Deep Learning for Deep Chemistry: Optimizing the Prediction of Chemical Patterns

Computational Chemistry is currently a synergistic assembly between ab initio calculations, simulation, machine learning (ML) and optimization strategies for describing, solving and predicting chemical data and related phenomena. These include accelerated literature searches, analysis and prediction of physical and quantum chemical properties, transition states, chemical structures, chemical reactions, and also new catalysts and drug candidates. The generalization of scalability to larger chemical problems, rather than specialization, is now the main principle for transforming chemical tasks in multiple fronts, for which systematic and cost-effective solutions have benefited from ML approaches, including those based on deep learning (e.g. quantum chemistry, molecular screening, synthetic route design, catalysis, drug discovery). The latter class of ML algorithms is capable of combining raw input into layers of intermediate features, enabling bench-to-bytes designs with the potential to transform several chemical domains. In this review, the most exciting developments concerning the use of ML in a range of different chemical scenarios are described. A range of different chemical problems and respective rationalization, that have hitherto been inaccessible due to the lack of suitable analysis tools, is thus detailed, evidencing the breadth of potential applications of these emerging multidimensional approaches. Focus is given to the models, algorithms and methods proposed to facilitate research on compound design and synthesis, materials design, prediction of binding, molecular activity, and soft matter behavior. The information produced by pairing Chemistry and ML, through data-driven analyses, neural network predictions and monitoring of chemical systems, allows (i) prompting the ability to understand the complexity of chemical data, (ii) streamlining and designing experiments, (ii) discovering new molecular targets and materials, and also (iv) planning or rethinking forthcoming chemical challenges. In fact, optimization engulfs all these tasks directly.

The design of generalized cause/effect models, and the scaling-up of the contributions that are being made, containing high-dimensional data, and following the open-science basis (i.e., completely accessible, with precise metadata and practical formats) are critical challenges, that may, however, facilitate the routine implementation of data mining in chemistry and expedite new discoveries.
The amount and quality of chemical data generated by experiments and simulations have been the mainstay of the new data-driven paradigm, that establishes the bridge between theory, experiment, computation, and simulation.
This review describes, in a critical and comprehensive way, relevant contributions carried out recently and involving the development of chemistry ML approaches. An exhaustive account of the theoretical foundations and applications published in the early years of AI and ML in Chemistry falls beyond the scope of this review. The reader is referred to Lecun et al. (2015), Coveney Peter et al. (2016), Goh et al. (2017), Elton et al. (2019), Gromski et al. (2019), and Mater and Coote (2019) for a full description of these efforts.
Until 10 years ago, only a few 100 studies on the use of ML in Chemistry were published, resulting from the contributions made over four decades. In 2018, ca. 8,000 articles in the Web of Science database included these keywords, corresponding to an increase in ca. 35% for just one decade. In this review, there is room to mention only a small fraction of these applications.
Despite the increasing number of works on the topic, the models proposed and practices carried out by chemists are entailing serious concerns (Chuang and Keiser, 2018a). Several technical challenges, pitfalls, and potentials of ML, and also the reliability of the results, have been discussed by some authors Chuang and Keiser, 2018a,b;Estrada et al., 2018) corroborating some critical remarks on the fragility of purely data-based approaches (Microsoft, 2018). "If data can speak for themselves, they can also lie for themselves." This reflects the need for an in-depth understanding of chemical patterns, data-driven and theory-driven models, and algorithms, before their application.
Although significant progress has been made connecting specific neural network predictions to chemical input features, understanding how scientists should analyze and interpret these models to produce valid and conclusive assumptions about the system under study, still remains to be fully defined.
In Figure 1 an overview of the information generated during the last decade and ranked in the research domain of "Science Technology" of the Web of Science database, is presented.
The purpose of assessing the different facets of ML in Chemistry across the respective sub-fields is 3-fold: (i) to be able to quickly identify areas that have benefited most from the development and implementation of ML approaches, and those that still lack of such an optimization, as evidenced by the type of outcome, (ii) to identify the most relevant ML outcomes in each sub-field, and (iii) to assess the dynamics of ML outcomes over the 2008-2019 period and how these are related, giving rise to relevant research trends.
An extensive literature search on ML contributions in 30 Chemistry sub-fields is carried out, using a global set of 270 co-occurring keywords, each composed of three main terms, machine learning, type of outcome and the sub-field in which they co-occur (e.g., first co-occurrence: Machine learning AND Quantum chemistry AND Quantum models, second co-occurrence: Machine learning AND Medicinal Chemistry AND Molecular screening). A total of 5,279 contributions (including books, articles, reviews, editorials and letters) on ML in Chemistry, with 81,248 citations, and published between 2008 and June 30, 2019, are found in the worldwide Web of Science database, corresponding to a 4-fold increase over the previous four decades. Considering the compiled data and the selected Chemistry fields (organic, inorganic, physical, analytical, and biochemical), nine different ML outcomes embracing the most frequent chemical challenges are defined, including (i) text mining and system description, (ii) quantitative structure-activity/property relationships, (iii) DFT functionals and interatomic potentials, (iv) generative models and inverse molecular design, (v) molecular screening, (vi) synthesis/characterization of new compounds and materials, (vii) catalytic technologies, (viii) analytical techniques, and (ix) quantum models, algorithms, and quantum sensing. Note how these have a strong relation with the seven overall applications presented above (i-vii).
The heatmap represented in Figure 1 reflects the impact of each type of ML outcomes on Chemistry sub-fields. The analysis of co-occurring keywords is thus performed in order to find the number of publications that appeared simultaneously in the selected sub-field. This relation is established with greater or lesser impact depending on the frequency of each set of keywords in the selected time-span.
The natural clusters generated from the most important co-occurring relationships are also identified. Considering the dendrogram for the Chemistry sub-fields, it can be observed that these are organized in two main groups, which discriminates, in general, classical Chemistry sub-fields (organic, inorganic, and physical) from analytical and biochemical sub-fields. This structure suggests a significant similarity in the type of ML outcomes within each group. Group 1 have benefitted from a significant production on catalytic technologies, DFT functionals and interatomic potentials, quantum models and quantum sensing. The most representative ML outcomes in group 2 are associated to text mining, analytical techniques, generative models and inverse design, molecular screening, structure activity relationships, and synthesis of new compounds and materials. Examination of the similarity between the type of ML outcomes reveals that there are three main groups, corresponding to (i) text mining, analytical techniques, generative modes and inverse design, and molecular screening (group 1), (ii) structure-activity relationships and synthesis of new compounds and materials (group 2), and (iii) catalytic technologies, DFT functionals and interatomic potentials, and quantum models and quantum sensing (group 3).
Historically, researchers have introduced numerical approximations to Schrödinger's equation, and the popular DFT calculations in ab initio approaches. However, the computational cost inherent to these classical approximations have limited the size, flexibility, and extensibility of the studies. Larger searches on relevant chemical patterns, have been successfully conducted since several research groups have developed ML models and algorithms to predict chemical properties using training data generated by DFT, which have also contributed to the increase of public collections of molecules coupled with vibrational, thermodynamic and DFT computed electronic properties (e.g., Behler and Parrinello, 2007;Rupp et al., 2012;Behler, 2016;Hegde and Bowen, 2017;Pronobis et al., 2018;Chandrasekaran et al., 2019;Iype and Urolagin, 2019;Marques et al., 2019;Schleder et al., 2019).
