Assessing the Accuracy of Machine Learning Thermodynamic Perturbation Theory: Density Functional Theory and Beyond

Abstract

Machine learning thermodynamic perturbation theory (MLPT) is a promising approach to compute finite temperature properties when the goal is to compare several different levels of ab initio theory and/or to apply highly expensive computational methods. Indeed, starting from a production molecular dynamics trajectory, this method can estimate properties at one or more target levels of theory from only a small number of additional fixed-geometry calculations, which are used to train a machine learning model. However, as MLPT is based on thermodynamic perturbation theory (TPT), inaccuracies might arise when the starting point trajectory samples a configurational space which has a small overlap with that of the target approximations of interest. By considering case studies of molecules adsorbed in zeolites and several different density functional theory approximations, in this work we assess the accuracy of MLPT for ensemble total energies and enthalpies of adsorption. It is shown that problematic cases can be detected even without knowing reference results and that even in these situations it is possible to recover target level results within chemical accuracy by applying a machine-learning-based Monte Carlo (MLMC) resampling. Finally, on the basis of the ideas developed in this work, we assess and confirm the accuracy of recently published MLPT-based enthalpies of adsorption at the random phase approximation level, whose high computational cost would completely hinder a direct molecular dynamics simulation.

Coupled cluster finite temperature simulations of periodic materials via machine learning

“…As discussed thoroughly in Ref. 32 for systems similar to the one considered here, the occurrence of this issue can be identified even if the exact target trajectory is unknown. Thermodynamic perturbation theory is based on the reweighting of the statistics sampled by the production trajectory to obtain the target level statistics (see Eq.…”

“…In practice, this effect can be measured by the I w index, as defined in Ref. 32. This index assumes the value of 0.5 in the optimal configuration overlap case and tends to 0 for decreasing overlaps.…”

“…This procedure, described in detail in Ref. 32, uses Metropolis MC 46 to resample the canonical ensemble at the CCSD(T) and MP2 levels of theory. At each MC step, configurational energies are computed with the production approximation (PBE+D2), and subsequently evaluated at the post-HF level level using the same ML model of MLPT.…”

“…The second fundamental ingredient is an approach that couples machine learning and thermodynamic perturbation theory (TPT) 28 , that will be denoted as MLPT [29][30][31][32] . Within this approach an ab initio molecular dynamics simulation is first performed at an affordable level of theory (semi-local DFT) and the statistical distribution is subsequently reweighted to obtain observables at a higher level of theory (e.g.…”

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

“…Alternatively, one could parametrize several potentials that are trained to model the 2′- O -transesterification reaction in different RNA environments and then perform sampling with each potential when exploring the mechanism in an RNA environment not included in the training. In the abovementioned discussion, the trained MLPs are used to perform the sampling; however, MLPs can also be utilized in another strategy whereby an uncorrected reference potential is sampled, and an MLP is trained to a small number of configurations to estimate the target potential energies required for thermodynamic perturbation. ,− …”