Machine learning models predict calculation outcomes with the transferability necessary for computational catalysis

Virtual high throughput screening (VHTS) and machine learning (ML) have greatly accelerated the design of single-site transition-metal catalysts. VHTS of catalysts, however, is often accompanied with high calculation failure rate and wasted computational resources due to the difficulty of simultaneously converging all mechanistically relevant reactive intermediates to expected geometries and electronic states. We demonstrate a dynamic classifier approach, i.e., a convolutional neural network that monitors geometry optimization on the fly, and exploit its good performance and transferability for catalyst design. We show that the dynamic classifier performs well on all reactive intermediates in the representative catalytic cycle of the radical rebound mechanism for methane-to-methanol despite being trained on only one reactive intermediate. The dynamic classifier also generalizes to chemically distinct intermediates and metal centers absent from the training data without loss of accuracy or model confidence. We rationalize this superior model transferability to the use of on-the-fly electronic structure and geometric information generated from density functional theory calculations and the convolutional layer in the dynamic classifier. Combined with model uncertainty quantification, the dynamic classifier saves more than half of the computational resources that would have been wasted on unsuccessful calculations for all reactive intermediates being considered.


Introduction.
Virtual high-throughput screening (VHTS) 1-8 powered by density functional theory (DFT) coupled with machine learning (ML) [9][10][11][12][13][14][15] has shown promise to accelerate the discovery of materials. This acceleration is necessary because exploring large spaces of candidate materials introduces combinatorial challenges. Exemplary of the challenges that arise from combinatorial explosion is single-site inorganic catalyst design, where metals, ligands, and substrates all must be considered. [16][17][18] To address this challenge, ML has been applied to predict thermodynamic quantities to rapidly screen this combinatorial design space in both homogeneous 5, 19-23 and heterogeneous catalyst [24][25][26][27][28][29][30] design. Combined with active learning [31][32][33] and global optimization algorithms [34][35][36] , catalysts with optimal catalytic properties can be quickly identified under a given mechanism. However, it is often difficult to experimentally characterize all mechanistically relevant intermediates due to their transient nature 37 and thus computational efforts towards reaction mechanism exploration are desired. [38][39] In this case, ML combined with automated VHTS workflows can accelerate the exploration of potential reactive intermediates and reaction pathways. [40][41][42][43][44][45] Many promising catalysts are comprised of mid-row transition metals, which give rise to favorable reactivity due to their unpaired electrons and superior tunability in response to changing coordination environment. [46][47][48][49][50][51][52][53] However, these exact same characteristics of transition metal catalysts often lead to failed geometry optimizations due to converging to unintended geometries or unexpected electronic states. [54][55] Because we require the knowledge of all relevant intermediates to compute the full thermodynamic landscape of a catalyst or to explore multiple possible reaction mechanisms, the VHTS of catalysts is usually accompanied by high overall failure rates and wasted computational resources.
Recently, ML models have been developed to predict the computational cost [56][57] or suggest the most inexpensive density functional that still will be of reasonable accuracy 58 for a calculation to optimize the use of finite computational resources. These approaches, however, do not overcome wasted computational time due to their assumption that the calculations will eventually succeed. On the other hand, one can directly predict the likelihood of success for a calculation to avoid failed calculations. In our previous work 54 , we built ML models to directly classify outcomes (i.e., success or failure) of transition metal complex geometry optimizations using the 2D molecular graph-based descriptors (i.e., revised-autocorrelations or RACs 59 ) as inputs. While achieving 88% accuracy on the set-aside test data, the RACs-based models failed to generalize to chemical spaces that are distinct to the training data due to its explicit dependence on chemical compositions as inputs.