Based on the heatmap it can be determined that groups of Chemistry sub-fields have similar, but distinct ML-based contributions.
The increase in chemical data and scientific documents has boosted data mining and text mining processes to manage the huge amount of chemical information and to extract useful and non-trivial knowledge in different scenarios (Krallinger et al., 2017).
It is interesting to inspect if certain ML outcomes are produced in combination with each other.
Other strong correlations are found between generrative models & inverse design and the two abovementioned ML applications, molecular screening (0.95) and text mining (0.93). This can be explained by the fact that many researchers have proposed machine learning frameworks based on a variety of Frontiers in Chemistry | www.frontiersin.org generative models for modeling molecules, which differ in the respective model structure and in the selected input features (Kadurin et al., 2017;Gupta et al., 2018;Jørgensen et al., 2018b;Arús-Pous et al., 2019;Brown et al., 2019;Jensen, 2019;Xu et al., 2019).
Also relevant are the correlations between generative models and inverse design and synthesis of new compounds and materials (0.90), and between generative models and inverse design and analytical techniques (0.85). The former relation evidences the significant effort that has been made on applying ML models, in particular those based on accurate DL architectures, to find and select lead molecules (e.g., drugs), displaying desired properties (Varnek and Baskin, 2012;Mitchell, 2014;Rupp, 2015;Lo et al., 2018). These properties are to be translated into a more simplified information on the molecular structures, and encoded into the respective chemical fingerprint (i.e., a set of binary characteristics of molecules). The process continues with the screening of the available databases for finding molecules that possess similar fingerprints to the generated ones. Generative models and deep neural networks (DLNs) have thus allowed generating molecules and promising candidates for useful drugs, basically from scratch, making it possible to "design perfect needles instead of searching for a needle in a haystack" (White and Wilson, 2010;Benjamin et al., 2017;Gómez-Bombarelli et al., 2018;Harel and Radinsky, 2018;Kang and Cho, 2018;Li et al., 2018b;Merk et al., 2018;Nouira et al., 2018;Popova et al., 2018;Sanchez-Lengeling and Aspuru-Guzik, 2018;Schneider, 2018).
It is also observed that there are other ML contributions that are interrelated: structure activity relationships with (i) molecular screening and (0.84), (ii) synthesis/characterization of new compounds and materials (0.78), and (iii) generative models and inverse design (0.75), DFT functionals and interatomic potentials with quantum models and quantum sensing (0.83), and synthesis/characterization of new compounds and materials with analytical techniques (0.79).
Both generative models and analytical techniques have been extensively used in the qualitative/quantitative search of patterns underlying chemical systems (Elton et al., 2019;Ghosh et al., 2019;Stein et al., 2019a,b). It should be noted the use data from large repositories (e.g., Protein Data Bank and Cambridge Structural Database) and ML methods are not new (Hiller et al., 1973;Gasteiger and Zupan, 1993;Behler, 2016). The latter have been employed as classification tools in pioneering works, encompassing, for e.g., the analysis of spectra (Thomsen and Meyer, 1989), quantification of structure-activity relationships (QSARs) (Agrafiotis et al., 2002), and prediction of binding sites of biomolecules (Keil et al., 2004).
The range of ML applications is now quite extended as a result of a deep integration of ML in analytical, theoretical and computational chemistry. Despite of some initial skepticism in understanding the foundations and structure of ML methods, their use has been accelerated and maturated in recent years essentially due to their suitability to new applications and industry needs, including chemical and pharmaceutical sectors.

MACHINE LEARNING FOR OPTIMIZATION: CHALLENGES AND OPPORTUNITIES
Designing models from chemical observations to study, control, and improve chemical processes and properties is the basis of optimization approaches. The understanding of chemical systems, and the respective underlying behavior, mechanisms and dynamics, is currently facilitated by the development of descriptive, interpretative, and predictive models, i.e., approximations that represent the target system or process. Applications of such models have included the (i) optimization of reaction parameters and process conditions, e.g., changing the type of reagents, catalysts, and solvents, and also varying systematically, concentration, addition rate, time, temperature, or solvent polarity, (ii) suggestion of new reactions based on critical functional groups, (iii) prediction of reaction/catalyst design, and optimization of heterogeneous/homogeneous catalytic reactions, (iv) acceleration and discovery of new process strategies for batch reactions, (v) establishment of trade-offs in the reaction rate and yield of organic compounds, (vi) description and maximization of the production rate and conversion efficiency of chemical reactions, (vii) prediction of the potential toxicity of different compounds, and also the (viii) rational design of target molecules and guided exploration of chemical space (Kowalik et al., 2012;Zielinski et al., 2017;Häse et al., 2018;Min et al., 2018;Zhou et al., 2018;Ahn et al., 2019;Choi et al., 2019;Gromski et al., 2019;Matsuzaka and Uesawa, 2019).
ML provides the tools to scrutinize and extract useful information to be employed in modeling and system-solving solutions (Artrith and Urban, 2016;Ward and Wolverton, 2017). In Chemistry domains, researchers have had access to multidimensional data of unprecedented scale and accuracy, that characterize the systems/processes to be modeled. Specifically, ML contributions have involved a variety of systems including drugs (Griffen et al., 2018), polymers (Li et al., 2018a), polypeptides Müller et al., 2018), energetic materials (Elton et al., 2018), metal organic frameworks (He et al., 2018;Jørgensen et al., 2018a;Shen et al., 2018), and organic solar cells (Jørgensen et al., 2018a).
Advances in analytical methods, laboratory equipment and automation have rapidly improved the performance of experimental procedures (e.g., miniaturizing experiments for reactions, and connecting analytical instruments to advanced software based on decision-making algorithms and optimization tools) (Stevens et al., 2010;Smith et al., 2011;Richmond et al., 2012;. The implementation of ML-based approaches have allowed developing innovative capabilities, such as cost-effective experiments, advanced algorithms for automation, and designing of experiments, chemoinformatics tools for dealing with high-dimensional analytical data, and accelerated in situ/in line analysis of chemical transformations (e.g., polymerization reactions, heterogeneous catalytic processes, aggregation of nanoparticles) Häse et al., 2018).
However, there are critical challenges that ML in Chemistry must face, including the control of experiments, the detailed description of chemical space, the flexibility and generalization of models, robustness, and accuracy of predictions, and the establishment of effective cross-disciplinary collaborations Hansen et al., 2015;Kishimoto et al., 2018;Smith et al., 2018a).
A clear definition of ML, as well as the distinction from other purely mathematical regression methods is not straightforward, and can be associated to some degree of arbitrariness (Behler, 2016). Standard ML methods include, artificial neural networks, support vector machines, and Gaussian processes, which have contributed to the rational design of compounds and materials, and to the improvement of computational frameworks (Goh et al., 2017;Mater and Coote, 2019). The latter have been applied for e.g., in QSAR models and drug design (Kadurin et al., 2017;Chen et al., 2018;Fleming, 2018;Green et al., 2018;Gupta et al., 2018;Li et al., 2018b;Lo et al., 2018;Popova et al., 2018;Simões et al., 2018) aiming at identifying systems, molecules and materials with optimal properties (e.g., conductivity, aqueous solubility, bioavailability, bioactivity, or toxicity) (Kadurin et al., 2017;Freeze et al., 2019). This can be made via extensive searches, in large databases, of latent relationships between the atomic structures. The structures, can thus be encoded using multiple descriptors, and target properties.
