Using Machine Learning to Predict Chemical Reaction Outcomes in Environmental Applications

Abstract

Volatile organic compounds (VOCs), emitted by natural and anthropogenic sources, interact with solar radiation and participate in complex photochemical processes in the atmosphere. They influence air quality and climate on a local, regional, and global scale, either as greenhouse gases or through the formation of secondary aerosols. Understanding their emission sources, chemical transformations, and impacts remains a significant challenge for predicting climate change and developing environmental control and monitoring strategies. The results presented in this work correspond to the application of machine learning models, in conjunction with chemoinformatics tools, to predict the formation of organic compounds from molecules present in diesel fuel. Specific chemical oxidation reactions involving OH radicals, ozone, and atomic oxygen were studied using resources from the RDKit library in Python. The set of 261 reactant molecules in diesel were generated using a generative neural network. Multiclass classification models were also built to predict the toxicity (mutagenicity - Ames test) of these molecules using quantitative structureactivity relationship (QSAR), along with the ISSSTY database, providing good predictive results.

Keywords:
machine learning; chemical reactions; RDKit; mutagenicity

Introduction

Large quantities of volatile organic compounds (VOCs) are emitted into the atmosphere daily by anthropogenic and natural sources. These molecules interact with solar radiation, creating an intense and complex photochemical system in the atmosphere. This system involves studying the sources, sinks, and residence times of the molecules and is the subject of several current studies. These compounds can influence local, regional, and even global photochemistry, having the potential to impact the climate, both due to their properties (as greenhouse gases) and their ability to form aerosol particles through oxidation. The formation of gaseous and particulate byproducts caused by the oxidation of VOCs is one of the greatest unknowns in quantitatively predicting Earth’s climate on a regional and global scale, affecting local air quality.¹-³ Studies to model and control the impact of these compounds are essential to understanding the sources of VOCs, their distribution in the atmosphere, and the chemical transformations they undergo.

The formation of photochemical smog is a complex phenomenon that occurs due to a series of chemical reactions between compounds present in the atmosphere. This process is driven by the presence of sunlight, molecular oxygen (O₂), nitrogen oxides (NO_x), and volatile hydrocarbons.¹,⁴ These compounds react with each other under the influence of ultraviolet radiation present in sunlight, forming a mixture of secondary pollutants, such as ozone (O₃) and oxygenated organic compounds, which make up photochemical smog.⁴,⁵ Molecular oxygen is essential for the formation of smog, as it acts as a substrate in the formation of tropospheric ozone.¹,⁴ Nitrogen oxides, derived primarily from combustion processes, play a crucial role in the photochemical cycle. The NO₂ is photolyzed by UV radiation, forming nitric oxide (NO) and a reactive oxygen atom, which subsequently contributes to the generation of ozone. These reactions establish a dynamic cycle between NO, NO₂, and O₃, which is essential for maintaining photochemical smog.¹,⁴ VOCs, emitted by natural and anthropogenic sources such as vegetation, fossil fuels, and industrial solvent use and refining, are oxidized in the atmosphere, forming alkyl radicals, peroxyl radicals, and water. These products promote the oxidation of NO to NO₂, essential for ozone recycling in photochemical smog.¹,⁴ Understanding the chemical and environmental basis of this process is of paramount importance for implementing actions aimed at mitigating pollution.

The study of the toxicity of a compound involves analyzing the effects caused by the exposure of ecosystems, whether simple or complex, to different chemical substances. These effects can range from mild manifestations to serious consequences, including the death of organisms.⁶ Such responses, which can be reversible or irreversible, depend on the absorption, distribution, metabolism, and excretion characteristics of the compound-or its metabolites-in the organism. These properties directly influence how these substances interact with cellular macromolecules.⁷ In toxicological assessment, the main objectives involve the diagnosis, treatment, and prevention of intoxications caused by xenobiotics. A central aspect of toxicology is the possibility of investigating and mapping complex interactions between chemical compounds and biological systems. For this, methodologies and principles from biology, chemistry, and computer science are employed, allowing us to understand the degree of resilience of living systems to the toxic effects of different substances.⁸

