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Title: Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation

Abstract

Classical molecular dynamics simulates the time evolution of molecular systems through the phase space spanned by the positions and velocities of the constituent atoms. Molecular-level thermodynamic, kinetic, and structural data extracted from the resulting trajectories provide valuable information for the understanding, engineering, and design of biological and molecular materials. The cost of simulating many-body atomic systems makes simulations of large molecules prohibitively expensive, and the high-dimensionality of the resulting trajectories presents a challenge for analysis. Driven by advances in algorithms, hardware, and data availability, there has been a flare of interest in recent years in the applications of machine learning – especially deep learning – to molecular simulation. Furthermore, these techniques have demonstrated great power and flexibility in both extracting mechanistic understanding of the important nonlinear collective variables governing the dynamics of a molecular system, and in furnishing good low-dimensional system representations with which to perform enhanced sampling or develop long-timescale dynamical models. It is the purpose of this article to introduce the key machine learning approaches, describe how they are married with statistical mechanical theory into domain-specific tools, and detail applications of these approaches in understanding and accelerating biomolecular simulation.

Authors:
 [1];  [2]; ORCiD logo [1]
+ Show Author Affiliations
  1. University of Chicago, IL (United States)
  2. University of Illinois at Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
OSTI Identifier:
1651117
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Molecular Physics
Additional Journal Information:
Journal Volume: 118; Journal Issue: 5; Journal ID: ISSN 0026-8976
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Machine learning; molecular simulation; deep learning; enhanced sampling; collective variables

Citation Formats

Sidky, Hythem, Chen, Wei, and Ferguson, Andrew L. Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation. United States: N. p., 2020. Web. doi:10.1080/00268976.2020.1737742.
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Sidky, Hythem, Chen, Wei, & Ferguson, Andrew L. Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation. United States. https://doi.org/10.1080/00268976.2020.1737742
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Sidky, Hythem, Chen, Wei, and Ferguson, Andrew L. Tue . "Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation". United States. https://doi.org/10.1080/00268976.2020.1737742. https://www.osti.gov/servlets/purl/1651117.
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@article{osti_1651117,
title = {Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation},
author = {Sidky, Hythem and Chen, Wei and Ferguson, Andrew L.},
abstractNote = {Classical molecular dynamics simulates the time evolution of molecular systems through the phase space spanned by the positions and velocities of the constituent atoms. Molecular-level thermodynamic, kinetic, and structural data extracted from the resulting trajectories provide valuable information for the understanding, engineering, and design of biological and molecular materials. The cost of simulating many-body atomic systems makes simulations of large molecules prohibitively expensive, and the high-dimensionality of the resulting trajectories presents a challenge for analysis. Driven by advances in algorithms, hardware, and data availability, there has been a flare of interest in recent years in the applications of machine learning – especially deep learning – to molecular simulation. Furthermore, these techniques have demonstrated great power and flexibility in both extracting mechanistic understanding of the important nonlinear collective variables governing the dynamics of a molecular system, and in furnishing good low-dimensional system representations with which to perform enhanced sampling or develop long-timescale dynamical models. It is the purpose of this article to introduce the key machine learning approaches, describe how they are married with statistical mechanical theory into domain-specific tools, and detail applications of these approaches in understanding and accelerating biomolecular simulation.},
doi = {10.1080/00268976.2020.1737742},
journal = {Molecular Physics},
number = 5,
volume = 118,
place = {United States},
year = {Tue Mar 10 00:00:00 EDT 2020},
month = {Tue Mar 10 00:00:00 EDT 2020}
}
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Works referenced in this record:

Reduced Models in Chemical Kinetics via Nonlinear Data-Mining
journal, January 2014

  • Chiavazzo, Eliodoro; Gear, Charles; Dsilva, Carmeline
  • Processes, Vol. 2, Issue 1
  • DOI: 10.3390/pr2010112

Charting molecular free-energy landscapes with an atlas of collective variables
journal, November 2016

  • Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino
  • The Journal of Chemical Physics, Vol. 145, Issue 17
  • DOI: 10.1063/1.4966262

A self-learning algorithm for biased molecular dynamics
journal, September 2010

  • Tribello, Gareth A.; Ceriotti, Michele; Parrinello, Michele
  • Proceedings of the National Academy of Sciences, Vol. 107, Issue 41
  • DOI: 10.1073/pnas.1011511107

Girsanov reweighting for metadynamics simulations
journal, August 2018

  • Donati, Luca; Keller, Bettina G.
  • The Journal of Chemical Physics, Vol. 149, Issue 7
  • DOI: 10.1063/1.5027728

Using sketch-map coordinates to analyze and bias molecular dynamics simulations
journal, March 2012

  • Tribello, G. A.; Ceriotti, M.; Parrinello, M.
  • Proceedings of the National Academy of Sciences, Vol. 109, Issue 14
  • DOI: 10.1073/pnas.1201152109

Graph Laplacian Tomography From Unknown Random Projections
journal, October 2008

  • Coifman, R. R.; Shkolnisky, Y.; Sigworth, F. J.
  • IEEE Transactions on Image Processing, Vol. 17, Issue 10
  • DOI: 10.1109/TIP.2008.2002305

Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
journal, February 1977

Transferable Neural Networks for Enhanced Sampling of Protein Dynamics
journal, March 2018

  • Sultan, Mohammad M.; Wayment-Steele, Hannah K.; Pande, Vijay S.
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 4
  • DOI: 10.1021/acs.jctc.8b00025

Machine learning of single molecule free energy surfaces and the impact of chemistry and environment upon structure and dynamics
journal, March 2015

  • Mansbach, Rachael A.; Ferguson, Andrew L.
  • The Journal of Chemical Physics, Vol. 142, Issue 10
  • DOI: 10.1063/1.4914144

Molecular modeling studies of peptoid polymers
journal, January 2017

Nonlinear machine learning in simulations of soft and biological materials
journal, November 2017

Reaction coordinates and transition pathways of rare events via forward flux sampling
journal, October 2007

  • Borrero, Ernesto E.; Escobedo, Fernando A.
  • The Journal of Chemical Physics, Vol. 127, Issue 16
  • DOI: 10.1063/1.2776270

Large-amplitude nonlinear motions in proteins
journal, April 1992

Dynamical reweighting: Improved estimates of dynamical properties from simulations at multiple temperatures
journal, June 2011

  • Chodera, John D.; Swope, William C.; Noé, Frank
  • The Journal of Chemical Physics, Vol. 134, Issue 24
  • DOI: 10.1063/1.3592152

Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics
journal, June 2011

  • Prinz, Jan-Hendrik; Chodera, John D.; Pande, Vijay S.
  • The Journal of Chemical Physics, Vol. 134, Issue 24
  • DOI: 10.1063/1.3592153

Diffusion maps
journal, July 2006

  • Coifman, Ronald R.; Lafon, Stéphane
  • Applied and Computational Harmonic Analysis, Vol. 21, Issue 1
  • DOI: 10.1016/j.acha.2006.04.006

VAMPnets for deep learning of molecular kinetics
journal, January 2018

Kinetic Distance and Kinetic Maps from Molecular Dynamics Simulation
journal, September 2015

  • Noé, Frank; Clementi, Cecilia
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 10
  • DOI: 10.1021/acs.jctc.5b00553

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations
journal, April 2017

  • Wu, Hao; Nüske, Feliks; Paul, Fabian
  • The Journal of Chemical Physics, Vol. 146, Issue 15
  • DOI: 10.1063/1.4979344

Commute Maps: Separating Slowly Mixing Molecular Configurations for Kinetic Modeling
journal, October 2016

  • Noé, Frank; Banisch, Ralf; Clementi, Cecilia
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 11
  • DOI: 10.1021/acs.jctc.6b00762

