Ab initio generalized Langevin equation.

Area of Science:

• Computational Materials Science
• Theoretical Chemistry
• Statistical Mechanics

Background:

• Modeling slow collective variables (CVs) in materials and molecules is computationally challenging.
• Existing methods often struggle to capture dynamics across multiple scales.
• Atomistic simulations based on quantum mechanics are accurate but computationally expensive.

Purpose of the Study:

• To introduce a novel machine learning-based approach, ab initio generalized Langevin equation (AIGLE), for modeling slow CV dynamics.
• To enable efficient multiscale modeling by learning parameters from high-fidelity quantum mechanical simulations.
• To demonstrate AIGLE's capability in studying mesoscale processes in crystalline lead titanate.

Main Methods:

• Developed AIGLE using the Mori-Zwanzig formalism, incorporating force fields, memory kernels, and noise generators constrained by the fluctuation-dissipation theorem.
• Integrated AIGLE with deep potential molecular dynamics and electronic density functional theory.
• Applied AIGLE to study field-driven ferroelectric domain wall dynamics and lattice of coarse-grained electric dipoles in lead titanate.

Main Results:

• AIGLE successfully models mesoscale dynamics in crystalline lead titanate, including field-driven domain wall motion and dipole lattice dynamics.
• The approach extends ab initio simulations to noise-driven regimes inaccessible to traditional molecular dynamics.
• AIGLE demonstrates computational efficiency orders of magnitude greater than molecular dynamics while accurately reproducing low-frequency dynamics and far-infrared absorption.

Conclusions:

• AIGLE provides a powerful and efficient framework for multiscale modeling of slow dynamics in materials and molecules.
• The method accurately captures essential microscopic dynamics at low frequencies, crucial for understanding phenomena like far-infrared absorption.
• AIGLE opens new avenues for simulating complex systems where traditional methods are computationally prohibitive.