The possibilities of applying ML for optimization in Chemistry are endless. There are studies focused on ML approaches for inferring on the optimized geometry of a system (Zielinski et al., 2017;Venkatasubramanian, 2019), and finding minima on complex potential energy surfaces (Chen et al., 2015;Chmiela et al., 2018;Kanamori et al., 2018;Xia and Kais, 2018;Hughes et al., 2019), such as those of large water clusters (Bose et al., 2018;Chan et al., 2019).
The most innovative aspects of ML in Chemistry are related to the availability of large volumes of theoretical data (e.g., electrostatic energy contributions in force fields, atomic charges, structural properties, and representations of the potential energies), obtained from automatic and accurate electronic structure calculations (Behler, 2016).
However, the intricate nature of the configuration space and its exponential dependence on system size and composition, have hampered the screening of the entire set of candidate structures directly by electronic structure calculations (Behler, 2016;Welborn et al., 2018).

Signs of Controversy
Despite the usefulness of ML approaches being indisputable, with the promise to modernize molecular simulations, synthesis, materials science, and drug discovery, the respective endorsement and practical aspects in some chemical sub-fields is far from consensual Chuang and Keiser, 2018a,b).
Ten years ago, there were only a few publications on applications of ML in Chemistry, but currently there are thousands of published works. The controversy has highlighted the potential (instructive) pitfalls of some practices using ML. It has been argued that ML algorithms may lead to overestimated performances and deficient model generalizations, due to their sensitivity to the presence of maze-like variables and experimental artifacts (Chuang and Keiser, 2018a). For instance, Ahneman et al. (2018) have recently designed a ML model to predict yields of cross coupling reactions with high accuracy, containing isoxazoles, as reaction inhibitors, which were incorporated for assessing the robustness of the reaction. Input data for the proposed algorithm included yields and reagent parameters of 3,000 reactions, such as NMR shifts, dipole moments, and orbital energies. The most significant features of the proposed algorithm were found to be the descriptors of additives. However, the experimental design of this original work has been contested by Chuang and Keiser (2018b), who warned for potential artifacts associated to the original work. These authors demonstrated that the model also identified reaction additives as the descriptors displaying the greatest impact on the reactions, suggesting that high additive feature contributions cannot be discriminated from the hidden structure within the dataset, i.e., the procedure of the original paper was not sufficient for establishing isoxazole additives as the most important descriptors (Chuang and Keiser, 2018b). A meticulous preprocessing of input data and validation of the model hypothesis was then suggested. The Y-randomization test in the original work was taken into account just the information rooted in the structure of the data set, irrespective to the intended outcome. The classical approach based on multiple hypotheses to assess alternative descriptions of the performance of the ML model was implemented (Chuang and Keiser, 2018b). The effect of different reaction parameters (e.g., additives, catalyst, and aryl halide) in an extensive combinatorial layout generated over several independent reactions was duly explored, providing the underlying structure of the data (Chuang and Keiser, 2018b).
An alternative assumption considering that ML algorithms deal with patterns within the experimental design, instead of learning from the most relevant chemical features was therefore investigated. It was concluded that ML is prone to explore data irrespective to their size and structure. This aspect was illustrated by extracting and replacing the chemical features (e.g., electrostatics, NMR shifts, dipole moments) from each molecule with random (Gaussian distributed) numeric strings. It was shown that the predictions were similar to the original ones. Chuang and Keiser (2018a) have also introduced technical and conceptual standpoints, including the use of adversarial controls to evaluate the predictive performance of ML models, focusing on the design of rigorous and deliberated experiments, ensuring accurate predictions from suitable and significant models (Chuang and Keiser, 2018a). By revising the original information, a number of variations of the test sets was introduced by Estrada et al. (2018) for assessing the performance of predictions, considering alternatives to the random-forest model. It was therefore demonstrated that ML models are in fact quite sensitive to such imposed features, and the reagent-label models are relevant representations of the data set and useful for comparing performances in generalization assessments.
The original assumptions regarding the significance and validity of the random-forest (chemical-feature) model to describe important and general chemical features were also confirmed .
A lesson that chemists may draw from such constructive discussions is that as the size of the data set increases, the performance of ML models also increases, but with the possibility of obtaining unexpected results and irrelevant patterns, as the rules for ML algorithms to detect and deal with potential technical and conceptual gaps are not well-established. Specifically, the description of chemical reactivity underlying a data set is required in order to ensure the reaction prediction, by using data and reagent-label models to evaluate the scope and restraints of chemical characterization.
ML provides new opportunities to increase the quality and quantity of chemical data, which are essential to promote optimization, implementation of rational design and synthetic approaches, prioritization of candidate molecules, decisionmaking, and also for guiding of innovative ideas.

Deep Learning, Deep Chemistry
In this section, an introductory overview into the core concepts of DL, and DLNs is provided. Focus is given to the unique properties of DL, that distinguish these algorithms from traditional machine learning approaches, with emphasis on chemical applications rather than providing theoretical and mathematical details.
ML is a branch of computer science dedicated to the development of algorithms capable of learning and making decisions on complex data (Samuel, 1959;Mitchell, 1997). This learning process involves specific tasks that are commonly classified in (i) supervised learning, for establishing the relationship between input and output data (e.g., linear regressions and classification techniques), (ii) unsupervised learning, for finding hidden patterns or features in data, without any previous information on such characteristics and interrelations (e.g., clustering and dimension reduction techniques), and (iii) reinforcement learning, for performing a particular task through repeated dynamic interactions e.g., optimization of molecules (Zhou et al., 2018) and chemical reactions (Zhou et al., 2017).
Deep learning is a fast-moving sub-area of ML, focused on sophisticated learning and extrapolation tasks, fostered by the wide range of chemistry literature, open-source code, and datasets (Goh et al., 2017).
The ability of DL to establish the relevant phenomena, expedite chemical reactions, and predict relevant properties, optimal synthesis routes, solve critical analytical uncertainties, and reduce costs and resources, is invaluable in Chemistry. Its success in modeling compound properties and reactions, depends, among other aspects, on the access to FIGURE 3 | Schematic representation of an artificial neuron (top), and a simple neural network displaying three basic elements: input, hidden and output layers (bottom-left), and a deep neural network showing at least two hidden layers, or nodes (bottom-right). The calculation is performed through the connections, which contain the input data, the pre-assigned weights, and the paths defined by the activation function. If the result is far from expected, the weights of the connections are recalibrated, and the analysis continues, until the outcome is as accurate as possible.
There are barriers to be surpassed, including cleaning data, production of meaningful and accurate chemical information (free of bias), lack of standardization of chemical data, expertise and familiarity with ML and DL in chemistry sectors, and also lack of collaboration opportunities) (Mater and Coote, 2019).
The majority of DL algorithms currently developed are based on artificial neural networks (Lecun et al., 2015).
