Constant size descriptors for accurate machine learning models of molecular properties

Two different classes of molecular representations for use in machine learning of thermodynamic and electronic properties are studied. The representations are evaluated by monitoring the performance of linear and kernel ridge regression models on well-studied data sets of small organic molecules. One class of representations studied here counts the occurrence of bonding patterns in the molecule. These require only the connectivity of atoms in the molecule as may be obtained from a line diagram or a SMILES string. The second class utilizes the three-dimensional structure of the molecule. These include the Coulomb matrix and Bag of Bonds, which list the inter-atomic distances present in the molecule, and Encoded Bonds, which encode such lists into a feature vector whose length is independent of molecular size. Encoded Bonds' features introduced here have the advantage of leading to models that may be trained on smaller molecules and then used successfully on larger molecules. A wide range of feature sets are constructed by selecting, at each rank, either a graph or geometry-based feature. Here, rank refers to the number of atoms involved in the feature, e.g., atom counts are rank 1, while Encoded Bonds are rank 2. For atomization energies in the QM7 data set, the best graph-based feature set gives a mean absolute error of 3.4 kcal/mol. Inclusion of 3D geometry substantially enhances the performance, with Encoded Bonds giving 2.4 kcal/mol, when used alone, and 1.19 kcal/mol, when combined with graph features.