Neural Network for Principle of Least Action

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Abstract

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 LJ38from 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.

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APA

Wang, B., Jackson, S., Nakano, A., Nomura, K. I., Vashishta, P., Kalia, R., & Stevens, M. (2022, July 25). Neural Network for Principle of Least Action. Journal of Chemical Information and Modeling. American Chemical Society. https://doi.org/10.1021/acs.jcim.2c00515

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