17, 18]. In sol-gel synthesis, a “sol” (a colloidal solutionof particles in a solvent) is first heated to form a “gel”, which is then typically heated in multiple
consecutive steps to form the desired product [19, 20]. Common heating steps in both synthesis
methods include calcination, where a mixture of compounds is heated to a high temperature to remove
impurities and unwanted volatile substances, often through thermal decomposition [17], and sintering,where a compound is heated at a temperature (often higher than that reached by calcination) to induce
nucleation and grain growth [17].

2

Methods

Our dataset consists of two publicly released materials synthesis databases (in JSON format) textmined from scientific literature using a combination of NLP and rule-based extraction techniques[6]. The first is a solid-state synthesis database [6] containing 31,782 inorganic solid-state chemical
reactions, while the second is a sol-gel synthesis database [6] containing 9,518 inorganic sol-gel
chemical reactions. Each entry in the synthesis database contains a target material: the stoichiometricformula of the target compound synthesized in the reaction, precursor materials: the starting materials
reacted together to form the target material, where a precursor is defined as a compound which shares
one or more elements with the target material, excluding abundant elements that can be found in air(e.g. oxygen, hydrogen), and processing actions and synthssis conditions: the sequence of synthesis
actions (e.g. mix, grind, calcine, sinter, dry) that were performed on the precursor materials totransform them into the target material. Relevant synthsis conditions for these processing actions
include temperatures and times (when reported in the synthesis). The datasets report an overall
extraction accuracy of 93% [6].
To make predictions for synthesis conditions we used (see Appendix) a conditional variational autoencoder (CVAE) with a convolutional encoder and recurrent decoder. A depiction of the modelarchitecture is shown in Fig. 1. Temperatures and times of the four heating steps of interest (calcination, sintering, annealing, and drying) were represented as an 8-dimensional vector and standardized.
Targets and precursors (represented by their chemical formulas, see Appendix) were used as conditions and encoded and concatenated with the latent space representation using convolutional layers
over sequences of one-hot vectors, where the total vocabulary is a character set consisting of thedifferent elements and the numerical digits. Two dataset splits were investigated: a random split,
and a compositional-based split based on [21] where the train, validation, and test set do not containmaterials involving the same set of elements. For instance, if LiFePO4 is in the test set, then no othermaterials in the Li-Fe-P-O phase system (such as LiFeP2O7) would be allowed in the training or
validation sets.
As shown in Fig. 2, we plot the overall distribution of calcination, sintering, annealing, and drying
temperatures and times for both solid-state and sol-gel synthesis methods. The dataset is mainlycomposed of unique compounds, with the majority of the entries reporting novel target compositions.
Notably, calcination temperatures follow a common trend such that nitride > oxide > carbonate> nitrate > acetate, alkoxide, acetylacetonate, oxalate which is correlated to bonding strength
between cations and anions [22]. However, these trends are not absolute, as other factors such as
decomposition reactions, reactivity of precursors, and identity of the target material play a role in thechosen calcination temperature.

3

Results and Discussion

In Fig. 3, we plot the predicted calcination and sintering temperatures for a selection of samples
in the held-out test set. The CVAE model indeed learns a meaningful relationship between thecomposition of the target material, the identities of the precursors in the synthesis, and a range within
2

Figure 1: Architecture of CVAE used for temperature and time generation. The encoder embeds thesynthesis conditions x to a latent vector z, and the decoder reconstructs the synthesis conditions fromthe latent vector. The latent vector is concatenated with learned representations of the target andprecursor materials as well as a binary indicator of the synthesis route.

Figure 2: Temperature distributions for extracted operations for (a) solid-state and (b) sol-gel synthesis
methods. (c) Calcination and (d) sintering time-temperature distributions for solid-state synthesis.

which the appropriate temperature for these heating operations should occur. For instance, in Fig.
3 (a)-(b) it is evident that when a compound consisting primarily of barium is doped with cesium,
yttrium, and zirconium, it should require higher calcination and sintering temperatures than if dopedwith europium and copper. Moreover, the CVAE learns the common synthesis trend that sintering
temperatures tend to be higher than calcination temperatures by the order of 100-300◦ C. In Fig. 3(c)-(d), we show the parity plots for predicted vs. true mean calcination and sintering temperatures inthe test set.
The quantitative performance metrics of the CVAE model are presented in Table 1, including mean
absolute error (MAE), root-mean-square error (RMSE), mean relative error (MRE), and coefficient ofdetermination (R2 ). In experimental synthesis, suggesting approximate initial temperatures would be
sufficiently helpful to inform experiments and accelerate synthesis of novel materials. On a held-out
test set, the CVAE predicts the mean calcination temperature with a mean absolute error of 132.4 ◦ C
and mean sintering temperature with a MAE of 129.9 ◦ C. To evaluate model performance against
physically meaningful baselines, we leverage two common heuristics in the materials synthesis field
as predictors on the dataset. Tamman’s rule [23] is a synthesis heuristic which approximates reaction
temperature as two-thirds the melting point of the lowest melting temperature reactant. For sintering
temperature, we use a heuristic which approximates the value as 200 ◦ C above the calcination
temperature predicted by Tamman’s rule, which is the average difference between sintering andcalcination temperatures in the dataset. From Table 1, it is clear that the CVAE outperforms bothheuristics by a factor of three to four.
Another factor to consider in evaluating model performance is the structure of the dataset itself. In
scientific literature, the majority of publications report the unique synthesis of a single compoundor family of compounds, meaning the reported synthesis temperature may not be representative ofeither the optimal temperature or the range of temperature within which it is feasible to synthesize
the compound. Thus, since the dataset is comprised of single experimental data points per material,
comparing the means of generated distributions of temperatures to single experimental points likely
underestimates model performance. For instance, in Fig. 4 (a)-(b), we plot the MAE and R2 metrics
3