Computational modeling of the toxicity of organic compounds constitutes a significant challenge, mainly due to the wide diversity of biological assays available for bioactivity assessment. These assays involve different organisms and biological systems, including animals, cell lines, and microorganisms, and present methodological variations and multiple data sources. This heterogeneity makes the process of building predictive models particularly complex. In the literature, a wide variety of approaches focused on both classification and regression can be observed. There are consolidated classification models,⁹-¹¹ as well as regression models applied to the quantitative prediction of toxicity.¹²-¹⁴ However, these methodologies have specificities and limitations inherent to their datasets, molecular descriptors, and domains of applicability.¹⁵,¹⁶

Methodology

Molecular generator

The molecular generator was built using a generative neural network described in Silva et al.,¹⁷ aided by a multiobjective evolutionary algorithm. It uses a variational autoencoder (VAE) as a generative model, with the aid of a multi-objective evolutionary algorithm to navigate the “latent chemical space”. This latent space refers to exploring the mathematical space where the generative model represents the molecules. In a VAE, each molecule is converted into a numerical vector in this space, where each point corresponds to a possible molecule. Evolutionary algorithms modify these vectors, generate new molecules, and select those with the best properties specified by the users. By repeating this process several times, the method moves through the latent space until it finds regions that produce more promising molecules.¹⁷

The VAE was pre-trained on a dataset of 1.8 million chemical compounds extracted from the ChEMBL database.¹⁸ To perform the multi-objective optimization, the Non-Dominated Sorting Genetic Algorithm III (NSGAIII)¹⁹ was used, with reference points constructed by the Riesz energy method,²⁰ defining their number equal to the population size. The evolutionary process used the twopoint recombination operator (applied with probability 0.9) and Gaussian mutation (σ = 0.01, applied with a probability of 0.1). The algorithm was run for 100 generations with a fixed population size of 640. The framework is open source and available (see Data Availability Statement section).

Atmospheric reactions

The RDKit library is an open-source toolkit for chemoinformatics and machine learning (ML).²¹ The open-source library contains algorithms for 2D and 3D molecular operations, Quantitative Structure-Activity Relationship (QSAR) descriptor generation for ML, and many other features updated annually. Molecular manipulation is done using the SMILES representation. This has been modified and expanded to include new features, dubbed SMARTS (Smiles Arbitrary Target Specification).²² This coding is generated in this work only for chemical reactions, and done exclusively with the Marvin Sketch software v.22.13,²³ due to its restrictive and complex rule system.²⁴ Chemical reactions are plotted on the main screen using appropriate icons representing atoms and chemical bonds, culminating in atom mapping. Only the main reactant and main product molecules are drawn and plotted. The reaction pattern is designed to be executed by specific functions in the RDKit²¹ library in Python. This work was developed using the Google Colab IDE (Integrated Development Environment - Google Inc, USA, version 2025), a cloud-based integrated development environment offered by Google for creating and executing Python code (version 3.11) and programs.

Toxicity models

The ISSSTY²⁵ database on mutagenicity (AMES test) with strains of the bacterium Salmonella typhimurium has 7367 rows (raw data), each containing: compound name, CAS number, SMILES code, molecular weight, general formula, general AMES test result (overall), and specific test results. The overall result is divided into three labels: label 1 (negative), label 2 (doubtful), and label 3 (positive) to confirm that the tested substance generates mutagenicity in the bacteria. The raw database was reduced after confirming the existence of SMILES codes, validated through the CAS number within the PubChem database.²⁶ The sample set was reduced to 6226, after a general verification of the existence of canonical SMILES codes and the removal of the results designated as “inconclusive”. A new spreadsheet was generated with 123 QSAR indices (columns) and 5827 rows, calculated by the RDKit library. The Scikit-Learn²⁷ library has variable selection methods that can also be used for dimensionality reduction in sample sets. We used these methods (Feature selection and Feature importance) in this work to improve the results when applying the Extra Tree Classifier and Keras Classifier neural network models. In their default application conditions, we reduced the QSAR matrix from 123 to 70 columns. Both models used the same sample sets: a total of 5827, considering 4661 training samples (80%) and 1166 testing samples, randomly selected by the train_test_split function, with unbalanced classes due to an unequal number of labels in the original dataset. The Multiclass models have: label 1 (negative), label 2 (doubtful), and label 3 (positive). The working parameters for the models were:

• (i) Extra Trees Classifier model: estimators = 100, minimum leaves = 2.