Demonstrating the Transferability and the Descriptive Power of Sketch-Map
journal, February 2013

  • Ceriotti, Michele; Tribello, Gareth A.; Parrinello, Michele
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 3
  • DOI: 10.1021/ct3010563

Collective variable discovery and enhanced sampling using autoencoders: Innovations in network architecture and error function design
journal, August 2018

  • Chen, Wei; Tan, Aik Rui; Ferguson, Andrew L.
  • The Journal of Chemical Physics, Vol. 149, Issue 7
  • DOI: 10.1063/1.5023804

How Fast-Folding Proteins Fold
journal, October 2011

Nonlinear Machine Learning of Patchy Colloid Self-Assembly Pathways and Mechanisms
journal, April 2014

  • Long, Andrew W.; Ferguson, Andrew L.
  • The Journal of Physical Chemistry B, Vol. 118, Issue 15
  • DOI: 10.1021/jp500350b

Discovering Mountain Passes via Torchlight: Methods for the Definition of Reaction Coordinates and Pathways in Complex Macromolecular Reactions
journal, April 2013

High-Resolution Markov State Models for the Dynamics of Trp-Cage Miniprotein Constructed Over Slow Folding Modes Identified by State-Free Reversible VAMPnets
journal, August 2019

  • Sidky, Hythem; Chen, Wei; Ferguson, Andrew L.
  • The Journal of Physical Chemistry B, Vol. 123, Issue 38
  • DOI: 10.1021/acs.jpcb.9b05578

Variational Approach to Molecular Kinetics
journal, March 2014

  • Nüske, Feliks; Keller, Bettina G.; Pérez-Hernández, Guillermo
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 4
  • DOI: 10.1021/ct4009156

Unmasking Clever Hans predictors and assessing what machines really learn
journal, March 2019

  • Lapuschkin, Sebastian; Wäldchen, Stephan; Binder, Alexander
  • Nature Communications, Vol. 10, Issue 1
  • DOI: 10.1038/s41467-019-08987-4

SchNet – A deep learning architecture for molecules and materials
journal, June 2018

  • Schütt, K. T.; Sauceda, H. E.; Kindermans, P. -J.
  • The Journal of Chemical Physics, Vol. 148, Issue 24
  • DOI: 10.1063/1.5019779

Deep clustering of protein folding simulations
journal, December 2018

Automated design of collective variables using supervised machine learning
journal, September 2018

  • Sultan, Mohammad M.; Pande, Vijay S.
  • The Journal of Chemical Physics, Vol. 149, Issue 9
  • DOI: 10.1063/1.5029972

Automatic Method for Identifying Reaction Coordinates in Complex Systems †
journal, April 2005

  • Ma, Ao; Dinner, Aaron R.
  • The Journal of Physical Chemistry B, Vol. 109, Issue 14
  • DOI: 10.1021/jp045546c

Integrating diffusion maps with umbrella sampling: Application to alanine dipeptide
journal, April 2011

  • Ferguson, Andrew L.; Panagiotopoulos, Athanassios Z.; Debenedetti, Pablo G.
  • The Journal of Chemical Physics, Vol. 134, Issue 13
  • DOI: 10.1063/1.3574394

Spectral gap optimization of order parameters for sampling complex molecular systems
journal, February 2016

  • Tiwary, Pratyush; Berne, B. J.
  • Proceedings of the National Academy of Sciences, Vol. 113, Issue 11
  • DOI: 10.1073/pnas.1600917113

Collective motions in proteins: A covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations
journal, November 1991

  • Ichiye, Toshiko; Karplus, Martin
  • Proteins: Structure, Function, and Genetics, Vol. 11, Issue 3
  • DOI: 10.1002/prot.340110305

Machine Calculation of Thermodynamic Properties of a Simple Fluid at Supercritical Temperatures
journal, December 1967