Figure 3: Generated solid-state (a) calcination and (b) sintering temperature distributions for aselection of samples in the held-out test set. Parity plots for predicted vs. true means of test set
distributions of (c) calcination and (d) sintering temperatures. In the key, the target material ispresented first (above) and precursor materials are presented second (below) for each entry.
Table 1: Dataset-wide performance of CVAE model compared to baseline heuristics
Model

Prediction Task

MAE (◦ C)

RMSE (◦ C)

MRE (%)CVAE (random split)
CVAE (comp. split)
Tamman’s Rule

Mean Calcination Temp.
Mean Calcination Temp
Mean Calcination Temp.

132.4
147.0
679.2

180.9
190.9
596.8

16
18
60

0.40
0.32
-8.68

CVAE (random split)
CVAE (comp. split)
Sintering Heuristic

Mean Sintering Temp.
Mean Sintering Temp
Mean Sintering Temp.

129.9
147.4
529.0

173.4
191.8
613.9

13
15
45

0.60
0.43
-5.03

R2

as a function of the minimum number of literature data points for each example in the test set,showing marked improvement as the minimum number of points increases from one to five. With
the experimental mean comprised of at least five points, the MAE is 57.0 ◦ C and R2 is 0.90 for
sintering and 75.3 ◦ C and 0.59 for calcination, respectively. We note that the MAE for calcination
increases slightly as the minimum number of literature data points increases from 4 to 5 and the R2
for calcination decreases slightly as the minimum number of literature data points increases from
3 to 5, which can be attributed to anthropomorphic factors in data reporting and systematic error
discussed later.
To show that the CVAE also learns the appropriate trends in synthesis route and precursor substitutions,we plot in Fig. 4(c) the predicted calcination temperature distributions for the synthesis of Sr2FeO4from Sr(NO3)2 and Fe(NO3)3, conditioning on either sol-gel or solid-state synthesis. Evidently, the
CVAE learns the relationship that if we change our choice of synthesis route from solid-state tosol-gel, the calcination and sintering temperatures should decrease as well, reflective of the calcination
temperature distributions in both datasets. We also plot in 5(a)-(b) the predicted calcination andsintering temperatures for the synthesis of Li4Fe7O12 from Li2CO3 while varying the identity of theiron-based precursor. The CVAE model recognizes that when we alter our choice of precursor fromhigh bonding strength candidates such as Fe3O4 and Fe2O3 to lower bonding strength candidates suchas Fe(NO3)3, FePO4, and FeC2O4, the calcination and sintering temperatures should appropriately
decrease. These trends are reflective of the overall shift in calcination and sintering temperatureacross the entire dataset portrayed in Fig. 5 (c)-(d). However, these trends are not absolute, as for4

Figure 4: (a) MAE and (b) R2 metrics as a function of minimum number of literature data points
in the test set. (c) Generated calcination temperature distributions conditioned on either sol-gel orsolid-state synthesis routes.

example the generated calcination temperature distribution using FePO4 is higher than what would be
expected simply by comparing with the literature-wide trends. While reported trends in synthesis
temperatures and average bonding strength do correlate to an extent, other factors such as reactivityof precursors, intermediate reactions such as decomposition, the identity of the target compound,errors in automated extraction, and anthropomorphic factors [22, 24] such as experimentalist bias
and past reported literature success all affect reported reaction conditions and influence the learned
distributions.

Figure 5: Generated solid-state (a) calcination and (b) sintering temperatures for the synthesis of
Li4Fe7O12 from Li2CO3 and various iron-containing precursors. (c) Calcination and (d) sintering
temperature trends as a function of iron-containing precursors across the dataset. The inset number isthe frequency of the reported precursor in the dataset.

4Conclusions

We propose a CVAE model which suggests appropriate distributions for calcination and sintering
temperatures in inorganic synthesis based on synthesis route, precursor identity, and the desired
target compound. The model captures physics-based trends in the doping of target materials as well
as choice of precursor and significantly outperforms common heuristics in the field in suggesting
predictions of synthesis temperatures. We envision this model as a stepping-stone to high-throughput
inorganic synthesis, where laboratory experiments will ultimately be informed by machine learning
to hasten the synthesis and optimization of inorganic materials with desirable properties.

