Neural Network for Principle of Least Action

The principle of least action is the cornerstone of classical mechanics, theory of relativity, quantum mechanics, and thermodynamics. Here, we describe how a neural network (NN) learns to find the trajectory for a Lennard-Jones (LJ) system that maintains balance in minimizing the Onsager-Machlup (OM) action and maintaining the energy conservation. The phase-space trajectory thus calculated is in excellent agreement with the corresponding results from the ground-truth molecular dynamics (MD) simulation. Furthermore, we show that the NN can easily find structural transformation pathways for LJ clusters, for example, the basin-hopping transformation of an LJ(38) from an incomplete Mackay icosahedron to a truncated face-centered cubic octahedron. Unlike MD, the NN computes atomic trajectories over the entire temporal domain in one fell swoop, and the NN time step is a factor of 20 larger than the MD time step. The NN approach to OM action is quite general and can be adapted to model morphometrics in a variety of applications.

Automated summary

The principle of least action is fundamental in classical mechanics, theory of relativity, quantum mechanics, and thermodynamics. This paper describes how a neural network learns to find trajectories in a Lennard-Jones system and successfully predicts structural transformation pathways for LJ clusters. The neural network approach allows for efficient computation of atomic trajectories over time.