DLNs are now a proving-ground for research in chemical sciences (Goh et al., 2017;Jha et al., 2018;Popova et al., 2018;Segler et al., 2018;Elton et al., 2019;Mater and Coote, 2019;Xu et al., 2019). Similarly to artificial neural networks, DLNs are produced to resemble the brain, in which the information passes through a series of interconnected nodes comparable to neurons (Lecun et al., 2015). Each node analyzes segments of information and transfer that information to adjacent nodes (see Figure 3).
The computational model consists of multiple hidden layers (in higher number comparing to more conventional approaches) which confer the ability of DLNs to learn from highly complex data and perform correlation and reduction. This means that the algorithm discovers correlated data, while discarding irrelevant information. Each layer combines information collected from the previous layer, and subsequently infers on the respective significance and send the relevant information to the next layer. The hidden term is used to represent layers that are not direct neighbors of the input or output layers.
The process allows constructing increasingly complex and abstract features, by adding layers and/or increasing the number of neurons per layer. However, the use of more than a single hidden layer requires determining error attributions and corrections to the respective weights. This is carried out via a backpropagation, i.e., a backward process starting from the predicted output, and back through the neural network (Goh et al., 2017). In this process a gradient descent algorithm is employed to determine the minimum in the error surface created by each respective neuron, when generating the output. Note that, this gradient descent approach is conceptually similar to the steepest descent algorithm implemented in classical MD simulations (Goh et al., 2017). The major difference lies on the use of an iterative process, in which an error function of the target output of the neural network is minimized, and the weights of the neurons are updated, instead of iteratively minimizing an energy function and updating atomic coordinates for each step.
A complete description of the main core concepts and architecture of DL applied to chemistry is given in Goh et al. (2017) and Mater and Coote (2019).
A summary of the main contributions of DL for solving relevant chemical challenges, as well as an illustration of the general components of a DL framework are presented in Figure 4.
DL is not only a cost-cutting effort, but also an innovative source of new perspectives.

CUTTING-EDGE APPLICATIONS
In recent years, ML has been evoked in chemistry-related tasks. The use of ML and, in particular, DL-based approaches across prediction of binding, activity and other relevant molecular properties, compound/material design and synthesis, as well as applications of genetic algorithms are highlighted in what follows.
Researchers in chemical sciences have started exploring the capabilities of ML using data collected from computations and experimental measurements. Data mining is traditionally adopted to explore high-dimensional data sets, in order to identify and establish relevant connections for the chemical features of compounds and materials.
Other more ambitious approaches, including quantum mechanics, which integrates physics-based computations (e.g., DFT) and ML methods in the search for novel molecular components, have also been implemented (Curtarolo et al., 2013).
Amongst the major achievements of DL in Chemistry, are the outstanding performances in predicting activity and toxicity, in the context of the Merck activity prediction challenge in 2012, and the Tox21 toxicity prediction challenge launched by NIH in 2014, respectively. In the former, DL was very successful in the competition outperforming Merck's internal baseline model. In the second challenge, DL models also achieved top positions (Goh et al., 2017).
Similarly to what happens to the majority of the modern computational chemists who no longer build their own code to perform MD simulations or quantum chemical calculations, due to the existence and availability of well-established software packages, DL researchers have also use several software packages for training neural networks including Torch, Caffe, Theano, and Tensorflow (Goh et al., 2017).
Apart from the influence of software improvements, the continuous growth of chemical data in public databases, such as PubChem and Protein Data Bank has also facilitated the FIGURE 4 | Overview of (top) the contribution of DL algorithms for solving different chemical challenges and the respective tasks, and (bottom) the general components of a DL framework, including the input data, the learning model able to interpret the data and the prediction space, from which the model performance can be inspected. The model represents an optimization cycle containing interconnected components: prediction, evaluation, and optimization. Reprinted with permission from Mater and Coote (2019). Copyright (2019) American Chemical Society. raise of ML and DL applications in Chemistry, including quantum chemistry, property prediction and materials design, drug discovery, QSAR, virtual screening, and protein structure prediction (Goh et al., 2017;Christensen et al., 2019).
For instance, the prediction of the refractive index of ionic liquids based on quantum chemistry calculations and an extreme learning machine (ELM) algorithm has been conducted . Specifically, 1,194 experimental data points for 115 ionic liquids at different temperatures were collected from more than 100 literature reports. Quantum chemistry calculations were performed for obtaining the structures and descriptors of the ionic liquids. The model was designed using a stepwise regression algorithm and the R 2 and AARD% values were 0.841 and 0.855%, respectively. It was found that prediction of the refractive index was significantly affected by ionic liquid anions, comparing to the cations. Better performances were achieve using the ELM algorithm, with the R 2 and AARD% values of 0.957 and 0.295%, respectively .
ML has also contributed for modeling the water behavior, shedding light on important phenomena related to water molecules interactions and the resulting density. Morawietz et al. (2016) have calculated ice's melting point from fundamental quantum mechanics, demonstrating the predictive power of ab initio MD simulations and highlighting the critical role of van der Waals forces (Morawietz et al., 2016). It was evidenced that ice occupies a larger volume than liquid water as hydrogen bonds display water molecules in a rigid 3D network. These hydrogen bonds weaken when ice melts, and water molecules approximate, becoming dense with an extreme value at 4 • C (Morawietz et al., 2016). Note that these processes can also be rationalized resorting to ab initio MD approaches based on DFT; however, such calculations are associated to highly demanding computations. In addition to this, DFT approaches are not able to accurately reproduce minute but relevant van der Waals forces. The same authors have trained a neural network to reproduce DFT results with less computer power, and employed a previously-existing van der Waals correction. Water density changes, hydrogen bond network flexibility, and competition effects in terms of the nearest shell's contraction, after cooling, were explained based on the simulations (Morawietz et al., 2016).
One of the current challenges is to answer the question of whether chemical-physical properties, that often require quantum mechanics (e.g., dipole moments, binding and potential energies, and thermodynamics), can be represented and predicted by ML methods (Hansen et al., , 2015Montavon et al., 2013;Faber et al., 2016;Iype and Urolagin, 2019;Jaquis et al., 2019). Several attempts have been made on the topic with some successful examples Faber et al., 2017). Rupp et al. (2012) have developed a model based on nuclear charges and atomic positions for predicting molecular atomization energies of various organic compounds. A matrix composed of molecular elements and configuration was built, describing the potential energy of each individual atom and the Coulomb repulsion between nuclear charges. A non-linear regression scheme was employed for solving and mapping the molecular Schrödinger equation.
The regression models were trained and compared to atomization energies calculated with hybrid DFT, transforming a 1-h run (on average) of hybrid DFT per each atomization energy into milliseconds using ML. Cross-validation over more than seven thousand organic molecules yielded a mean absolute error below 10 kcal/mol. The authors have trained the ML algorithm on a set of compounds in a database, comparing the respective matrices to determine differences between molecules, so as to develop a landscape of such differences. Based on the atomic composition and configuration, the unknown molecule can be positioned in the landscape and the respective atomization energy can be estimated by the contributions (weights) obtained from the differences between the unknown and all known molecules .
