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Statistical learning for predicting density–matrix-based electron dynamics

Journal Article · · Stat
DOI:https://doi.org/10.1002/sta4.439· OSTI ID:2421471
 [1];  [2];  [2];  [2]
  1. Univ. of California, Merced, CA (United States); OSTI
  2. Univ. of California, Merced, CA (United States)
+ Show Author Affiliations
In this study, we consider the problem of learning density-dependent molecular Hamiltonian matrices from time series of electron density matrices, all in the context of Hartree–Fock theory. Prior work developed a solution to this problem for small molecular systems with density and Hamiltonian matrices of size at most 6 × 6. Here, using a battery of techniques, we scale prior methods to larger molecular systems with, for example, 29 × 29 matrices. This includes systems that either have more electrons or are expressed in large basis sets such as 6-311++G**. Scaling the method to larger systems enhances its relevance for realistic applications in chemistry and physics. To achieve this scaling, we apply dimensionality reduction, ridge regression and analytic computation of Hessians. Through the combination of these techniques, we are able to learn Hamiltonians by minimizing an objective function that encodes local propagation error. Importantly, these learned Hamiltonians can then be used to predict electron dynamics for thousands of steps: When we use our learned Hamiltonians to numerically solve the time-dependent Hartree–Fock equation, we obtain predicted dynamics that are in close quantitative agreement with ground truth dynamics. This includes field-off trajectories similar to the training data and field-on trajectories outside of the training data.
Research Organization:
Univ. of California, Merced, CA (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0020203
OSTI ID:
2421471
Alternate ID(s):
OSTI ID: 1867716
Journal Information:
Stat, Journal Name: Stat Journal Issue: 1 Vol. 11; ISSN 2049-1573
Publisher:
WileyCopyright Statement
Country of Publication:
United States
Language:
English

References (9)

Electron dynamics with real-time time-dependent density functional theory journal February 2016
The Elements of Statistical Learning book January 2001
Fundamentals of Time-Dependent Density Functional Theory book January 2012
Machine learning a molecular Hamiltonian for predicting electron dynamics journal October 2020
A family of embedded Runge-Kutta formulae journal March 1980
Real-Time Time-Dependent Electronic Structure Theory journal August 2020
A time-dependent Hartree–Fock approach for studying the electronic optical response of molecules in intense fields journal January 2005
Electronic optical response of molecules in intense fields: Comparison of TD-HF, TD-CIS, and TD-CIS(D) approaches journal June 2007
Perspective: Fundamental aspects of time-dependent density functional theory journal June 2016

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Related Subjects

59 BASIC BIOLOGICAL SCIENCES
97 MATHEMATICS AND COMPUTING
Hamiltonian
Mathematics
electron density
electron dynamics
statistical learning