Molecular Learning Dynamics

TL;DR

This paper proposes a physics–learning duality for molecular systems, where each nucleus is treated as an agent minimizing a loss that depends on invariants of other particles. By inferring a quadratic agent loss from CP2K water simulations, the authors build a learning-based molecular dynamics framework that reproduces key water properties while delivering massive computational speedups. The approach uncovers distinct invariant sensitivities for hydrogen and oxygen, demonstrates practical MD performance via Verlet integration and Nosé–Hoover thermostating, and highlights potential for scalable simulations and broader complex-system applications. It also acknowledges limitations in assuming pairwise interactions and simple loss forms, outlining paths toward richer, non-local representations and higher-order losses in future work.

Abstract

We apply the physics-learning duality to molecular systems by complementing the physical description of interacting particles with a dual learning description, where each particle is modeled as an agent minimizing a loss function. In the traditional physics framework, the equations of motion are derived from the Lagrangian function, while in the learning framework, the same equations emerge from learning dynamics driven by the agent loss function. The loss function depends on scalar quantities that describe invariant properties of all other agents or particles. To demonstrate this approach, we first infer the loss functions of oxygen and hydrogen directly from a dataset generated by the CP2K physics-based simulation of water molecules. We then employ the loss functions to develop a learning-based simulation of water molecules, which achieves comparable accuracy while being significantly more computationally efficient than standard physics-based simulations.

Figures (7)

• Figure 1: Kinetic energy evolution in the water simulation performed with CP2K
• Figure 2: Relative RMSE \ref{['eq:rel_rmse']} for oxygen (left) and hydrogen (right).
• Figure 3: Time evolution of the kinetic energy in the CP2K physics-based simulation (blue) and the learning-based simulation (green).
• Figure 4: Mean distance and standard deviation of the O-H bond.
• Figure 5: Time evolution of the O-H bond for four random hydrogen atoms in the CP2K physics-based simulation (dashed) and in the learning-based simulation (solid).