Support vector machine regression (LS-SVM)-an alternative to artificial neural networks (ANNs) for the analysis of quantum chemistry data?

A multilayer feed-forward artificial neural network (MLP-ANN) with a single, hidden layer that contains a finite number of neurons can be regarded as a universal non-linear approximator. Today, the ANN method and linear regression (MLR) model are widely used for quantum chemistry (QC) data analysis (e. g., thermochemistry) to improve their accuracy (e. g., Gaussian G2-G4, B3LYP/B3-LYP, X1, or W1 theoretical methods). In this study, an alternative approach based on support vector machines (SVMs) is used, the least squares support vector machine (LS-SVM) regression. It has been applied to ab initio (first principle) and density functional theory (DFT) quantum chemistry data. So, QC + SVM methodology is an alternative to QC + ANN one. The task of the study was to estimate the Moller-Plesset (MPn) or DFT (B3LYP, BLYP, BMK) energies calculated with large basis sets (e. g., 6-311G(3df, 3pd)) using smaller ones (6-311G, 6-311G*, 6-311G**) plus molecular descriptors. A molecular set (BRM-208) containing a total of 208 organic molecules was constructed and used for the LS-SVM training, cross-validation, and testing. MP2, MP3, MP4(DQ), MP4(SDQ), and MP4/MP4(SDTQ) ab initio methods were tested. Hartree-Fock (HF/SCF) results were also reported for comparison. Furthermore, constitutional (CD: total number of atoms and mole fractions of different atoms) and quantum-chemical (QD: HOMO-LUMO gap, dipole moment, average polarizability, and quadrupole moment) molecular descriptors were used for the building of the LS-SVM calibration model. Prediction accuracies (MADs) of 1.62 perpendicular to 0.51 and 0.85 +/- 0.24 kcal mol(-1) (1 kcal mol(-1) = 4.184 kJ mol(-1)) were reached for SVM-based approximations of ab initio and DFT energies, respectively. The LS-SVM model was more accurate than the MLR model. A comparison with the artificial neural network approach shows that the accuracy of the LS-SVM method is similar to the accuracy of ANN. The extrapolation and interpolation results show that LS-SVM is superior by almost an order of magnitude over the ANN method in terms of the stability, generality, and robustness of the final model. The LS-SVM model needs a much smaller numbers of samples (a much smaller sample set) to make accurate prediction results. Potential energy surface (PES) approximations for molecular dynamics (MD) studies are discussed as a promising application for the LS-SVM calibration approach.