More recently, the impact of selecting regressors and molecular representations on the construction of fast ML models of several electronic ground-state properties of organic molecules has also been investigated (Faber et al., 2017). The performance of each combination between regressor, representation, and property was evaluated with learning curves, which allowed reporting out-of-sample errors, as a function of the size if the training set (ca. 118 k molecules). The QM9 database (Ramakrishnan et al., 2014) was used for extracting the molecular structures and properties at the hybrid DFT level of theory, and included data on dipole moment, polarizability, enthalpies and free-energies of atomization, HOMO/LUMO energies and gap, heat capacity, zero point vibrational energy, and the highest fundamental vibrational frequency.
Several regression methods including linear models (Bayesian ridge regression and elastic net regularization), random-forest, kernel ridge regression, and neural networks (graph convolutions and gated graph networks) were tested. It was concluded that out-of-sample errors were strongly affected by the molecular properties, and by the type of representation and regression method. Molecular graphs and graph convolutions displayed better performances for electronic properties, while kernel ridge regression and histograms of dihedrals were suitable for describing energy-related properties [see Faber et al. (2017) for details on other relevant combinations]. Predictions based on the ML model for all properties have shown lower deviations from DFT (B3LYP) than the latter deviated from experiment. ML models displayed thus an improved prediction accuracy than hybrid DFT, since experimental or explicitly electron correlated quantum data were available.
In terms of drug development Brockherde et al. (2017) have developed a ML algorithm for predicting the behavior of molecules with potential to be used as pharmaceuticals and in the design of new molecules, able to enhance the performance of emerging energetic materials, including solar cells, battery technologies, and digital displays. The main goal was to identify the underlying patterns in the molecular behavior, by employing the ML algorithm for understanding atomic interactions within a molecule and using such information to predict new molecular phenomena.
Specifically, the algorithm was created and trained on the basis of a small sample set of the molecule under study, and applied to simulate the intricate chemical behavior within selected molecules, including malonaldehyde. A directed learning of the density-potential and energy-density maps was conducted, as illustrated in Figure 5, and the first MD simulation of with a ML density functional on malonaldehyde was performed, allowing to describe the intramolecular proton transfer process (Brockherde et al., 2017).
In more detail, one of the key tasks in atomistic modeling is the prompt and automated analysis of the simulation results, in order to provide a comprehensive understanding of the behavior of individual atoms and target collective properties. The main supervised and unsupervised machinelearning methods directed at classifying and coarse-graining of molecular simulations were recently summarized and discussed in Ceriotti (2019). A schematic overview of these methods, and also of a workflow reflecting the application of a ML scheme to an atomic-scale system is presented in Figure 6.
Also relevant is the development of improved molecular force fields, commonly used in MD simulations, using ML. On the other hand, the intrinsic operational aspects of MD simulations, in which the dynamic evolution of the chemical system is detailed in a fixed period of time, and for which interparticle forces and potential energies are often estimated using interatomic potentials, or molecular mechanics force fields, are perfectly suited for ML. In fact, some of the timesteps can be used as a training phase for estimating consecutive ones, assuming that each of the timesteps of MD simulation is strongly correlated with the preceding timestep and is adequate for sampling the phase space rapidly and accurately, allowing to estimate any meaningful property (Behler, 2016). MD simulations often sample abnormal, but probably relevant configurations, requiring the implementation of a decision tool for dealing with the unusual configuration, and from which ML may turn off and start learning (Botu and Ramprasad, 2015a;Smith et al., 2018a). These conditions have also been previously discussed and applied to ab initio MD (Botu and Ramprasad, 2015a).
In MD, the energies and forces for a vast number of atomic configurations are required, which can be obtained by performing the electronic structure calculations along the trajectory, or by evaluating the direct functional relation between the atomic configuration and the energy (Mansbach and Ferguson, 2015). This analytic expression, defined before running the simulation, is often recognized as a force field, an interatomic potential, or a potential-energy surface. Calculations of electronic structures are very demanding, even for DFT. DFT-based ab initio MD simulations are restricted to a few 100 atoms and shorter simulation times (Ahn et al., 2019).
The requirements for calculating ML potentials are very similar to conventional empirical potentials, and are duly discussed in Behler (2016). More recent conventional force fields are developed and validated for very specific systems, being limited by the functional form upon which they were constructed. On the other hand, despite requiring a training set, ML-based force fields are adaptive and more robust upon configurations not previously sampled (Botu and Ramprasad, 2015a). Furthermore, these force fields can be extended rapidly to different types of atoms and molecules, as they can learn and apply the physical laws, rather than starting from strarch (Botu et al., 2017).
Several improved force fields, and accurate predictions of thermodynamics and kinetics signatures, as well as their influence in molecular structures have been provided by performing ML-based atomistic and ab initio MD simulations. For instance, Chmiela et al. (2018) have incorporated spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model for constructing flexible molecular force fields from high-level ab initio calculations, with a great potential to be used to improve spectroscopic accuracy in molecular simulations. The sGDML model was able to reproduce global force fields at quantum-chemical CCSD(T) level of accuracy and produced converged MD simulations with fully quantized electrons and nuclei (Chmiela et al., 2018).
The parameterization of force fields and semiempirical quantum mechanics have also been performed integrating ML and evolutionary algorithms , which were successfully applied in MD . Constructing coarse-grained molecular models has been a common approach to extend the time/length-scales accessible to large or complex systems . These models have allowed establishing suitable interaction potentials for properties of highresolution models or experimental data. Wang et al. (2019) have reformulated coarse-graining as a supervised machine learning problem, by using statistical learning theory for decoupling the coarse-graining error, and cross-validation for choosing and comparing the performance of distinct models. For that purpose, the authors developed a DL model, that learned coarse-grained free-energy functions and was trained by a force-matching strategy (see Figure 7).
The proposed framework automatically learned multiple terms necessary for accurate coarse-grained force fields, i.e., was able to keep relevant invariances and incorporate physics knowledge, avoiding the sampling of unphysical structures.
The class of coarse-grained directed neural networks can thus be trained with the force-matching principle and can encode all physically relevant invariances and constraints, including invariance of (i) the free-energy and mean force with respect to translation of the molecule, (ii) the free-energy and variance of the mean force associated to molecular rotation, and considering (iii) the mean force being a conservative force field generated by the free-energy, and (iv) a prior energy for preventing deviations of the simulations with coarse-grained neural networks into unphysical state space regions, i.e., states displaying overstretched bonds or clashing atoms, which are captured out of the training data.
The proposed strategy also outperformed classical coarsegraining approaches, which generally failed to capture relevant features of the free-energy surface, providing the all-atom explicit-solvent free-energy surfaces estimated with models including just a few coarse-grained beads, in the absence of solvent .