To overcome this issue, we introduced a dynamic classifier 54,60 , which monitors a geometry optimization on the fly and terminates a calculation if it is predicted to be unproductive. This neural network dynamic classifier takes step-series inputs of both the geometric and electronic structure features (e.g., energy gradient and Mulliken bond orders) and predicts the likelihood of success during a geometry optimization ( Figure 1). Since this model uses incremental information gathered over the course of a DFT optimization, the dynamic classifier can generalize well across different chemical spaces. 54 This good transferability is particularly important in catalyst design, since we would like to only train a single model that works well for all reactive intermediates possibly involved in a reaction. A similar idea has also been recently adopted in predicting trajectories of molecular dynamics simulations [61][62] and the dynamic control of tokamak reactors [63][64] . The radical rebound mechanism for direct partial oxidation of methane to methanol. The cycle proceeds clockwise from the resting state (1) to the metal−oxo intermediate (2) formed by two-electron oxidation with N2O, followed by hydrogen atom transfer to form a metal-hydroxo intermediate (3), and rebound to form a methanol-bound intermediate (4). (top right) Success rate for geometry optimizations for each intermediate (blue) and cumulative success rate when a catalyst proceeds to each intermediate after success of the previous intermediate in the catalytic cycle (red). (bottom) Schematic of a multi-task dynamic classifier. Electronic structure and geometric features are collected from DFT geometry optimization and used as inputs to an ANN classifier with a convolutional layer followed by a fully connected layer. The model has multiple outputs that predicts calculation success with respect to geometry, ⟨S 2 ⟩ deviation, and metal spin deviation.
In this work, we exploit and demonstrate the general nature of the transferability of our dynamic classifier for catalyst design. We show that a dynamic classifier can perform equivalently well on all reactive intermediates in a representative reaction. Despite being trained on only one reactive intermediate in a reaction cycle, this dynamic classifier generalizes to unseen intermediates within that same cycle. In addition, this dynamic classifier makes accurate predictions on reactive intermediates with distinct chemistry that are absent in the training data.
We further incorporate uncertainty quantification when using dynamic classifier for job control, saving more than half of the computational resources that would have been wasted on failed calculations.

2.
Results and discussion.

Generalizing the dynamic classifier across a catalytic cycle
The design of selective and active C−H activation catalysts for direct methane-tomethanol conversion remains a grand challenge. [65][66] Here, we focus on the radical rebound mechanism on representative Mn and Fe catalysts with macrocyclic tetradentate ligands, which have shown promise for exhibiting favorable thermodynamics for partial methane oxidation. [67][68][69] The "whole cycle" (WC) data set consists of a number of intermediates bound to these catalysts ( Figure 1 and see Computational Details). 35 Starting from a resting state structure (1), a metaloxo intermediate (2) is formed via two-electron oxidation with a terminal oxidant (here, N2O).
The newly formed terminal oxo can undergo hydrogen atom transfer step where a hydrogen atom is abstracted from CH4 to form a metal-hydroxo intermediate (3). Lastly, CH3· recombines with the metal-hydroxo intermediate to form a methanol-bound intermediate (4). Thus, properties of both the resting state (1) and each of the three reactive intermediates (i.e., 2, 3, and 4) must be obtained to evaluate the full thermodynamic landscape of a catalyst (see Computational Details).
We focus here on only the reactive intermediates because we follow the convention of prior work 68 to evaluate (1) as a single point energy (i.e., without geometry optimization) on intermediate 2 with the oxo removed. Even if the success rate is high on each individual intermediate, the cumulative success rate can decay rapidly since multiple intermediates are necessary to obtain reaction energetics. We observe an overall success rate of only 33% for the whole catalytic cycle although all three intermediates have individual success rates ranging from 60% to 83% (Figure 1 and ESI Table S1).
We first train our dynamic classifier as a multi-task classification model for predicting three optimization outcomes, geometry, ⟨S 2 ⟩ deviation, and metal spin deviation, on all three reactive intermediates in the WC set (see Computational Details). The first property, good geometry, corresponds to whether a structure optimizes to the intended connectivity expected for the structure and is general even to closed shell systems such as organic molecules. The latter two properties, ⟨S 2 ⟩ deviation, and metal spin deviation, correspond to whether the structure has a large degree of spin contamination (i.e., ⟨S 2 ⟩ differs from its expected value) or if the spin does not reside on the metal. Importantly, a geometry can be good while the spin is not localized to the metal or ⟨S 2 ⟩ deviation is too large and vice versa. We focus on these three properties because they are the most common sources of failure or indicate low reliability of single-reference DFT results in VHTS.
