Comparison of the Performance of Machine Learning Models in Representing High-Dimensional Free Energy Surfaces and Generating Observables

Abstract

Free energy surfaces of chemical and physical systems are often generated using a popular class of enhanced sampling methods that target a set of collective variables (CVs) chosen to distinguish the characteristic features of these surfaces. While some of these approaches are typically limited to low (∼1− 3)-dimensional CV subspaces, methods such as driven adiabatic free-energy dynamics/temperature-accelerated molecular dynamics have been shown to be capable of generating free energy surfaces of quite high dimension by sampling the associated marginal probability distribution via full sweeps over the CV landscape. These approaches repeatedly visit conformational basins, producing a scattering of points within the basins on each visit. Consequently, they are particularly amenable to synergistic combination with regression machine learning methods for filling in the surfaces between the sampled points and for providing a compact and continuous (or semicontinuous) representation of the surfaces that can be easily stored and used for further computation of observable properties. Given the central role of machine learning techniques in this combined approach, it is timely to provide a detailed comparison of the performance of different machine learning strategies and models, including neural networks, kernel ridge regression, support vector machines, and weighted neighbor schemes, for their ability to learn these high-dimensional surfaces as a function of the amount of sampled training data and, once trained, to subsequently generate accurate ensemble averages corresponding to observable properties of the systems. In this article, we perform such a comparison on a set of oligopeptides, in both gas and aqueous phases, corresponding to CV spaces of 2−10 dimensions and assess their ability to provide a global representation of the free energy surfaces and to generate accurate ensemble averages.

Machine learning-accelerated quantum mechanics-based atomistic simulations for industrial applications

“…MD and MC simulations of complex atomistic systems can yield data that are challenging or time-consuming to interpret for humans, such as MD trajectories with frames (atomic coordinates) from billions of time steps. Strategy (3) uses ML techniques for the analysis of simulation data, for example for the automatic identification of crystal structures [65] or the extraction of free energy surfaces from enhanced-sampling MD simulations [66,67].…”

Small data materials design with machine learning: When the average model knows best

“…From this, it quickly becomes clear why ML approaches are considered data hungry, and why their rise coincides with that of big data. 4,12,15,16,28 For a sufficiently large dataset, the performance measures will not be influenced much by the details of how the data were split, assuming a random splitting. 4938 However, for very small datasets, this is not the case.…”

“…3,9,[19][20][21][22][23][24][25] In general, these achievements are rooted in the access to suitable large datasets, both theoretically and experimentally. [14][15][16][26][27][28] However, even though such big datasets (and access to them) are becoming common place, 3,27,[29][30][31][32] they do not represent the datasets most materials researchers work with on a day-to-day basis. Within general experimental material research projects, researchers generally produce no more than a hand full of data points (c.q.…”

“…For example, the computational cost of highquality quantum-mechanical material simulations rises steeply with the system size and model accuracy. 33,34 Given the success of ML in computational materials design within the context of large data sets, [28][29][30][31] there is a natural desire to also apply these methods on the small datasets produced in materials research and reap their benefits. The use of AI and ML in such cases is often aimed at the improvement of design of experiments for materials optimization, quite often in combination with robotic or other automation.…”

“…A behavior also observed by Cendagorta et al in their performance study of ML models for high-dimensional free energy surfaces. 28 In contrast, Menon et al presented a Hierarchical Machine Learning (HML) model, which provides useful predictions on the mechanical properties of elastomers or predict novel dispersants using only a handful of experiments. 46,47 Although these examples show that, even in the context of small datasets, the use of AI and ML can be successful for materials research, the quality of the obtained models is often defined in an ad hoc fashion and their dependence on the used dataset is not discussed.…”