Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics.

Barry K Carpenter,Stavros C Farantos,Gregory S Ezra,Stephen Wiggins,Zeb C Kramer

doi:10.1021/acs.jpcb.7b08707

Abstract

Classical Hamiltonian trajectories are initiated at random points in phase space on a fixed energy shell of a model two degrees of freedom potential, consisting of two interacting minima in an otherwise flat energy plane of infinite extent. Below the energy of the plane, the dynamics are demonstrably chaotic. However, most of the work in this paper involves trajectories at a fixed energy that is 1% above that of the plane, in which regime the dynamics exhibit behavior characteristic of chaotic scattering. The trajectories are analyzed without reference to the potential, as if they had been generated in a typical direct molecular dynamics simulation. The questions addressed are whether one can recover useful information about the structures controlling the dynamics in phase space from the trajectory data alone, and whether, despite the at least partially chaotic nature of the dynamics, one can make statistically meaningful predictions of trajectory outcomes from initial conditions. It is found that key unstable periodic orbits, which can be identified on the analytical potential, appear by simple classification of the trajectories, and that the specific roles of these periodic orbits in controlling the dynamics are also readily discerned from the trajectory data alone. Two different approaches to predicting trajectory outcomes from initial conditions are evaluated, and it is shown that the more successful of them has ∼90% success. The results are compared with those from a simple neural network, which has higher predictive success (97%) but requires the information obtained from the "by-hand" analysis to achieve that level. Finally, the dynamics, which occur partly on the very flat region of the potential, show characteristics of the much-studied phenomenon called "roaming." On this potential, it is found that roaming trajectories are effectively "failed" periodic orbits and that angular momentum can be identified as a key controlling factor, despite the fact that it is not a strictly conserved quantity. It is also noteworthy that roaming on this potential occurs in the absence of a "roaming saddle," which has previously been hypothesized to be a necessary feature for roaming to occur.

Highlights

There is burgeoning interest in the application of machine learning (ML) methods to problems in computational chemistry,[1−21] with special attention having been paid to the fitting of potential energy surfaces (PES) for chemical reactions.[22−29] So far, there has been less attention paid to using ML techniques for analysis of chemical trajectory data,[8,29] it appears that this could be a fruitful area of research
We show how phase-space structures controlling the dynamics can be inferred from simple classifications of the trajectories, and how these are related to unstable periodic orbits that can be identified on the analytical potential
When all data are plotted with same point size, there is no overlap among AA, BB, and CC sets, as confirmed in the right-hand panel of Figure 7

Summary

Introduction

There is burgeoning interest in the application of machine learning (ML) methods to problems in computational chemistry,[1−21] with special attention having been paid to the fitting of potential energy surfaces (PES) for chemical reactions.[22−29] So far, there has been less attention paid to using ML techniques for analysis of chemical trajectory data,[8,29] it appears that this could be a fruitful area of research. As a first step to undertaking such studies, we present here an analysis of trajectory data generated on a simple two degrees of freedom (2DoF) potential, which allows us to compare information derived from an empirical analysis of the trajectory data alone with that obtainable by a more conventional dynamical systems theory approach. In the Method section we present the potential and describe the generation of the trajectory data from it. The Results and Discussion contains three subsections. We show how phase-space structures controlling the dynamics can be inferred from simple classifications of the trajectories, and how these are related to unstable periodic orbits that can be identified on the analytical potential. In the second subsection we present two different algorithms for predicting the outcomes of trajectories from their initial conditions alone.

Methods

Results

Conclusion