• (ii) Keras neural network classification model, optimized with the Optuna package,²⁸ and with features to prevent overfitting. Architecture: input layer with 70 neurons, two hidden layers, the first with 35 neurons and the second with 17 neurons, and one output layer (70-35-17-3), dropout rate = 0.11698, optimizer: Adam, learning rate = 8.103 × 10^-4, validation split rate = 0.2, maximum training epochs = 100, batch size = 32, loss function = categorical_crossentropy, evaluation metric = accuracy, early stopping feature. Cross validation feature. The equations for the model evaluation metrics are shown in the Supplementary Information (SI) section.²⁹

Cross-validation feature: for each proposed set of hyperparameters, the Optuna package (version 4.5.0),²⁸ has functions that perform model evaluation through cross-validation. In this procedure, the dataset is partitioned into multiple subsets (folds). The model is then repeatedly trained using different combinations of subsets for training and validation, ensuring that all sample combinations are used for both training and validation at some point. At the end of this process, a performance metric is calculated for each fold, and the average of this metric is used as the final estimate of the performance of that set of hyperparameters. This average obtained in the cross-validation constitutes the value of the objective function that Optuna seeks to optimize. Thus, each trial results in a numerical value that represents the quality of the model under that specific configuration. Based on these results, the optimization algorithm adjusts its subsequent choices in an iterative process. This process continues for a predefined number of attempts or until a stopping criterion established by the user is reached. At the end of the optimization process, the set of hyperparameters shows the best average performance in the cross-validation is selected as the optimal solution.

Results and Discussion

Molecular generator

Diesel was chosen as the reagent class for study in chemical reactions because it is a significant component of environmental emissions and has been the best-selling fuel in Brazil in recent years, according to the Agência Nacional de Petróleo (ANP).³⁰ The relative distribution of hydrocarbons in the chemical composition of this fuel depends on the storage process and fuel processing scheme. Component contents depend on the nature of the crude oil and stored blends, as well as processing and refining parameters.³¹,³² References on chemical analysis of fuel provide technical specifications such as carbon number ranges, flash point, and cetane number,³² but, in general, it consists primarily of saturated (paraffinic and naphthenic) and aromatic hydrocarbons, which distill in the temperature range of 130 to 380 °C.³¹,³³

To be able to work with a set of specific organic molecules present in diesel fuel, we chose to work with a molecular generator, based on a generative neural network with a multi-objective evolutionary algorithm.¹⁷ To generate structures similar to the diesel composition, a set of 27 experimentally validated molecules was used as similarity targets.³⁴ Molecular chemical similarity was assessed and quantified using the Tanimoto coefficient³⁵ based on Morgan fingerprints with radius = 2.³⁶ Each of the 27 reference molecules was treated as an independent target, resulting in a 27-dimensional optimization problem whose objective was to maximize structural similarity with all targets simultaneously. As is characteristic of multi-objective evolutionary algorithms, no single optimal solution emerged; instead, a diverse set of Paretoapproximate solutions was obtained, representing tradeoffs between the similarity objectives. From the final output of the algorithm, 261 unique molecular structures were selected and used in this work. The molecules produced comply with the technical specifications of this fuel³¹-³³ in relation to the number of carbons, aromaticity distribution and molecular weight, as shown in Figures 1, 2 and 3. All analyses shown in these figures, including the direct classification of molecules, were performed with specific resources of the RDKit library, using Python programming (see Data Availability Statement section).

Figure 1
Distribution of number of carbon atoms for the 261 molecules generated by the molecular generator.

Figure 2
Molecular weight distribution for the 261 molecules generated by the molecular generator.

Figure 3
Aromaticity distribution and classification for the 261 molecules generated by the molecular generator. The aliphatic molecules in the figure on the right include a mixture of alkanes and alkenes.

