Machine learning potential energy surfaces for predictive simulations

Computer simulations have augmented the traditional pillars of science, namely experiment and theory, by introducing a third dimension to scientific discovery. In molecular science, simulations offer a unique lens through which the dynamic behaviour of molecules and materials can be explored at the atomic scale and the in silico examination of molecular processes has emerged as a crucial component of research, contributing to a range of discoveries and advancements. Unfortunately, the Schrödinger equation, which contains all the information necessary to describe chemical processes, cannot be solved exactly except for the smallest systems. Due to this limitation, potential energy surfaces (PESs) are employed to bypass the need for directly solving the Schrödinger equation. On the one hand, the potential energy of a molecular system can be modelled using force fields, which approximate the interactions using physically grounded functions. For example, atoms are modelled as point charges and bonds are harmonic springs. This makes force fields efficient to evaluate but limits their accuracy. On the other hand, machine learning has revolutionised our ability to model molecular systems with unprecedented precision. Contrary to force fields, machine learning allows to learn the PES from ab initio data without relying on a predefined function form.
This thesis improves and develops machine learning-based PESs with the aim of enabling predictive simulations. First, local PESs are employed in second-order vibrational perturbation theory analyses, which allows quantitative agreement with experiment for various molecules. While the same analysis using ab initio techniques requires the calculation of computationally expensive Hessians, this is circumvented altogether in the presented approach. Then, the focus is shifted to achieving CCSD(T)-quality PESs for molecules with sizes that were unattainable so far. This is achieved by employing transfer learning to improve a given low-level PES to a higher level of theory using a small amount (25 to 100 structures) of high-level information. The predictiveness of the resulting PESs is assessed by computing tunneling splittings and comparing them to experiment. Since the efficiency of such machine-learned PESs lies in between ab initio approaches and traditional force fields, the use of compact, yet accurate neural networks for the representation of PESs is explored for gas-phase and condensed-phase systems. Finally, before the challenges of the presented approaches and future avenues are discussed, a novel approach for the accurate prediction of vibrational frequencies in monohydrates is introduced.