Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo

Otis, Leon; Neuscamman, Eric

doi:10.1039/c9cp02269d

Title: Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo

Abstract

We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors.

Authors:

Otis, Leon ^[1];

^[2]

Univ. of California, Berkeley, CA (United States). Dept. of Physics
Univ. of California, Berkeley, CA (United States). Dept. of Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Division

Publication Date:: Tue Jan 01 00:00:00 EST 2019

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1567167

Alternate Identifier(s):: OSTI ID: 1529687

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Physical Chemistry Chemical Physics. PCCP

Additional Journal Information:: Journal Volume: 21; Journal Issue: 27; Journal ID: ISSN 1463-9076

Publisher:: Royal Society of Chemistry

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats


                    Otis, Leon, and Neuscamman, Eric. Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo.  United States: N. p., 2019. 
Web.  doi:10.1039/c9cp02269d.

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                    Otis, Leon, & Neuscamman, Eric. Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo.  United States.  https://doi.org/10.1039/c9cp02269d

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                    Otis, Leon, and Neuscamman, Eric. Tue .  
"Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo".  United States.  https://doi.org/10.1039/c9cp02269d.  https://www.osti.gov/servlets/purl/1567167.

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@article{osti_1567167,

  title        = {Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo},

  author       = {Otis, Leon and Neuscamman, Eric},

  abstractNote = {We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors.},

  doi          = {10.1039/c9cp02269d},

  journal      = {Physical Chemistry Chemical Physics. PCCP},

  number       = 27,

  volume       = 21,

  place        = {United States},

  year         = {Tue Jan 01 00:00:00 EST 2019},

  month        = {Tue Jan 01 00:00:00 EST 2019}

}

Copy to clipboard

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Works referencing / citing this record:

Multireference configuration interaction and perturbation theory without reduced density matrices
journal, December 2019

Mahajan, Ankit; Blunt, Nick S.; Sabzevari, Iliya
The Journal of Chemical Physics, Vol. 151, Issue 21
DOI: 10.1063/1.5128115

An accelerated linear method for optimizing non-linear wavefunctions in variational Monte Carlo
journal, January 2020

Sabzevari, Iliya; Mahajan, Ankit; Sharma, Sandeep
The Journal of Chemical Physics, Vol. 152, Issue 2
DOI: 10.1063/1.5125803

A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo
text, January 2019

Blunt, Nick S.
arXiv
DOI: 10.48550/arxiv.1908.04158

An accelerated linear method for optimizing non-linear wavefunctions in variational Monte Carlo
text, January 2019

Sabzevari, Iliya; Mahajan, Ankit; Sharma, Sandeep
arXiv
DOI: 10.48550/arxiv.1908.04423

Multireference configuration interaction and perturbation theory without reduced density matrices
text, January 2019

Mahajan, Ankit; Blunt, Nick S.; Sabzevari, Iliya
arXiv
DOI: 10.48550/arxiv.1909.06935

A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo
journal, November 2019

Blunt, Nick S.
The Journal of Chemical Physics, Vol. 151, Issue 17
DOI: 10.1063/1.5123146

Accelerating Stochastic Quantum Chemistry
text, January 2019

Neufeld, Verena A.; Thom, Alex J. W.
arXiv
DOI: 10.48550/arxiv.1910.05210

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Title: Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo

Abstract

Citation Formats

Improved Speed and Scaling in Orbital Space Variational Monte Carlo journal, November 2018

Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules journal, May 2008

Photoswitches: From Molecules to Materials journal, April 2010

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Equation of Motion Theory for Excited States in Variational Monte Carlo and the Jastrow Antisymmetric Geminal Power in Hilbert Space journal, July 2016

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Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods text, January 2007

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Stochastic Gradient Approximation: An Efficient Method to Optimize Many-Body Wave Functions journal, August 1997

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Excited State Specific Multi-Slater Jastrow Wave Functions journal, January 2019

Solving the quantum many-body problem with artificial neural networks journal, February 2017

Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo journal, May 2016

Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory. text, January 2017

Wave function optimization in the variational Monte Carlo method text, January 2005

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Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene journal, January 2012

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Molecular hydrogen adsorbed on benzene: Insights from a quantum Monte Carlo study journal, October 2008