Atmospheric reactions

Chemical reactions involving the OH radical, ozone, and atomic oxygen are shown in algorithms written in Python (see Data Availability Statement section). All selected reactions were based on references.¹,²,³⁷-⁴⁵ All reactions are specific to the degradation of organic compounds in the troposphere, and are produced by photochemical smog due mainly to emissions from combustion engines and specific industrial processes.¹,²,⁴ Nine specific chemical reactions (see SI section) were chosen based on their directness in product formation (in agreement with the cited references). Several other possibilities (mechanisms) for achieving the same products are available in the literature, so we chose these nine specific reactions. All chemical reactions were modeled using Marvin Sketch software (version 22.13.0, Chemaxon Ltd., Budapest, Hungary, 2022) and are described in detail in the SI section. An example of a simplified chemical reaction can be seen in Figure 4. The reaction is constructed by drawing parts (fragments) of the main reactant and product, generating a reaction pattern. Atom mapping is then performed to determine all possible products formed. This procedure explicitly specifies which atom reacts-that is, which chemical bond is broken and which is formed. This chemical reaction pattern is then saved (exported) in SMARTS format. This procedure is performed by Marvin Sketch software, one of the few free programs (using an academic license) that generates the SMARTS reaction patterns, which have complex and specific rules.²⁴

Figure 4
Part of the main panel of the Marvin Sketch software, showing the attack reaction (No. 2) on the double bond of aliphatic alkenes, via the OH radical.

The SMARTS representation for this chemical reaction (#2) in Figure 4 is: [#6:1]\[#6:2]=[#6:3]\[#6:4]>>[#6:4][#6:3]-[#6:2](-[#6:1])-[#8]

This chemical reaction is modeled by executing a sequence of Python codes derived from the RDKit library, written line by line, in order of execution, on the Google Colab platform. Before execution, a text file (in TXT format) is loaded by the main program, containing several lines (‘diesel-smiles.txt’), where each line represents a reactant molecule written in SMILES encoding.⁴⁶ Once the SMARTS code has been read, specifically by the AllChem. ReactionFromSmarts function, all product molecules formed will follow the atomic indexing rule specified in this code. In SMARTS code, aliphatic and aromatic reactants are differentiated. This pre-existing condition determines whether or not products will be formed, depending on the type of reactant used in the reactions. All products formed are written and saved in an ASCII file named “saida.txt”, excluding repetitions. As an example, Table 1 shows some reactant molecules in SMILES format present in the file “diesel-smiles.txt” and the corresponding product molecules, as a result of the main program’s processing, for the reaction shown in Figure 4. The Python codes for each specific reaction can be found at (see Data Availability Statement section). The reaction pattern shown in Figure 4 represents an oxidation process and simulates the attack of the hydroxyl radical (^•OH) on the double bonds present exclusively in aliphatic chains.

Table 1
Some examples of reactant and product molecules, in SMILES format, from the chemical reaction (#2) in Figure 4

#	Reactants	Products
1	CCCCCCC(CC(C)C)n1ccnc1	-
2	CCCC(C)C1(C(C)C)C=CC(C)C(=O)N1	CCCC(C)C1(C(C)C)NC(=O)C(C)CC1O
3	CCC1CCCC1	-
4	CC1=C(C(C)C)C(C(C)C)NCC1	CC(C)C1NCCC(C)C1(O)C(C)C
5	CCN1CC=C(CC(C)=O)CC1	CC(C)C1NCCC(C)(O)C1C(C)C

Each molecule, i.e., the reaction product formed, is confirmed and analyzed by a process (function) called “Sanitization,” where each atom is checked according to the following conditions: its valence state, its corresponding chemical bonds, and the “neighborhood” of the main bond. If any of the checks are incorrect in relation to the previous conditions, an error code is generated, and no product is recorded in the “saida.txt” file. In Table 1, no products were formed for the reactants in the first and third rows, in accordance with the reaction pattern defined by the SMARTS representation shown above. In this case, the main preconditions analyzed are: reactant 1 is aromatic; for reactant 3, there is no double bond in the molecule. Current SMARTS coding does not allow working with reaction stoichiometry, nor establishing relationships between the concentration of reactants and products formed, their physical states, or the influence of external factors such as pressure or temperature. Table 2 shows the total number of unique products formed by the nine oxidation reactions tested (detailed in the SI section). Unique products were so named because symmetrical reagents (geometric symmetry present in the molecule when observing the axis of the main chemical bond) produce geometrically identical products, which were therefore counted only once. The reaction #1 consists of a simple attack by the OH radical on a secondary carbon within an aromatic ring, resulting in the loss of its hydrogen. Reaction #2 occurs when the OH radical encounters a double bond in an aliphatic carbon chain, generating a single bond in its place. Reactions #3 and #4 are exclusive to the reagent ozone. In the first case, the attack on a double bond in an aliphatic chain forms two new products, a carboxylic acid and a ketone. For reaction #4, ozone breaks the benzene ring, forming a linear chain product with unsaturations, where at the ends there will be a carboxylic acid group on one side and an aldehyde group on the other. Reactions #5 to #9 are specific oxidations with atomic oxygen. In reaction #5, atomic oxygen attacks a secondary carbon in a double bond present in an aliphatic chain, generating a carboxyl group.