The dynamic classifier systematically improves when the inputs consist of an increasing number of optimization steps ( Figure 2 and ESI Figure S1). The model performs equivalently well on all three intermediates (ESI Figure S1). For the first few steps of the geometry optimization, the relatively poor model accuracy (ca. 0.85) on the geometry classification task may result in false negative predictions that incorrectly terminate calculations that could be expected to converge successfully. To overcome this challenge, we previously introduced a classification-model-specific uncertainty quantification metric, the latent space entropy (LSE) 54 , to ensure high model confidence during prediction. Using the LSE as a guide for model uncertainty, we only act on model predictions if the LSE value is below a user-defined cutoff (here, 0.3). Using this requirement for model certainty, we achieve uniformly high model accuracy (i.e., > 0.95) for all optimization step numbers and intermediates for all three tasks ( Figure 2 and ESI Figure S2). As the dynamic classifier is provided more information about the optimization (i.e., with an increasing number of steps), model confidence grows and the data fraction that falls below the LSE cutoff increases (Figure 2 and ESI Figure S2). 54 We visualize the latent space (i.e., the outputs of the last hidden layer in a dynamic classifier) to understand why our dynamic classifier performs equivalently well on all three classification tasks simultaneously. We find that calculations corresponding to each failure mode cluster into distinct regions of the latent space ( Figure 3). The bad calculations reside in a distinct portion of latent space from those that correspond to good calculations. The relative orientation of each of the three types of clusters is also intuitive. There is a cluster of calculations with both high ⟨S 2 ⟩ deviation and metal spin deviation since these two failure modes both stem from the unexpected electronic structure and are typically concurrent (ESI Figure S3). Similarly, the boundary between calculations with good or bad geometry is the least well separated, consistent with this being the most challenging task among the three for our models to predict ( Figure 2).   The difference for all three tasks is shown separately: blue for geometry, red for ⟨S 2 ⟩ deviation, and green for metal spin deviation. A dashed line is shown for no difference.

Transferability of the dynamic classification model to out-of-distribution catalysts
We next tested the transferability of the dynamic classifier to intermediates and catalysts beyond the initial set, which is essential for its use in catalyst discovery applications. To do so, we curated three additionaly data sets that are chemically distinct from the WC set but are applicable to catalyst screening focused on direct methane-to-methanol conversion. The first set is the functionalized whole cycle (FWC) data set, where tetradentate macrocycles were functionalized with electron-withdrawing and electron-donating groups to introduce Hammett tuning effects on catalyst energetics ( Figure 5 and ESI Figure S6). In the FWC set, we functionalize all three reactive intermediates as in the WC set. In the Ru-oxo (RO) data set, we randomly sampled 300 metal-oxo species (metal = Mn, Fe) from the WC set and substituted the metal centers with Ru prior to re-optimization ( Figure 5). We use the RO set as an example of catalyst design with isovalent metals, motivated by the fact that Ru compounds are promising  We find that the dynamic classifier trained only on the metal-oxo intermediate in the WC set shows exceptional transferability to all three test sets despite differences in chemical composition. The accuracy for the most difficult prediction task (i.e., geometry classification) is comparable among all four data sets (i.e., WC, FWC, RO, and CS). Namely, we observe geometry classification performance accuracy to be within 5% for all four data sets, regardless of the number of steps used for dynamic classification ( Figure 6). In addition, the accuracy for the other two tasks, ⟨S 2 ⟩ deviation and metal spin deviation, is identical for the out-of-distribution FWC, RO, CS sets relative to the in-distribution WC set (ESI Figure S9). More interestingly, the model confidence (i.e., average LSE) of the dynamic classifier on the three out-of-distribution test sets is comparable relative to the in-distribution WC set-aside test set for all three classification tasks ( Figure 6 and ESI Figure S9). This observation suggests that our oxo-only dynamic classifier has similar confidence for making predictions on a compound that is chemically distinct from the training data due to good transferability across chemical compositions. We can further rationalize the transferability of our dynamic classifier from an analysis of the inputs to the model. These inputs are electronic structure and geometric features generated from DFT calculations on the fly, which make them agnostic to catalyst chemical composition.  Another reason for the good transferability is expected to be due to the fact that the dynamic classifier learns from trends in how electronic structure and geometric features evolve over the course of a geometry optimization rather than solely from the value of each feature at a single optimization step. This is inherent to the dynamic classifier model architecture, which involves a 1D convolution through the dimension of the optimization step.  After introducing an LSE cutoff of 0.3 as a UQ metric, we achieve uniformly high accuracy for all prediction tasks, i.e., > 0.90 for geometry and > 0.97 for both ⟨S 2 ⟩ and metal spin deviation, for all four data sets at all optimization steps (ESI Figure S10). This consistent performance is surprising because the dynamic classifier was only trained on the metal-oxo intermediates in the WC set. Overall, this high accuracy leads to a reduction of more than 1/2 of the computational time that would have been wasted due to failed calculations along with a negligible false negative rate (< 2%) for each of the four data sets (Figure 9). Thanks to the uniformly good performance across chemically distinct out-of-distribution test sets especially when paired with uncertainty quantification, the dynamic classifier can be expected to be transferable for other mechanistic studies and catalyst screening efforts. We anticipate the dynamic classifier to be readily transferable across catalysts with different metal, oxidation state, spin state, and ligand environment but would expect it to require additional training data when it is applied to catalysts with different coordination number and geometry type.