The integration of ML in MD simulations have also been useful for understanding the rate and yield of chemical reactions and providing key mechanistic details (Christensen et al., 2019;Häse et al., 2019). For instance, an unsupervised ML analysis FIGURE 5 | (A) Illustrative summary of the mappings proposed by Brockherde et al. (2017). E[v] is a conventional electronic structure calculation, i.e., Kohn-Sham density functional theory (KS-DFT) and is represented by the bottom vector. The ground-state energy is determined by solving KS equations given the external potential, v. E[n] corresponds to the total energy density functional. The Hohenberg-Kohn map n[v] (red vector) from external potential to its ground state density is also presented. (B) Top: graphical representation of the dependency of the energy error on the number of training points (M), for ML-OF and ML-HK, considering different basis sets for the one-dimensional problem. Bottom: errors in the Perdew-Burke-Ernzerhof (PBE) energies and the ML maps as a function of interatomic spacing, R, for H 2 with M = 7. (C) Schematic illustration of the strategy for obtaining predictions based on the proposed machine learning Hohenberg-Kohn (ML-HK) map. Molecular geometry is represented by Gaussians, several independent Kernel ridge regression models allows predicting each basis coefficient of the density. The performance of data-driven (ML) and common physical basis representations for the electron density is assessed. tool based on Bayesian neural networks (BNNs) was proposed by Häse et al. (2019) to extract relevant information from ab initio MD simulation of chemical reactions (Häse et al., 2019). BNNs have been optimized to predict a specific outcome of an ab initio MD simulation corresponding to the dissociation time of the unmethylated and tetramethylated 1,2-dioxetane molecules, from the initial nuclear geometry and velocities. Predictions based on BNNs showed that an earlier dissociation was related to the planarization of the two formaldehyde moieties and also to the symmetric shortening of the C-O bonds, respecting the octet rule, i.e., the relation between bond order and bond length and orbital hybridization (Häse et al., 2019). Rupp et al. (2012) have developed a ML algorithm based on non-linear statistical regression to predict the atomization energies of organic molecules. The proposed model employed a subset of seven thousand elements of the database, and a library of more than 100 stable and synthetically-tractable organic compounds. The target data used to train the model included atomization energies of the compounds calculated using the PBE0 hybrid functional. Cartesian coordinated and nuclear charge were used as descriptors in a "Coulomb" matrix representation. A mean-absolute error accuracy of 14.9 kcal/mol was achieved using a small fraction of the compounds for the training set. Similar accuracy, ca. 15.3 kcal/mol, was obtained considering an external validation set of 6,000 compounds showing the potential transferability of the model within in-class compounds. It was notable to outline QM-calculated energies, with a mean-absolute error of ca. 15 kcal/mol, without using the Schrodinger Equation in the ML algorithm. It was also suggested that the DLNs-based model should outperform the traditional ML-approach (Goh et al., 2017).
More recently, an alternative approach based ML algorithms for supplementing existing QM algorithms was proposed . A -learning approach, involving a ML correction term was developed. Such correction was used in DFT calculated properties for predicting the corresponding quantity at the G4MP2 level of theory. This combined QM/ML approach gathers approximate but fast legacy QM approximations and big-data based QM estimates, trained on results across chemical space, despite being applied using only traditional ML algorithms . Gómez-Bombarelli et al. (2018) have applied DL for generating and optimizing functional compounds, such as druglike molecules. The proposed model allowed converting discrete representations of molecules from and into a multidimensional continuous representation, and generating new molecules for exploration and optimization.
A DLN was trained on a a large set of existing chemical structures to build an encoder, which converts the discrete representation of a molecule into a continuous vector, a decoder, that transforms the continuous vector into discrete molecular representations (e.g., SMILES string), and a predictor, FIGURE 7 | (I) Machine-learned coarse-graining of dynamics in (a) a two-dimensional potential, showing the (b) exact free-energy along x, comparison of (c) the instantaneous forces and the learned mean forces using feature regression and coarse-grained neural network models with the exact forces, and (d) the potential-of-mean-force along x, predicted by feature regression, and coarse-grained neural network models with the exact free energy. (II) Free-energy profiles and representative structures of alanine dipeptide simulated using all-atom and machine-learned coarse-grained models: (a) free-energy reference as a function of the dihedral angles, obtained from the histograms of all-atom simulations, (b) standard coarse-grained model using a sum of splines of individual internal coordinates, (c) regularized coarse-grained neural network models, (d) unregularized networks, (e) representative structures extracted from the free-energy minima, from atomistic simulation (ball-and-stick representation) and regularized coarse-grained neural network simulation (licorice representation). (III) Free-energy landscape of Chignolin for the different models, obtained from the (a) all-atom simulation, as a function of the first two TICA coordinates, (b) spline model, as a function of the same two coordinates used in the all-atom model, (c) coarse-grained neural network model, as a function of the same two coordinates. (d) Comparison of the one-dimensional free-energy profile as a function of the first TICA coordinate, reflecting the folding/unfolding transition, for the all-atom (blue), spline (green), and coarse-grained neural network models (red). (e) Representative Chignolin conformations in the three minima from (a-c) all-atom simulation and (a ′ -c ′ ) coarse-grained neural network model. Reprinted with permission from Wang et al. (2019). which estimates chemical properties from the latent continuous vector representation of the molecule. These representations allowed generating new chemical structures automatically by employing simple operations in the latent space (e.g., decoding random vectors, perturbing defined chemical structures, and interpolating between molecules), and applying gradient-based optimization for a oriented-search of functional molecules (Gómez-Bombarelli et al., 2018).
DLNs have also been applied for exploring the molecular conformational space of proteins. Some authors (Degiacomi, 2019) have demonstrated that generative neural networks trained on protein structures, extracted from molecular simulation, can be employed to create new conformations complementing pre-existing ones. The model was trained and tested in a protein-protein docking scenario to account for specific motions occurring upon binding.
The fewer examples of DLNs applications in quantum chemistry suggest that it is still in an earlier stage of development compared to other approaches including computational structural biology and computer-aided drug design.

Planning and Predicting Reactions and Routes
Some practical questions in organic chemistry have been addressed by ML approaches, including the identification of the most suitable synthesis method for a specific compound and the optimal conditions (reactants, solvent, catalyst, temperature, and among others) for ensuring region/chemo/stereo selectivity and obtaining the highest yields, estimating the precise rate, yield and time for the reaction, predicting major/minor product, and also evaluating similarity between reactions (Wei et al., 2016;Ahneman et al., 2018).
Making predictions in reactive chemical systems can also resort to DL. Segler and Waller (2017) and Segler et al. (2018) have predicted reaction rules considering fundamental substructures of reactants and products, allowing to return a product, given a reactant as input, and vice versa. In simple terms, a reaction rule is a pattern guiding the interaction process for a set of reactants and suggesting potential chemical products. As the knowledge available in often inaccurate, such rules are often ambiguous or even incomplete (Kishimoto et al., 2018). However, there are some successful examples, such as the recent outcomes of Chematica. Grzybowski et al. (2018) have assembled the relevant transformations that connect chemical species into a large network. The latter have codified and organized the known pathways through chemical space and displays nodes of molecules, elements and chemical reactions, collected by linking reactants to products on the basis of core reactions.
The Chematica platform comprises network theory, highperformance computing, artificial intelligence, and expert chemical knowledge to accelerate the design of synthetic pathways leading to new targets. However, the experimental verification of the respective predictions was carried out recently (Grzybowski et al., 2018). The authors have described the results of a systematic approach in which synthetic pathways leading to eight targets with distinct structures and of medicinal relevance were designed without human supervision and experimentally validated. There are other prominent products such as ChemPlanner, and Synthia created from databases of rules for chemical transformations. Both platforms incorporate ML algorithms and allows navigating through chemical space using those rules and suggesting to the user possible ways to synthesize a target molecule. Synthia also employs MD, quantum mechanics, and electronic properties to infer on the viability of a transformation and on the stability of an intermediate along a synthesis route (Klucznik et al., 2018).