Table 2
Number of unique products produced in the chemical reactions studied, considering the 261 reagent molecules

#	Main reaction	Mechanism	Number of unique productsa
1	OH radical	aromatic chains	319
2		aliphatic chains	10
3	ozone	aliphatic chains	8
4		aromatic chains	338
5 6 7	atomic oxygen	aliphatic chains (A) aliphatic chains (B) aliphatic chains (C)	8 6 5
8		alkanes	1040
9		aromatic chains	246

• ^a
  Total of 1980 molecules.

In reaction #6, the same reaction situation as #5 occurs,but with the replacement of a hydrogen atom by an OH group in the double bond. In reaction #7, the double bond of the aliphatic chain is replaced by an epoxy group (cyclic ether with three atoms). Reaction #8 occurs when an alkane undergoes an attack by atomic oxygen, generating a product with a carboxyl group at the end of this chain (which could be a ketone or an aldehyde). Finally, in reaction #9, the attack on benzene rings generates a phenolic product.

The atomic oxygen reaction (#8), considering only reagents with open aliphatic chains, produced the largest number of products. The atomic oxygen reaction (#7), which attacks unsaturated cyclic chains, forming an epoxide, yielded the fewest products. The molecular structures of these products and their number per reagent can be seen (see Data Availability Statement section).

This modeling of chemical reactions in the troposphere allows us to study and predict all chemical possibilities, generate specific products, and store them as a new database. With this information, we can calculate and predict the toxicity of these molecules (as discussed in the next section), support studies of bioaccumulation and biotransformation,¹⁵,⁴⁷ aerosol formation,⁴⁸ and secondary particulate matter,³ and, in practical terms, study specific chemical reactions while saving time, using diverse reagents, and generating no laboratory waste.

Toxicity models

Modeling the toxicity of organic compounds is not a straightforward process due to the large number of existing assays (bioactivity) for different species tested (different types of living animals, cells, bacteria, etc.), and their diverse sources. There is a wide variety of classification models⁹-¹¹ and regression models¹²-¹⁴ in this area, with many specificities and limitations.¹⁵,¹⁶ We chose to develop a classification model based on the AMES mutagenicity tests⁴⁹ using a large public ISSSTY²⁵ database containing 6226 compounds, testing two robust classification models.

The QSAR descriptors are important because they greatly contribute to the results of regression models, considering the variable selection features available in the Scikit-Learn library for this purpose. Studies with QSAR descriptors provide support in regulatory areas as a tool for assessing the risks posed by compounds to the environment and to humans. The physicochemical properties of compounds can be described quantitatively if they are expressed through appropriate physicochemical parameters or structural descriptors.⁵⁰,⁵¹

Feature selection, present in the Scikit-Learn library, is a tool used to automatically select the most relevant variables (characteristics) based on the weights or ‘importances’ learned by a supervised regression model. The process is based on the absolute value of the regression coefficients. The method reads these importances and removes the variables below a certain threshold. The result is a new dataset containing only the relevant variables.⁵² The 70 QSAR variables/descriptors selected and used in our models are presented in Table S1 (SI section).

Extra Trees Classifier model

The Extra Trees Classifier model performed well with the basic parameters chosen under the default conditions suggested by the Scikit-Learn library. We used estimators = 100 (total number of trees) and minimum leaves = 2, and even changing these parameters to larger values did not improve the model evaluation metrics.