Conclusions
Computational catalysis requires the rapid screening of both catalyst compositions and intermediates. As these screening efforts are increasingly carried out with automated workflows, it becomes essential to anticipate and detect when calculations fail. To address this, we built a dynamic classifier to predict geometry optimization outcomes on the fly for reactive intermediates. We demonstrated our approach on the challenging reaction of direct methane-tomethanol conversion via a radical-rebound mechanism. We demonstrate that the dynamic classifier trained on all reactive intermediates exhibits good, balanced performance on each In addition to expected catalytic intermediates, a true test of transferability for computational catalysis requires that the model generalize to reactive intermediates with distinct chemistry. We evaluated model performance on catalysts that were functionalized with small functional groups frequently employed in Hammett tuning, those with substituted transition metals (i.e., Ru instead of Fe), and intermediates with distinct metal-coordinating atoms (here, metal-carbonyl). For all three sets, we demonstrated that the oxo-only dynamic classifier generalized well on these intermediates with distinct chemical composition. We rationalized the transferability of dynamic classifier in two ways. First, the dynamic classifier only uses electronic structure and geometric features generated during DFT geometry optimizations. Thus, the model can be expected to be transferable because DFT-based descriptors are likely to be more comparable than chemical-composition-based ones. Second, the dynamic classifier utilizes a convolution layer for step-series features generated during an optimization, making it focus on the trends of a trajectory rather than the value of each feature that we observed to differ more significantly between catalysts.
We incorporated an uncertainty quantification metric in the form of the latent space entropy to ensure that the oxo-only dynamic classifier made predictions only where it was most confident. Using this approach, we demonstrated a greater than 50% reduction in computational time to carry out catalyst screening by avoiding unsuccessful calculations along with negligible false negative predictions (< 2%) for all intermediates considered in this work. The uniformly high reduction rate with few false negatives highlights how this dynamic classifier model is ready for use to improve the robustness of automated workflows, perhaps even beyond that which can normally be achieved via manual intervention. This uncertainty-aware dynamic classifier represents a promising approach to both accelerate and improve the fidelity of VHTS, and we expect our approach to be general to an even wider range of materials and catalyst screening studies than the mid-row transition metal catalysts studied here.  Table S2). Open-shell calculations were also deemed failed calculations in the data set following established protocols 19,[54][55] : i) if the expectation value of the S 2 operator deviated from its expected value of S(S + 1) by >1 μB 2 or ii) the combined Mulliken spin density on the metal and oxygen differed from the spin multiplicity by >1 μB (ESI Table S3).

Data sets
We calculated the radical rebound mechanism 88 for methane-to-methanol conversion on mononuclear Mn and Fe catalysts with realistic tetradentate macrocycles constructed from known ligand fragments 35 (ESI Figure S11). For these catalysts, two resting state oxidation states, M(II) and M(III), in their corresponding spin states were considered (ESI Table S4). For this catalytic cycle, we optimize three catalytic intermediates: metal-oxo, metal-hydroxo, and the methanol-bound species. The initial geometries for metal−oxo species were constructed using molSimplify, 86 which uses OpenBabel 89-90 as a backend to interpret SMILES strings for constructed tetradentate macrocycles. All metal−hydroxo geometries were generated by adding an H atom to the optimized metal−oxo structure, and all methanol-bound intermediates were generated by adding a methyl group to the optimized metal−hydroxo structures using a custom script in molSimplify, as in prior work 68 (ESI Figure S12) Figure S13). We refer to this combined data set of metal−oxo, metal−hydroxo, and methanol-bound intermediates as the "whole cycle" (WC) data set (ESI Table S1).
