Neural Network for Principle of Least Action

Area of Science:

• Computational physics and chemistry
• Machine learning applications in physical sciences

Background:

• The principle of least action is fundamental across physics, including classical mechanics, relativity, quantum mechanics, and thermodynamics.
• Calculating accurate phase-space trajectories and understanding structural transformations are critical challenges in molecular simulations.

Purpose of the Study:

• To develop and evaluate a neural network (NN) model for calculating phase-space trajectories in Lennard-Jones (LJ) systems.
• To demonstrate the NN's ability to balance the minimization of Onsager-Machlup (OM) action with energy conservation.
• To showcase the NN's capability in identifying structural transformation pathways for LJ clusters.

Main Methods:

• Utilizing a neural network (NN) trained to find trajectories that minimize Onsager-Machlup (OM) action while conserving energy.
• Comparing NN-calculated phase-space trajectories against "ground-truth" molecular dynamics (MD) simulations for a Lennard-Jones system.
• Applying the NN to identify structural transformation pathways, such as basin-hopping transformations in LJ clusters (e.g., LJ38).

Main Results:

• The NN successfully calculates phase-space trajectories in excellent agreement with MD simulations.
• The NN efficiently identifies structural transformation pathways for LJ clusters, exemplified by the LJ38 transformation.
• The NN computes atomic trajectories over the entire temporal domain in one step, with time steps 20 times larger than MD.

Conclusions:

• The developed NN approach effectively calculates trajectories and structural transformations for LJ systems, offering significant computational advantages over MD.
• The NN's ability to generalize and adapt to various applications, including morphometrics, highlights its potential impact.
• This method provides a novel and efficient computational tool for physical sciences research.