Decision tree models have shown better results with various sets of chemical data in regression and classification models.⁵³ This can be verified when we use/test different models in machine learning libraries, such as PyCaret.⁵⁴ This allows you to choose the best model from approximately 30 different algorithms. Once the model is chosen, we can adjust the evaluation parameters with the range of information present within the Scikit-Learn library page.²⁷

Extra Trees is a machine learning model that combines multiple decision trees, similar to Random Forest, but with additional randomization. Although both use multiple trees, Extra Trees generate completely random splits, without seeking optimal thresholds. Instead of limited sampling (like ‘bootstrap’), it typically uses the entire dataset for each tree, but maintains randomization by selecting random split points. Just like in Random Forest, for classification tasks, the forest predicts by majority vote (predictions of classes) among the trees, while for regression tasks, it averages the predictions. The strength of the model comes from its extreme randomization approach. This additional randomization makes Extra Trees generally faster to train, while maintaining performance comparable to Random Forests.²⁷

In Table 3, we see that the Extra Tree model presents good classification results when we analyze the average results (> 0.8 or 80%) of the evaluation parameters: accuracy, precision, recall, and F1-score. The last column shows the distribution of labels in relation to the total samples in the validation set.

Table 3
Evaluation metrics for the Extra Tree Classifier model, with validation set

Labels Precision	Recall	F1-score Accuracy	ROC AUC	Samples
1 0.80	0.80	0.80		455
2 0.60	0.12	0.19		26
3 0.85	0.88	0.87		685
Weighted 0.8256 average	0.8302	0.8241 0.8302	0.9131	1166

Despite having disproportionate classes in this dataset, the average accuracy (proportion of all correct classifications) is greater than 80%, showing good predictive capacity of the model. The average recall, which shows the proportion of all actual positives that were correctly classified as positive, is also greater than 80%. The same result applies to the average precision, which indicates the proportion of all positive classifications in the model that are actually positive. And lastly, the F1-score (harmonic mean of the precision and recall metrics) is also greater than 80%. This last parameter balances the importance of precision and recall and is a preferable assessment to accuracy for datasets with unbalanced classes.

The Multiclass Receiver Operating Characteristic Curve Area Under Curve (ROC AUC) core parameter presented an excellent result of 0.9131, considering that the dataset is not balanced and that label 2 significantly hinders the classification prediction of the model, making it a “doubtful” result, according to the Benigni.⁴⁹ The Extra Trees model has better ROC AUC Score results than those reported by Karim et al.,⁵⁵ who used the Tox21 dataset⁵⁶ and combined a Decision Tree with a Neural Network. It is also better than the results obtained by Setiya et al.,⁵⁷ who integrated TOXNET,⁵⁸ T3DB⁵⁹ and KEGG⁶⁰ datasets in a model combining Random Forest, Neural Network, and Light Gradient Boosting Machine.

The other evaluation parameters (metrics) yield very similar results. Principal Component Analysis (PCA) was tested on the QSAR data matrix, but without improvement in the evaluation metrics. Figure 5 shows the confusion matrix (used to evaluate a classifier whenever the dataset is unbalanced), where the main diagonal shows the correct classification results achieved by the model. Despite the label 2 variable, the model still managed to correctly classify 3 samples (11% of the total). The labels 1 (negative) and 3 (positive) variables had a large number of correct classifications when we look at the total true values (last column of Table 3).

Figure 5
Confusion matrix obtained for the Extra Trees Classifier model.

Keras neural network classification model

Models based on deep learning neural networks have grown significantly in recent years in the field of chemistry.⁶¹-⁶⁵ Therefore, we used a neural network from the Keras package (Tensor Flow/Keras library) to compare results with the previous model.⁶⁶,⁶⁷ This model was trained with the same sample sets as the Extra Tree model and also underwent a process of optimization of its configuration and training parameters using the Optuna library.²⁸,⁶⁸ This library provides a framework for hyperparameter optimization through an iterative process, with cross validation feature. In the case of this Keras neural network, the optimized hyperparameters were the number of layers, the number of neurons in each layer, the optmization function, the dropout rate, and the learning rate, described in the Methodology section.