Reaction prediction and retrosynthesis are the mainstays of organic chemistry. Retrosynthesis has been used for planning synthesis of small organic molecules, in which target molecules are recursively converted into progressively simpler precursors (Segler and Waller, 2017). However, the results obtained from the in silico version of this process are not, in general, adequate. Rulebased procedures have been extensively employed for solving, computationally, both reaction prediction and retrosynthesis. However, reactivity conflicts are often generated, since reaction rules tend to ignore the molecular context. It is often difficult to predict how a compound would behave in practice, unless an experiment is carried out (Granda et al., 2018). Evaluating a candidate sequence of reaction steps means that the synthesis of a given compound is also difficult. In chemical synthesis planning, Szymkuć et al. (2016) have discussed these issues. Segler and Waller have reported (Segler et al., 2018) that the prioritization of the most suitable conversion rules, as well as the approach to conflicting or complexity raising issues can be achieved by learning with DLNs. The authors have trained their model on ca. three million reactions, exhibiting accuracies of 97 and 95% for reaction prediction and retrosynthesis, respectively, on a validation set of ca. one million reactions. Following this procedure, the same authors have applied Monte Carlo tree search and symbolic artificial intelligence to find retrosynthetic routes. DLNs were trained on the whole set of published organic reactions (Segler et al., 2018). Coley et al. (2017Coley et al. ( , 2018b have performed DL with features based on the alterations of reactants and have determined scores for putative products. The product was modeled as a true target molecule (product) if it was generated by a reaction covered by the patent literature, and as a false product otherwise. More recently Coley et al. (2018b) have put forward a new definition addressing the synthetic complexity in order to compare with the expected number of reaction steps required for producing target molecules, with known compounds as reasonable starting materials. Specifically, a neural network model was trained on 12 million reactions from the Reaxys database, imposing a pairwise inequality constraint and showing that the products of published chemical reaction are, on average, more synthetically complex than their corresponding reactants.
A graph-link-prediction-based procedure was formulated by Savage et al. (2017) to predict candidate molecules (reactants), given a target molecule (product) as input and to discover adequate synthesis routes for producing the targets. This was employed over the Network of Organic Chemistry constructed from eight million chemical reactions described in the US patent literature in the 1976-2013 period (Savage et al., 2017). The proposed evaluation demonstrated that Factorization Machines, trained with chemistry-specific information, outperforms similarity-based methods of chemical structures. In these approaches, a fingerprint is built from a graphical representation of the molecule, containing the respective structural information and chemical features. The latter can be selected using different approaches (Morgan, 1965;Rogers and Hahn, 2010). Some neural graph fingerprints have displayed significant predictive performance (Duvenaud et al., 2015). The detection of molecular active substructures (e.g., a moiety impacting on a disease and a moiety that confers structural stability) can also be performed with ML (Duvenaud et al., 2015).
Researchers have also designed a chemical-handling robot for screening and predicting chemical reactivity using ML. The authors have found four novel reactions, demonstrating the respective potential in discovering reactions. Chemical reactions related to many different pathways can lead to a desired molecule. To find the best pathways, discovering new chemical reactivity is crucial to make the processes that produce chemicals, pharmaceuticals and materials more sustainable, environmentally-friendly and efficient. However, discovering new reactions is usually an unpredictable and time-consuming process that's constrained by a top-down approach involving expert knowledge to target a particular molecule.
Other researchers (Granda et al., 2018) have created an organic synthesis robotic ML system able to explore the reactivity several reagents from the bottom-up with no specific target. By performing ca. 10% of 969 possible reactions from a set of 18 reagents, the proposed system allowed predicting the reactivity of the remaining 90% of reactions with an accuracy of 86%. The database was continuously updated by performing multiple experiments based on the reactivity data collected. This allowed discovering new reactions that were inspected to isolate and characterize the new compounds (Granda et al., 2018).

Supporting Analytical Chemistry and Catalysis
Analytical chemistry is possibly the area corresponding to the longest history, but also one that mostly displays embryonic applications of ML. A large number of statistical analyses and ML expert systems have been implemented in analytical chemistry for a long time (e.g., comparing and classifying mass spectra, NMR, or IR through assessments on available compounds) (Lipkowitz and Boyd, 1995;Mayer and Baeumner, 2019). Until recently, ML approaches were mainly employed to explain chemical reactions and to provide valuable predictive insights. Currently, it is possible to predict unexpected reactive outcomes, or relevant mechanistic insights for catalytic processes. A survey of some of these contributions can be found in Durand and Fey (2019).
Other groups (Ghosh et al., 2019) have proposed DL methods for predicting molecular excitation spectra. Considering the electronic density of the states of 132 k organic compounds, the authors have built three different neural network architectures: a multilayer perceptron (MLP), a convolutional neural network (CNN), and a DLNs. The coordinates and charge of the atoms in each molecule were used as inputs for the neural networks. The DLNs reached the best performance with a root-mean-square error (RMSE) of 0.19 eV, while MLP and CNN were able to learn spectra with a RMSE of 0.3 and 0.23 eV, respectively. Both CNN and DLNs allowed identifying subtle variations in the spectral shape. The structures of 10 k organic molecules previously unseen were scanned and the instant predictions on spectra were obtained to identify molecules for further applications (Ghosh et al., 2019).
A new computational approach, denoted as quantitative profile-profile relationship (QPPR) modeling, and based on ML techniques, has been proposed for predicting the predischarge chemical profiles of ammunition components from the components of the respective post-discharge gunshot residue (Gallidabino et al., 2019). The predicted profiles can be compared with other measured profiles to perform evidential associations in forensic investigations. Specifically, the approach was optimized and assessed for the prediction of GC-MS profiles of smokeless powders (SLPs) obtained from organic gunshot residues, considering nine ammunition types. A high degree of similarity between predicted and experimentally measured profiles was found, after applying 14 ML techniques, with a median correlation of 0.982 (Gallidabino et al., 2019). Receiver operating characteristic (ROC) analysis was employed to assess association performances, and allowed comparing predictedpredicted and predicted-measured profiles, producing areas under the curve (AUCs) of 0.976 and 0.824, respectively, in extrapolation mode. On the other hand, AUCs of 0.962 and 0.894 were obtained in the interpolation mode. These results were approximated to the values obtained from the comparison of the measured SLP profiles (AUC = 0.998), demonstrating excellent potential to correctly associate evidence in a number of different forensic situations (Gallidabino et al., 2019). The advantages of this approach are numerous and may be extended to other fields in analytical sciences that routinely experience mutable chemical signatures, including the analysis of explosive devices, toxicological samples and environmental pollutants (Gallidabino et al., 2019).
The integration of ML-based algorithms in a chemosensor has also pointed out the future of ML and the artificial internet of things applicability, i.e., optimized sensors, linked to a central data analysis unit via wireless (Mayer and Baeumner, 2019).
