Machine learning for potential energy surfaces: An extensive database and assessment of methods.

On the basis of a new extensive database constructed for the purpose, we assess various Machine Learning (ML) algorithms to predict energies in the framework of potential energy surface (PES) construction and discuss black box character, robustness, and efficiency. The database for training ML algorithms in energy predictions based on the molecular structure contains SCF, RI-MP2, RI-MP2-F12, and CCSD(F12*)(T) data for around 10.5 × 106 configurations of 15 small molecules. The electronic energies as function of molecular structure are computed from both static and iteratively refined grids in the context of automized PES construction for anharmonic vibrational computations within the n-mode expansion. We explore the performance of a range of algorithms including Gaussian Process Regression (GPR), Kernel Ridge Regression, Support Vector Regression, and Neural Networks (NNs). We also explore methods related to GPR such as sparse Gaussian Process Regression, Gaussian process Markov Chains, and Sparse Gaussian Process Markov Chains. For NNs, we report some explorations of architecture, activation functions, and numerical settings. Different delta-learning strategies are considered, and the use of delta learning targeting CCSD(F12*)(T) predictions using, for example, RI-MP2 combined with machine learned CCSD(F12*)(T)-RI-MP2 differences is found to be an attractive option.

Employing general fit-bases for construction of potential energy surfaces with an adaptive density-guided approach.

We present an approach to treat sets of general fit-basis functions in a single uniform framework, where the functional form is supplied on input, i.e., the use of different functions does not require new code to be written. The fit-basis functions can be used to carry out linear fits to the grid of single points, which are generated with an adaptive density-guided approach (ADGA). A non-linear conjugate gradient method is used to optimize non-linear parameters if such are present in the fit-basis functions. This means that a set of fit-basis functions with the same inherent shape as the potential cuts can be requested and no other choices with regards to the fit-basis functions need to be taken. The general fit-basis framework is explored in relation to anharmonic potentials for model systems, diatomic molecules, water, and imidazole. The behaviour and performance of Morse and double-well fit-basis functions are compared to that of polynomial fit-basis functions for unsymmetrical single-minimum and symmetrical double-well potentials. Furthermore, calculations for water and imidazole were carried out using both normal coordinates and hybrid optimized and localized coordinates (HOLCs). Our results suggest that choosing a suitable set of fit-basis functions can improve the stability of the fitting routine and the overall efficiency of potential construction by lowering the number of single point calculations required for the ADGA. It is possible to reduce the number of terms in the potential by choosing the Morse and double-well fit-basis functions. These effects are substantial for normal coordinates but become even more pronounced if HOLCs are used.