Machine learning fitted to flexible molecules predicts oxidation potentials and hydration energies

The work

Technical · from the record

The authors rewrite Kernel Ridge Regression over Boltzmann ensembles of molecular conformers in terms of Structured Orthogonal Random Features, giving a layered model (Multilevel SORF) with trigonometric activations and layers for ensembles, conformers, atoms and localized orbitals. Conformers were generated with the MMFF94 forcefield, encoded with several existing molecular representations, and models were fitted to two experimental datasets: oxidation potentials in acetonitrile (largest training set 474 molecules) and FreeSolv hydration energies (largest training set 514 molecules). Mean absolute error decreased with training set size for every representation tested, and for oxidation potentials the combinations with aSLATM, SLATM, FCHL19 and cMBDF gave errors similar, within statistical error, to the 0.2 eV reported earlier for SLATM with KRR. Replacing each ensemble with only the lowest-MMFF94-energy conformer changed the errors by an amount comparable to the statistical error. The work also introduces self-consistent versions of the Huber and LogCosh loss functions used during hyperparameter optimization.

How AI was used

Supervised regression models were fitted in this study to predict two experimental molecular properties. For each molecule, conformers were generated with the Morfeus implementation of a conformer-generation algorithm using the MMFF94 forcefield in RDKit at 298.15 K, with low-weight conformers cut off at rho_cut = 0.05; Boltzmann weights were retained as conformer importance weights. Each conformer was encoded with one of several molecular representations (Coulomb Matrix, SLATM, aSLATM, FCHL19, cMBDF, SOAP, and FJK, the latter from Huckel calculations in PySCF with a 6-311G basis, Boys localized orbitals and SMD solvation). These representations were fed through stacks of SORF-based layers (feature, sum, switch, weighted-sum, normalization and mixed-extensive layers) whose dot products reproduce the corresponding kernel functions, with Nf = 32768 features at each feature layer and three Hadamard transforms. Regression coefficients were obtained from a singular value decomposition of the feature matrix. Hyperparameters (kernel widths, the regularizer lambda, and optional quantity shifts) were tuned by minimizing a self-consistent squared LogCosh loss on leave-one-out cross-validation errors, using L-BFGS and SLSQP from SciPy and the BOSS Bayesian optimization package for lambda. Trained models were then run over the held-out test molecules, and the whole workflow was rerun using only the lowest-energy conformer of each molecule as a comparison.