Additionally, researchers have used ML to develop tools for predicting catalytic components and dynamics. For instance, the identification and prediction of ligands for metal-catalyzed coupling reaction have been conducted for designing a synthetic economic and ecological route, with the potential to be expanded into a system of pharmaceutical interest (Durand and Fey, 2019). Durand and Fey have recently summarized calculations of several ligand descriptors, focusing on homogeneous organometallic catalysis. Different approaches for calculating steric and electronic parameters were also reviewed and assessed, and a set of descriptors for a wide range of ligands (e.g., 30 monodentate phosphorus (III) donor ligands, 23 bidentate P,P-donor ligands, and 30 carbenes) were collected.
Different case studies covering the application of these descriptors, including maps and models and DFT calculations, have been discussed, demonstrating the usefulness of descriptororiented studies of catalysis for guiding experiments and successfully evaluate and compare the proposed models (Durand and Fey, 2019).
Li and Eastgate (2019) have designed a ML-based tool for acting on transition metal-catalyzed carbon-nitrogen coupling reactions encompassing phosphine ligands, which are often involved in pharmaceutical syntheses. The data set of the system was composed of literature documents reporting coupling reactions with phosphine ligands. The input variables were the molecular features of ligand electrophiles and nucleophiles, and the phosphine ligands were de output obtained in successful reactions. The tools used substrate fingerprints, to build a multiclass predictive model and identify the ligands prone to function in a Pd-catalyzed C-N coupling reaction. The resulting probabilities were associated to the corresponding ligand (cPMIs) to determine a probability-weighted predicted holistic PMI for the transformation, considering the synthesis of the ligand. This novel ML approach were developed for estimating the probability of success for ligands, given specified electrophile and nucleophile combinations, illustrated in the a Pd-catalyzed C-N coupling context. The neural network allowed thus improving the predictive performance of the top-N accuracy over other ML approaches. Further application of this tool will foster the development of frameworks based on criteria-decision analytics, optimizing the design of manufacturing processes.
Designing catalysts using computational approaches is also a major challenge in chemistry. Conventional approaches have been restricted to calculate properties for a complex and large number of potential catalysts. More recently, innovative approaches for inverse design have emerged, for finding the desired property and optimizing the respective chemical structure. The chemical space has been explored by combining gradient-based optimization, alchemical transformations, and ML. These efforts have been duly reviewed in the context of inverse design and relevance to developing catalytic technologies (Freeze et al., 2019). These approaches have offered new opportunities for identifying catalysts using efficient methods that circumvent the need for high-throughput screening and reduce the array of compounds and materials displaying the target properties and can be experimentally validated. For instance, inverse design can be employed for modulating catalytic activity via alterations in the first and second coordination spheres of the catalyst binding site (e.g., functionality of catalytic cofactors in enzymes).
One possible approach to inverse design is to use the synthetic accessibility score, commonly used for drug molecules, in the scoring functions of inverse design for ensuring synthetic feasibility. For that purpose, empirical parameters can be used to describe molecules without the cost of using 3D coordinates for an entire structure and without using a model to describe the complex interactions from geometries.
The major progress on inverse design relies on optimization algorithms, which govern the process for exploring a specific space, improving identification rates of parameters that allows optimizing the value of the scoring function. For example, the Classical Optimal Control Optimization algorithm, used for global energy minimization, is based on the diffeomorphic modulation under the observable-response-preserving homotopy algorithm, and lead the classical dynamics of a probe particle, driven by an external field for reaching the optimal value of a multidimensional function, by adjusting iteratively field control parameters over the gradient of the scoring function related to the controls. However, the respective use for scoring functions in inverse design applications still remain a challenge (Freeze et al., 2019). Scoring functions allow correlating molecular descriptors to catalytic properties for finding catalysts via gradient-based optimization. In a simple example, similar molecules often display distinct catalytic activity due to subtle effects that must be detected by scoring functions. Such effects may be determined by combining experimentation to build adequate training sets of systems with different values of selected properties for determining feature sets able to detect such properties. ML can also be used to evaluate performance scores for GA-based methods.
The application of autoencoders have allowed transforming SMILES representations of compounds into a continuous latent space in order to optimize chemical properties, including synthetic accessibility score and Quantitative Estimation of Drug Likeness. Additionally, by resorting to gradient-based methods the latent space can be intersected to predict new candidate structures for being synthesized and tested.
The integration of inverse design, gradient-based optimization and ML is a very promising strategy to shorten the long path toward catalyst discovery (Freeze et al., 2019). Also, other related methods that have been implemented to scrutinize the chemical space for drug development can be applied for catalyst discovery, as described in Freeze et al. (2019).

CONCLUDING REMARKS
This review has sought to provide a sample of ML approaches that support the major research trends in Chemistry, especially in computational chemistry, focusing on DLNs. Such an approaches have offered the possibility of solving chemical problems that cannot be described and explained via conventional methods. In the last few years, the application of ML to the optimization and prediction of molecular properties has become very popular, since more researchers are trained and acquired technical skills to develop and use such methods. ML applications are areadependent and follow, in fact, a more or less obvious pattern. For instance, medicinal chemistry excels in structure-activity relationships. In other words, each sub-field is progressing essentially in activities that belong to its core subjects. It seems that these fields are evolving naturally, and we cannot identify significant disruptive trends.
Despite the historical route of ML methods involving the implementation of clustering or dimensionality reduction approaches, to provide a simple, low dimensional, or coarsegrained representations of structural and dynamical patterns of complex chemical systems, the interplay between innovative ML-driven predictions and molecular simulations can be combined to make time-consuming electronic calculations feasible, obtain accurate interatomic potentials on complex systems, and provide a rational design of molecules and materials. However, the convergence between different ML algorithms is a major challenge to achieve a definite progress in the chemistry fields.
Unsupervised learning may also contribute to elucidate the operating aspects of supervised algorithms, while supervised approaches may contribute to the formulation of objective metrics to evaluate the performance of unsupervised approaches.
In Chemistry DL is still at an incipient stage, particularly in computational chemistry, although the pace of contributions has been increasing very recently. One of the major challenges is the disparity, quality and interpretability of the generated outcomes. Paired with the sophistication and ability of GPU-accelerated computing for training DLNs and the massive growth of chemical information used for training DLNs, it is anticipated that DL algorithms will be an invaluable engine for computational chemistry. DL uses a hierarchical cascade of non-linear functions allowing to learn representations and capture the required features from raw chemical data, necessary for predicting target physicochemical properties.
Considering the recent effort on the topic, DL models have been implemented in various Chemistry sub-fields, including quantum-chemistry, compound and materials design, with superior performances to conventional ML algorithms. There is still tremendous room for improved model accuracy and interpretability. While industrial sectors will continue driving many advances, academia will continue playing a critical role in supplying innovative technical and practical contributions, as well as in fostering cross-disciplinary cooperation.

AUTHOR CONTRIBUTIONS
TC performed the bibliometrics analysis, collected the relevant studies in the context of the review, structured, and wrote the paper. AP directed the work, contributed to the interpretation of the data, and to the structure of the review. Both authors reviewed the manuscript.

FUNDING
The Coimbra Chemistry Centre (CQC) was supported by the Portuguese Agency for Scientific Research, Fundação para a Ciência e a Tecnologia (FCT), through Project UID/QUI/00313/2019.