Starting from the WC data set, we generated three data sets inspired by common strategies and potential difficulties (i.e., overoxidation) in catalyst discovery: 1) the functionalized whole cycle (FWC) data set, where tetradentate macrocycles were functionalized with electron withdrawing and electron donating groups to introduce Hammett tuning effects, 2) the Ru-oxo species (RO) data set, where the metal (Mn or Fe) of 300 randomly sampled metaloxo species in WC is substituted by Ru, and 3) the carbonyl species (CS) data set, where a carbonyl ligand replaces any converged oxo moiety in catalysts from the WC set (ESI Table S5).
For the FWC, RO, and CS data sets, we follow the same procedure for geometry optimizations used for the WC data set. Additionally, the metal−oxo, metal−hydroxo, and methanol-bound intermediates in the FWC set were computed following the same workflow as in WC set (ESI Figures S12-S13). Each Ru-oxo complex in RO was initialized by a direct substitution of Mn or

ML models and representations
As in prior work 54, 91 , we train convolutional neural network dynamic classifiers using step-series electronic structure and geometric information generated during DFT geometry optimizations to directly predict the final classification outcomes of geometry fitness, <S 2 >, and spin density deviation (ESI Table S6 and Figure S14). The 28 electronic structure descriptors were computed from the Mulliken charge, bond order matrix, and the energy gradient of a complex (ESI Table S6). These properties were focused on components directly involved in the first-coordination sphere along with any long-range behavior captured by singular value decomposition of these quantities (ESI Table S6). The 7 geometric descriptors include the bond lengths and angular deviation from an ideal octahedron as well as the distortion of individual ligand (ESI Table S1). We trained two sets of multi-task dynamic classifiers: one on all three intermediates (i.e., metal−oxo, metal−hydroxo, and methanol-bound) of the WC data set, and the other only on the metal−oxo species subset of the WC data set. For all ML models, we adopted same sets of hyperparameters used in our prior work 54 and a random 80/20 train/test split, with 20% of the training data (i.e., 16% overall) used as a validation set (ESI Table S7). All ML models were trained using Keras 92 with Tensorflow 93 as a backend, using the Adam optimizer up to 2,000 epochs, and dropout, batch normalization, and early stopping to avoid over-fitting. Page S3 Figure S3 Venn diagrams for calculation failure modes Page S4 Figure S4 Histogram for prediction differences for two sets of dynamic classifier Page S4 Figure S5 UMAP visualization for oxo-only dynamic classifiers Page S5 Figure S6 Functional groups considered in the FWC set Page S5 Figure S7 UMAP visualization of the RACs-155 features Page S6 Figure S8 Distributions electronic structure-and geometry-based features Page S7 Figure S9 Accuracy and average LSE for the ⟨S 2 ⟩ and metal spin deviation tasks Page S8 Figure S10 Performance for all four data sets with a LSE cutoff of 0. 3 Page S9 Table S2 Criteria used in this work to classify electronic structure Page S9 Figure S11 Strategies of constructing tetradentate macrocycles Page S10 Table S3 Oxidation and spin states considered in this work Page S11 Figure S12 Details of how intermediates were functionalized Page S11 Figure S13 Schematic for order of operations in generating new intermediates Page S12 Table S4 Job statistics in WC set Page S12 Table S5 Job statistics in FWC, RO, and CS set Page S12 Table S6 Electronic features for the dynamic classifier model Page S12 Figure S14 Architecture of the multi-task dynamic classifier Page S14 Table S7 Hyperparameters for the geometry classification dynamic classifier Page S15

References
Page S15 Table S1. Geometry cutoffs used in this work. Geometry check metrics are the same as our prior work on transition metal-oxo catalysts. 1 Strict cutoffs applied on a completed optimization are indicated alongside loose cutoffs applied during each resubmission in parentheses. These geometry checks include: coordination number, which must be 6; mean and max. deviation of connecting-atom-metal-connecting atom angles; max. deviation of any metal-ligand bond length; max. deviation of metal-ligand bond lengths for equatorial ligands; max. root mean square deviation (RMSD) of the ligand from its initial structure; and mean and max. deviation of an expected linear ligand from a 180° angle (which are only computed for linear ligands). These checks are applied for all intermediates that are geometry optimized.  