Ab Initio Generalized Langevin Equation
arXiv:2211.06558 · doi:10.1073/pnas.2308668121
Abstract
We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multi-scale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of collective variables by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude, and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.
References in corpus (38)
- Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
- Maximally localized Wannier functions: Theory and applications
- Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
- On representing chemical environments
- Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
- SchNet - a deep learning architecture for molecules and materials
- Physics of thin-film ferroelectric oxides
- E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials
- Intrinsic ripples in graphene
- PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges
- Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
- First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO3
- Ab initio study of ferroelectric domain walls in PbTiO3
- Terahertz-Field-Induced Ferroelectricity in Quantum Paraelectric SrTiO
- Creep and depinning in disordered media
- Efficient stochastic thermostatting of path integral molecular dynamics
- A Variational Approach to Enhanced Sampling and Free Energy Calculations
- Nuclear quantum effects in solids using a colored-noise thermostat
- Colored-noise thermostats à la carte
- 86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy
- Langevin equation with colored noise for constant-temperature molecular dynamics simulations
- DeePCG: constructing coarse-grained models via deep neural networks
- A Unified Approach to Enhanced Sampling
- Data-driven parameterization of the generalized Langevin equation
- Deep neural network for the dielectric response of insulators
- Reinforced dynamics for enhanced sampling in large atomic and molecular systems
- A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
- Coarse-Grained Modelling Out of Equilibrium
- Efficient sampling of high-dimensional free energy landscapes using adaptive reinforced dynamics
- Generalized Langevin dynamics: Construction and numerical integration of non-Markovian particle-based models
- Learning macroscopic internal variables and history dependence from microscopic models
- Reduced-Order Models for Coupled Dynamical Systems: Data-driven Methods and the Koopman Operator
- Creep motion of elastic interfaces driven in a disordered landscape
- Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning
- Phase Field Crystal Model for Magneto-Elasticity in Isotropic Ferromagnetic Solids
- Machine learning memory kernels as closure for non-Markovian stochastic processes
- Model Reduction with Memory and the Machine Learning of Dynamical Systems
- Data-driven Langevin modeling of nonequilibrium processes