Analyzing the results in Table 4, we see that all evaluation parameters yield worse results than the previous Extra Tree model. The ROC AUC score decreased significantly, while the F1-score and precision parameters fell below 80%. The neural network showed more problems modeling label 2 (doubtful) with imbalanced data, failing to predict any samples.

Table 4
Evaluation metrics for the Keras classification model, with validation set

Labels Precision	Recall	F1-score Accuracy	ROC AUC	Samples
1 0.75	0.79	0.77		455
2 0	0	0		26
3 0.84	0.84	0.84		685
Weighted 0.7868 average	0.8036	0.7950 0.8036	0.8773	1166

The loss function results for the training and validation sets, as a function of epochs, are shown in Figure 6. Because of the early stopping feature used, the network never reached the maximum of 100 training epochs during any of the tested runs.

Figure 6
Loss function in relation to the number of epochs considering the Early stopping feature.

Figure 7 shows the confusion matrix, with the variables labels 1 (negative) and 3 (positive) having a much lower number of correct classifications than those predicted by the Extra Trees model.

Figure 7
Confusion matrix obtained for the Keras neural network classification model.

The specific code lines for these models are shown as informed in Data Availability Statement section.

Conclusions

The generation of a set of molecules present in diesel fuel using a generative neural network was quite satisfactory, with their molecular characteristics being accurately reproduced. This generation process allows the extension of its application to other fuel “blends” that also have environmental concerns regarding the use of petroleum as an energy source in current times.

The modeling of chemical reactions using machine learning/chemoinformatics methods demonstrates great potential for environmental applications, among others. It can model the potential formation of any reaction product, including toxic compounds, and enables the study of the formation of intermediate compounds in chemical reactions carried out in several steps. It can assist in predicting the environmental impact of these products (in conjunction with the development of machine learning models) and support policies on the emission and/or management of these compounds.

The growing number of environmental contaminants makes comprehensive toxicity testing a logistical challenge and a mathematical/statistical modeling problem. Laboratory pollutant toxicity testing is neither quick nor cheap. QSAR-based models predict toxicity based on the structural characteristics of molecules. Analytical behavior, physicochemical properties, and toxicity are linked to molecular structure. The classification models used in this work to predict mutagenicity with the Ames test (using public data) showed good results with the construction of a QSAR descriptor matrix calculated by the RDKit library. Variable selection, performed using resources from the Scikit-Learn library, allowed for better performance of the classification models, reducing the original set of QSAR descriptors from 123 to 70 relevant variables. These models can be used as management tools, for studies to update environmental legislation, and also for biodegradation studies.

Supplementary Information

Supplementary data are available free of charge at http://jbcs.sbq.org.br as PDF file.

Acknowledgments

This work was supported by the Brazilian agencies CNPq (309744/2022-9); and FAPERJ (E-26/010.001415/2019, E-26/211.357/2021, E-26/200.608/2022, E-26/210.372/2022, E-26/200.393-2023) Fernando Schimidt would like to thank Chemaxon for the academic license of Marvin Sketch v.22.13 software. Artificial intelligence tool (Gemini) was used to correct programming errors in Python.

Data Availability Statement

The framework is open source and available at: https://github..com/gmmsb-lncc/generative-optim.

All analyses shown in Figures 1-3, including direct classification of molecules, were performed with specific resources of the RDKit library, in the “diesel characterization” file; chemical reactions involving the OH radical, ozone, and atomic oxygen, molecular structures of the products and their number per reagent were performed using Python programming and can be seen at https://github.com/Schimidt99/atmospheric_reactions.

The specific code lines for these models are shown on the page https://github.com/Schimidt99/atmospheric_reactions, in the files ‘Mutagenicity_QSAR_Keras_NN_model’ and ‘Mutagenicity_ QSAR_ETclassifier_model’.

The research data and all programs in Python are available at https://github.com/Schimidt99/atmospheric_reactions

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Edited by

• Editor handled this article:
  Paula Homem-de-Mello (Executive)

Publication Dates

• Publication in this collection
  29 June 2026
• Date of issue
  2026

History

• Received
  26 Mar 2026
• Accepted
  14 May 2026