Ab initio generalized Langevin equation

Journal Article · Fri Mar 29 00:00:00 EDT 2024 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2308668121· OSTI ID:2331315

Xie, Pinchen ^[1]; Car, Roberto  ^[2]; E, Weinan  ^[3]

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1. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544
2. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, Department of Chemistry and Princeton Materials Institute, Princeton University, Princeton, NJ 08544, Department of Physics, Princeton University, Princeton, NJ 08544
3. AI for Science Institute, Beijing 100080, China, Center for Machine Learning Research and School of Mathematical Sciences, Peking University, Beijing 100084, China

We introduce a machine learning–based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) 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 multiscale 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 CVs 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0019394
• OSTI ID: 2331315
• Journal Information: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Vol. 121 Journal Issue: 14; ISSN 0027-8424
• Publisher: Proceedings of the National Academy of Sciences
• Country of Publication: United States
• Language: English