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Communication: A Jastrow factor coupled cluster theory for weak and strong electron correlation journal, November 2013

Zero-variance principle for Monte Carlo algorithms text, January 1999

Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm text, January 2011

Correlated geminal wave function for molecules: an efficient resonating valence bond approach text, January 2004

Excitation variance matching with limited configuration interaction expansions in variational Monte Carlo journal, October 2017

A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo journal, May 2017

Geminal wavefunctions with Jastrow correlation: a first application to atoms text, January 2003

An Efficient Variational Principle for the Direct Optimization of Excited States journal, July 2016

Optimization of quantum Monte Carlo wave functions by energy minimization journal, February 2007

Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods journal, August 2018

Realization of Quantum Chemistry without Wave Functions through First-Order Semidefinite Programming journal, November 2004

Energies of the first row atoms from quantum Monte Carlo journal, June 2007

Wave function optimization in the variational Monte Carlo method journal, June 2005

Energy and Variance Optimization of Many-Body Wave Functions journal, April 2005

Geminal wave functions with Jastrow correlation: A first application to atoms journal, October 2003

Finite size errors in quantum many-body simulations of extended systems text, January 1998

Approaching chemical accuracy with quantum Monte Carlo journal, March 2012

Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids text, January 2015

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules text, January 2008

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Zero-Variance Principle for Monte Carlo Algorithms journal, December 1999

Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids journal, March 2015

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State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve journal, October 2004

Recent progresses on diarylethene based photochromic switches journal, January 2004

Framework for constructing generic Jastrow correlation factors journal, September 2012

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo journal, April 2015

Energies of the first row atoms from quantum Monte Carlo text, January 2010

Quantum Monte Carlo simulations of solids journal, January 2001

Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide journal, October 2018

Improved Optimization for the Cluster Jastrow Antisymmetric Geminal Power and Tests on Triple-Bond Dissociations journal, June 2016

Approximating strongly correlated wave functions with correlator product states journal, December 2009

Communication: Variation after response in quantum Monte Carlo journal, August 2016

Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions journal, February 2015

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Correlated geminal wave function for molecules: An efficient resonating valence bond approach journal, October 2004

Ground-state properties of quantum many-body systems: entangled-plaquette states and variational Monte Carlo journal, August 2009

Optimization of Ground- and Excited-State Wave Functions and van der Waals Clusters journal, July 2001

σ -SCF: A direct energy-targeting method to mean-field excited states journal, December 2017

Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions text, January 1999

Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm journal, December 2011

Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz journal, November 2018

Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations journal, August 1997

Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory journal, March 2017

Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions journal, May 1999

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods journal, July 2007

Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow–Slater Expansions journal, October 2017

Improved Speed and Scaling in Orbital Space Variational Monte Carlo
journal, November 2018

Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
journal, May 2008

Photoswitches: From Molecules to Materials
journal, April 2010

Selected configuration interaction dressed by perturbation
journal, August 2018

Equation of Motion Theory for Excited States in Variational Monte Carlo and the Jastrow Antisymmetric Geminal Power in Hilbert Space
journal, July 2016

Dissecting the Hydrogen Bond: A Quantum Monte Carlo Approach
journal, July 2008

Heavy-tailed random error in quantum Monte Carlo
text, January 2009

Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction
journal, February 2018

Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
journal, April 2016

Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling
journal, August 2016

Excitation Variance Matching with Limited Configuration Interaction Expansions in Variational Monte Carlo
text, January 2017

Excited State Specific Multi-Slater Jastrow Wave Functions
text, January 2018

Clean and Convenient Tessellations for Number Counting Jastrow Factors
preprint, January 2018

Recent Progresses on Diarylethene Based Photochromic Switches
journal, May 2004

Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
text, January 2007

Accuracy of Electronic Wave Functions in Quantum Monte Carlo: the Effect of High-Order Correlations
text, January 1997

Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions
journal, March 2007

Stochastic Gradient Approximation: An Efficient Method to Optimize Many-Body Wave Functions
journal, August 1997

Configuration interaction calculations on the nitrogen molecule
journal, January 1974

Excited State Specific Multi-Slater Jastrow Wave Functions
journal, January 2019

Solving the quantum many-body problem with artificial neural networks
journal, February 2017

Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo
journal, May 2016

Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory.
text, January 2017

Wave function optimization in the variational Monte Carlo method
text, January 2005

Correlator product state study of molecular magnetism in the giant Keplerate Mo $_{72}$ Fe $_{30}$
journal, August 2012

Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene
journal, January 2012

A new generation of effective core potentials for correlated calculations
journal, December 2017

Molecular hydrogen adsorbed on benzene: Insights from a quantum Monte Carlo study
journal, October 2008

Clean and Convenient Tessellations for Number Counting Jastrow Factors
journal, November 2018

Communication: A Jastrow factor coupled cluster theory for weak and strong electron correlation
journal, November 2013

Zero-variance principle for Monte Carlo algorithms
text, January 1999

Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm
text, January 2011

Correlated geminal wave function for molecules: an efficient resonating valence bond approach
text, January 2004

Excitation variance matching with limited configuration interaction expansions in variational Monte Carlo
journal, October 2017

A Blocked Linear Method for Optimizing Large Parameter Sets in Variational Monte Carlo
journal, May 2017

Geminal wavefunctions with Jastrow correlation: a first application to atoms
text, January 2003

An Efficient Variational Principle for the Direct Optimization of Excited States
journal, July 2016

Optimization of quantum Monte Carlo wave functions by energy minimization
journal, February 2007

Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods
journal, August 2018

Realization of Quantum Chemistry without Wave Functions through First-Order Semidefinite Programming
journal, November 2004

Energies of the first row atoms from quantum Monte Carlo
journal, June 2007

Wave function optimization in the variational Monte Carlo method
journal, June 2005

Energy and Variance Optimization of Many-Body Wave Functions
journal, April 2005

Geminal wave functions with Jastrow correlation: A first application to atoms
journal, October 2003

Finite size errors in quantum many-body simulations of extended systems
text, January 1998

Approaching chemical accuracy with quantum Monte Carlo
journal, March 2012

Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids
text, January 2015

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules
text, January 2008

Structural Optimization by Quantum Monte Carlo: Investigating the Low-Lying Excited States of Ethylene
journal, March 2012

Zero-Variance Principle for Monte Carlo Algorithms
journal, December 1999

Iterative backflow renormalization procedure for many-body ground-state wave functions of strongly interacting normal Fermi liquids
journal, March 2015

Toward Intelligent Molecular Machines: Directed Motions of Biological and Artificial Molecules and Assemblies
journal, April 2005

Projector Quantum Monte Carlo Method for Nonlinear Wave Functions
text, January 2017

State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve
journal, October 2004

Recent progresses on diarylethene based photochromic switches
journal, January 2004

Framework for constructing generic Jastrow correlation factors
journal, September 2012

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo
journal, April 2015

Energies of the first row atoms from quantum Monte Carlo
text, January 2010

Quantum Monte Carlo simulations of solids
journal, January 2001

Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide
journal, October 2018

Improved Optimization for the Cluster Jastrow Antisymmetric Geminal Power and Tests on Triple-Bond Dissociations
journal, June 2016

Approximating strongly correlated wave functions with correlator product states
journal, December 2009

Communication: Variation after response in quantum Monte Carlo
journal, August 2016

Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions
journal, February 2015

Energy-consistent pseudopotentials for quantum Monte Carlo calculations
journal, June 2007

Correlated geminal wave function for molecules: An efficient resonating valence bond approach
journal, October 2004

Ground-state properties of quantum many-body systems: entangled-plaquette states and variational Monte Carlo
journal, August 2009

Optimization of Ground- and Excited-State Wave Functions and van der Waals Clusters
journal, July 2001

σ -SCF: A direct energy-targeting method to mean-field excited states
journal, December 2017

Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions
text, January 1999

Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm
journal, December 2011

Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz
journal, November 2018

Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations
journal, August 1997

Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory
journal, March 2017

Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions
journal, May 1999

Weak binding between two aromatic rings: Feeling the van der Waals attraction by quantum Monte Carlo methods
journal, July 2007

Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow–Slater Expansions
journal, October 2017

Size Consistent Excited States via Algorithmic Transformations between Variational Principles
journal, November 2017

Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo
journal, November 2017

Molecular hydrogen adsorbed on benzene: insights from a quantum Monte Carlo study
text, January 2008