5

Broader Impact

Inorganic materials play a crucial role in the advancement of fields such as energy storage, chemical
catalysis, thermoelectrics, and microelectronics. Therefore, new computational tools leveraging
machine learning and scientific data need to be developed in order to accelerate the design andrealization of novel materials with desirable properties. Our approach guides experimentalists withinitial suggestions to aid in synthesis planning for the discovery and design of new materials. Outsideof inorganic materials science, our approach can potentially be applied to a wide range of otherfields which are currently adapting machine learning-based tools to unify theoretical predictions andexperimental validation, such as drug discovery and electronic device manufacturing.
5

6

Acknowledgements

This material is based upon work supported by the National Science Foundation Graduate Research
Fellowship under Grant No. 1745302. The information, data, or work presented herein was also
funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department ofEnergy, under Award Number DE-AR0001209. The views and opinions of authors expressed herein
do not necessarily state or reflect those of the United States Government or any agency thereof.

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7

Appendix

7.1

TheoryIn a variational autoencoder (VAE), the loss function consists of the variational lower bound, also
known as the evidence lower bound (ELBO):
Lθ,φ = Eqφ (z|x) [log pθ (x|z)] − DKL (qφ (z|x)kpθ (z))(1)

where E is the expectation value, p and q are probability distributions, DKL is the Kullback–Leibler
divergence, and x and z are the data and latent spaces, respectively. The first and second terms areoften called the reconstruction loss and the KL loss, respectively. The reconstruction loss encourages
the decoder to learn to reconstruct the data, while the KL loss is a regularization term which measures
how similar the variational distribution encoded from the input data qφ (z|x) and the latent space
distribution pθ (z) are. We take pθ (z) to be a standard normal distribution with zero mean andunit variance, such that pθ (z) = N (0, 1). In a VAE, qφ (z|x) and pθ (x|z) are approximated by anencoder and a decoder, respectively. For a conditional variational autoencoder (CVAE), we embed7the conditional information as a vector (denoted by c) in the objective function of the VAE, leading to
the revised loss function as follows:Lθ,φ = Eqφ (z|x) [log pθ (x|z, c)] − DKL (qφ (z|x, c)kpθ (z|c))(2)

In our model architecture, the data x consists of standardized temperatures and times of the four
heating steps of interest (calcination, sintering, annealing, and drying) represented as an 8-dimensional
vector. The condition c consists of targets and precursors (represented by their chemical formulas),encoded and concatenated with the latent space representation using convolutional layers oversequences of one-hot vectors, where the total vocabulary is a character set consisting of the different
elements and the numerical digits. An additional condition (if desired) is the synthesis route, which
is a binary condition (solid-state or sol-gel). Using this framework, the CVAE model can generatetemperature and time distributions conditioned on the target and precursor materials of interest.
7.2

Model architecture

All neural network models were implemented in the Keras library using the TensorFlow backend. For
the conditional variational autoencoder (CVAE) model, convolutional layers encode the temperaturetime vector into a latent parameter space for means and variances of Gaussian variational posteriors,and outputs from a latent sampling function are concatenated with conditional inputs as inputs to arecurrent decoder. The encoder is comprised of three convolutional layers and the decoder comprisedof three gated recurrent unit (GRU) layers. In producing the results for this study, 3 latent dimensions
were used. Targets and precursors (represented by their chemical formulas) were used as conditions
and encoded and concatenated with the latent space representation using convolutional layers oversequences of one-hot vectors, where the total vocabulary is a character set consisting of the different
elements and the numerical digits. A period was included in the character set for targets to represent
non-stoichiometric target formulas. Training was conducted on two NVIDIA Titan Xp GPUs with abatch size of 128 and the Adam optimizer with default hyperparameters. Hyperparameter selection
was performed by grid searches, where the latent layer dimension was varied from 2 to 5 dimensions
and the standard deviation of the Gaussian prior was varied between 0.001 and 10.0. The data
was split in a 75/15/10 train/validation/test ratio using either random or compositional splits, andhyperparameters were selected based on minimizing validation loss.
7.3

Data post-processing

Our post-processing of the data was completed as follows. First, reactions with organic precursors andtargets, non-stoichiometric precursors, unsubstituted target stoichiometries, less than two or greaterthan five precursors, or not containing at least one relevant heating step with a reported temperature
were removed. Hydrate precursors were truncated to their base chemical formula. Temperatures andtimes were converted into units of Celsius and Hours and limited to between 100 ◦ C and 2000 ◦ C andless than 100 hours, and if an operation step was reported with more than one temperature or time,
the highest value was taken. If a relevant heating step occurred more than once in a recipe, the lastvalue was taken. Because not every synthesis recipe employed all four heating steps, data imputation
was conducted using the IterativeImputer module in scikit-learn with the BayesianRidge
estimator, default hyperparameters, and minimum and maximum imputation values set to those in
the dataset. To aid in accurate imputation, precursors were one-hot encoded and used as additionalfeatures. Temperatures and times were standardized by removing the mean and scaling to unit
variance per feature.

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