Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

Gradient domain machine learning (GDML) is based on kernel models that use derivatives of an unknown function to estimate both the function and its gradients [1]. It is particularly useful for applications that require models of both black-box functions and their gradients, such as, for example, the construction of potential energy surfaces (PES) and force fields (FF) for molecular dynamics simulations. In this work we show that GDML models can be significantly improved by increasing the complexity of model kernels. We combine an algorithm previously developed for enhancing pattern recognition performance of Gaussian process models [2] with the GDML approach to build models that produce more accurate results with less training data [3] than the corresponding GDML models. To illustrate this, we build global PES and FFs for ethanol, uracil, malonaldehyde and aspirin. For aspirin, the model with composite kernels at 1000 molecular geometries produces global 57-dimensional PES and FF with the mean absolute error 0.177 kcal/mol and 0.457 kcal/mol Å^-1. [1] Chmiela S, et al., Sci. Adv., 3(5), e1603015 (2017) [2] Duvenaud D, et al., Proc. of the 30th Int. Conf. on Mach. Learn., PMLR 28(3), 1166-1174 (2013) [3] Asnaashari K and Krems R V, Mach. Learn.: Sci. Technol. 3 015005 (2022)