Figure S1. Model accuracy versus the number of geometry optimization steps for the dynamic classifiers at each Nstep (i.e., 2, 5, 10, 15, 20, 30, and 40) evaluated on the set-aside test set of the WC set grouped by intermediate (blue for metal-oxo, green for metal-hydroxo, and orange for methanol-bound). The performance of each task: geometry (left), ⟨S 2 ⟩ deviation (middle), and metal spin deviation (right), is reported separately. The dynamic classifiers are trained on all three intermediates in the WC set. Note that the models make predictions on all set-aside test points at all steps (i.e., data fraction is always 1 and no LSE cutoff is used).  . Venn diagrams for fractions of failure modes (blue for geometry, red for ⟨S 2 ⟩ deviation, and green for metal spin deviation) of three intermediates: metal-oxo (left), metalhydroxo (middle), and methanol-bound (right) in the WC set. The distribution of failure modes is distinct for three intermediates and that the concurrence of ⟨S 2 ⟩ and metal spin deviation is high. Figure S4. Stacked histogram for absolute difference in predictions between the 40-step dynamic classifier trained on all three intermediates in the WC set and the 40-step dynamic classifier trained on only the metal-oxo intermediate in the WC set. All three predictions tasks are shown: blue for geometry, red for ⟨S 2 ⟩ deviation, and green for metal spin deviation. A zoomed-in view for the percentage of cases where the deviation between two dynamic classifiers is > 0.1 is shown as an inset. The output of each dynamic classifier is a probability from 0 (bad) to 1 (good). The difference is evaluated on the set-aside test set of the WC set with a bin size 0.025. Since histograms of three prediction tasks are stacked together, the total percentage should sum up to 300 across all bins.       Table S2. Electronic structure cutoffs used in this work. Metrics for classifying good and bad electronic structure metrics are the same as prior work on transition metal-oxo catalysts. 1 All geometry optimizations and single point energy calculations are required to pass these criteria to contribute to a reaction energy. For the metal-carbonyl species, only the spin density on the metal is considered due to the absence of the connecting oxo. electronic structure check cutoff <S 2 >-S(S+1) 1 μB 2 metal spin density + metal-oxo spin density -total spin density 1 μB Figure S11. Strategies of constructing tetradentate macrocycles used in our previous work 2 using 15 fragments (top) and 9 bridges (middle). All metal-coordinating atoms are highlighted by gray circles, and X is used to indicate the possibility of multiple metal-coordinating element types. Two fragment types in cis orientation are combined with up to three distinct bridges to construct a macrocycle. (bottom) An example macrocycle is shown that is constructed from two dimethylamine fragments and two pyrrole fragments joined via one phosphorus bridge, one methylene bridge, and two bridges with no atoms. This Figure is adapted from our prior work 2 .   Figure S12. Approach for generating a metal-hydroxo geometry from a geometry-optimized metal-oxo structure (left) and approach for generating a methanol bound geometry from a geometry optimized hydroxyl structure (right). For all metal-oxo geometries, the M-O bond was stretched to 1.84 Å, and the hydrogen atom was placed at an M-O-H angle of 120°, 1.00 Å from the oxygen atom. This was the initial geometry for all metal-hydroxo structures, which were subsequently optimized. For the methanol intermediate, the C-O-H angle was set to 106° in the initial geometry, and the C-O bond was set to 1.4 Å, based on the structure of a DFT-optimized methyl group of a methanol molecule. This Figure is adapted from the Supporting Information of our prior work 2 . Figure S13. Workflow for obtaining reaction energetics. The metal-oxo, metal-hydroxo, and metal-methanol intermediates were geometry optimized without constraints, and the resting state was simulated with a single point energy calculation. After each intermediate, the calculation is checked for fidelity. Only structures that pass all checks move on to the next intermediate. This Figure is adapted from the Supporting Information of our prior work 2 . Table S6. A complete list of the 26 electronic structure features 3 plus 2 additional spin densitybased features 4 for <DS 2 > and metal-spin deviation (for a total of 28 electronic structure descriptors) and the 7 geometry metric features 3 computed for the dynamic classifier model.  Figure S14. Architecture of the multi-task dynamic classifier composed of convolutional and fully-connected layer for prediction of calculation outcomes described in this work. The "?" in the schematic is the size of a batch, which can be flexible and were treated as a hyperparameter. Table S7. A summary of hyperparameters that are used in the dynamic classifiers for the geometry classification task trained on different numbers of steps of geometry optimization. 3 Note that L2-regularization is used in both the convolutional and the dense layer. 2  5  10  15  20  30  40  kernel size  2  3  4  4