  • McDonald, I. R.; Singer, K.
  • The Journal of Chemical Physics, Vol. 47, Issue 11
  • DOI: 10.1063/1.1701695

Design of therapeutic proteins with enhanced stability
journal, July 2009

  • Chennamsetty, N.; Voynov, V.; Kayser, V.
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 29
  • DOI: 10.1073/pnas.0904191106

Koopman operator-based model reduction for switched-system control of PDEs
journal, August 2019

Stochastic Gradient Descent Tricks
book, January 2012

Markov models of molecular kinetics: Generation and validation
journal, May 2011

  • Prinz, Jan-Hendrik; Wu, Hao; Sarich, Marco
  • The Journal of Chemical Physics, Vol. 134, Issue 17
  • DOI: 10.1063/1.3565032

Intrinsic map dynamics exploration for uncharted effective free-energy landscapes
journal, June 2017

  • Chiavazzo, Eliodoro; Covino, Roberto; Coifman, Ronald R.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 28
  • DOI: 10.1073/pnas.1621481114

Modeling Molecular Kinetics with tICA and the Kernel Trick
journal, January 2015

  • Schwantes, Christian R.; Pande, Vijay S.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 2
  • DOI: 10.1021/ct5007357

A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
journal, January 2013

  • Noé, Frank; Nüske, Feliks
  • Multiscale Modeling & Simulation, Vol. 11, Issue 2
  • DOI: 10.1137/110858616

Markov state models of biomolecular conformational dynamics
journal, April 2014

A variational conformational dynamics approach to the selection of collective variables in metadynamics
journal, November 2017

  • McCarty, James; Parrinello, Michele
  • The Journal of Chemical Physics, Vol. 147, Issue 20
  • DOI: 10.1063/1.4998598

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
journal, June 2015

  • Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W.
  • Journal of Nonlinear Science, Vol. 25, Issue 6
  • DOI: 10.1007/s00332-015-9258-5

Finite approximations of Frobenius-Perron operators. A solution of Ulam's conjecture to multi-dimensional transformations
journal, April 1996

Collective Variables from Local Fluctuations
journal, May 2018

  • Mendels, Dan; Piccini, GiovanniMaria; Parrinello, Michele
  • The Journal of Physical Chemistry Letters, Vol. 9, Issue 11
  • DOI: 10.1021/acs.jpclett.8b00733

Reweighted autoencoded variational Bayes for enhanced sampling (RAVE)
journal, August 2018

  • Ribeiro, João Marcelo Lamim; Bravo, Pablo; Wang, Yihang
  • The Journal of Chemical Physics, Vol. 149, Issue 7
  • DOI: 10.1063/1.5025487

Simplifying the representation of complex free-energy landscapes using sketch-map
journal, July 2011

  • Ceriotti, Michele; Tribello, Gareth A.; Parrinello, Michele
  • Proceedings of the National Academy of Sciences, Vol. 108, Issue 32
  • DOI: 10.1073/pnas.1108486108

Learning free energy landscapes using artificial neural networks
journal, March 2018

  • Sidky, Hythem; Whitmer, Jonathan K.
  • The Journal of Chemical Physics, Vol. 148, Issue 10
  • DOI: 10.1063/1.5018708

Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint
journal, May 2016

Data-Driven Model Reduction and Transfer Operator Approximation
journal, January 2018

Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
journal, April 2007

Nonlinear discovery of slow molecular modes using state-free reversible VAMPnets
journal, June 2019

  • Chen, Wei; Sidky, Hythem; Ferguson, Andrew L.
  • The Journal of Chemical Physics, Vol. 150, Issue 21
  • DOI: 10.1063/1.5092521

tICA-Metadynamics: Accelerating Metadynamics by Using Kinetically Selected Collective Variables
journal, May 2017

  • M. Sultan, Mohammad; Pande, Vijay S.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 6
  • DOI: 10.1021/acs.jctc.7b00182

Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias
journal, March 2017

  • Nüske, Feliks; Wu, Hao; Prinz, Jan-Hendrik
  • The Journal of Chemical Physics, Vol. 146, Issue 9
  • DOI: 10.1063/1.4976518

A generalized deep learning approach for local structure identification in molecular simulations
journal, January 2019

  • DeFever, Ryan S.; Targonski, Colin; Hall, Steven W.
  • Chemical Science, Vol. 10, Issue 32
  • DOI: 10.1039/C9SC02097G

Enhanced sampling in molecular dynamics
journal, August 2019

  • Yang, Yi Isaac; Shao, Qiang; Zhang, Jun
  • The Journal of Chemical Physics, Vol. 151, Issue 7
  • DOI: 10.1063/1.5109531

Metadynamics: Metadynamics
journal, February 2011

  • Barducci, Alessandro; Bonomi, Massimiliano; Parrinello, Michele
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 1, Issue 5
  • DOI: 10.1002/wcms.31

Systematic characterization of protein folding pathways using diffusion maps: Application to Trp-cage miniprotein
journal, February 2015

  • Kim, Sang Beom; Dsilva, Carmeline J.; Kevrekidis, Ioannis G.
  • The Journal of Chemical Physics, Vol. 142, Issue 8
  • DOI: 10.1063/1.4913322

Simulating materials failure by using up to one billion atoms and the world's fastest computer: Brittle fracture
journal, April 2002

  • Abraham, F. F.; Walkup, R.; Gao, H.
  • Proceedings of the National Academy of Sciences, Vol. 99, Issue 9
  • DOI: 10.1073/pnas.062012699

What Is the Relation Between Slow Feature Analysis and Independent Component Analysis?
journal, October 2006

Local elevation: A method for improving the searching properties of molecular dynamics simulation
journal, December 1994

  • Huber, Thomas; Torda, Andrew E.; van Gunsteren, Wilfred F.
  • Journal of Computer-Aided Molecular Design, Vol. 8, Issue 6
  • DOI: 10.1007/BF00124016

On the Use of Experimental Observations to Bias Simulated Ensembles
journal, March 2012

  • Pitera, Jed W.; Chodera, John D.
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 10
  • DOI: 10.1021/ct300112v

Machine learning for molecular and materials science
journal, July 2018

Unconstrained enhanced sampling for free energy calculations of biomolecules: a review
journal, July 2016

Predicting slow structural transitions in macromolecular systems: Conformational flooding
journal, September 1995

NSF’s Inaugural Software Institutes: The Science Gateways Community Institute and the Molecular Sciences Software Institute
journal, September 2018

Perspective: Computational chemistry software and its advancement as illustrated through three grand challenge cases for molecular science
journal, November 2018

  • Krylov, Anna; Windus, Theresa L.; Barnes, Taylor
  • The Journal of Chemical Physics, Vol. 149, Issue 18
  • DOI: 10.1063/1.5052551

Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics
journal, May 2017

  • Galvelis, Raimondas; Sugita, Yuji
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 6
  • DOI: 10.1021/acs.jctc.7b00188

The Protein Folding Problem
journal, June 2008

The reweighted path ensemble
journal, November 2010

  • Rogal, Jutta; Lechner, Wolfgang; Juraszek, Jarek
  • The Journal of Chemical Physics, Vol. 133, Issue 17
  • DOI: 10.1063/1.3491817

Determination of reaction coordinates via locally scaled diffusion map
journal, March 2011

  • Rohrdanz, Mary A.; Zheng, Wenwei; Maggioni, Mauro
  • The Journal of Chemical Physics, Vol. 134, Issue 12
  • DOI: 10.1063/1.3569857

A Global Geometric Framework for Nonlinear Dimensionality Reduction
journal, December 2000

Nonlinear principal component analysis using autoassociative neural networks
journal, February 1991

Coarse-grained dynamics of an activity bump in a neural field model
journal, July 2007

Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration
journal, December 2013

Atomic-Level Characterization of the Structural Dynamics of Proteins
journal, October 2010

Toward Achieving Efficient and Accurate Ligand-Protein Unbinding with Deep Learning and Molecular Dynamics through RAVE
journal, November 2018

  • Lamim Ribeiro, João Marcelo; Tiwary, Pratyush
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 1
  • DOI: 10.1021/acs.jctc.8b00869

TweTriS: Twenty trillion-atom simulation
journal, January 2019

  • Tchipev, Nikola; Seckler, Steffen; Heinen, Matthias
  • The International Journal of High Performance Computing Applications, Vol. 33, Issue 5
  • DOI: 10.1177/1094342018819741

Studies in Molecular Dynamics. I. General Method
journal, August 1959

  • Alder, B. J.; Wainwright, T. E.
  • The Journal of Chemical Physics, Vol. 31, Issue 2
  • DOI: 10.1063/1.1730376

LIII. On lines and planes of closest fit to systems of points in space
journal, November 1901

  • Pearson, Karl
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 2, Issue 11
  • DOI: 10.1080/14786440109462720

Protein folding and de novo protein design for biotechnological applications
journal, February 2014

The perceptron: A probabilistic model for information storage and organization in the brain.
journal, January 1958

Obtaining reaction coordinates by likelihood maximization
journal, August 2006

  • Peters, Baron; Trout, Bernhardt L.
  • The Journal of Chemical Physics, Vol. 125, Issue 5
  • DOI: 10.1063/1.2234477

Dynamic Mode Decomposition with Control
journal, January 2016

  • Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan
  • SIAM Journal on Applied Dynamical Systems, Vol. 15, Issue 1
  • DOI: 10.1137/15M1013857

Molecular dynamics simulations in biology
journal, October 1990

  • Karplus, Martin; Petsko, Gregory A.
  • Nature, Vol. 347, Issue 6294
  • DOI: 10.1038/347631a0

Adaptive enhanced sampling by force-biasing using neural networks
journal, April 2018

  • Guo, Ashley Z.; Sevgen, Emre; Sidky, Hythem
  • The Journal of Chemical Physics, Vol. 148, Issue 13
  • DOI: 10.1063/1.5020733

ACS Central Science Virtual Issue on Machine Learning
journal, August 2018

Rapid Exploration of Configuration Space with Diffusion-Map-Directed Molecular Dynamics
journal, July 2013

  • Zheng, Wenwei; Rohrdanz, Mary A.; Clementi, Cecilia
  • The Journal of Physical Chemistry B, Vol. 117, Issue 42
  • DOI: 10.1021/jp401911h

Multiensemble Markov models of molecular thermodynamics and kinetics
journal, May 2016

  • Wu, Hao; Paul, Fabian; Wehmeyer, Christoph
  • Proceedings of the National Academy of Sciences, Vol. 113, Issue 23
  • DOI: 10.1073/pnas.1525092113

Landmark diffusion maps (L-dMaps): Accelerated manifold learning out-of-sample extension
journal, July 2019

  • Long, Andrew W.; Ferguson, Andrew L.
  • Applied and Computational Harmonic Analysis, Vol. 47, Issue 1
  • DOI: 10.1016/j.acha.2017.08.004

Simulating materials failure by using up to one billion atoms and the world's fastest computer: Work-hardening
journal, April 2002

  • Abraham, F. F.; Walkup, R.; Gao, H.
  • Proceedings of the National Academy of Sciences, Vol. 99, Issue 9
  • DOI: 10.1073/pnas.062054999

Extending Data-Driven Koopman Analysis to Actuated Systems
journal, January 2016

Molecular Dynamics with On-the-Fly Machine Learning of Quantum-Mechanical Forces
journal, March 2015

Using Ulam's method to calculate entropy and other dynamical invariants
journal, January 1999

Calculation of absolute protein-ligand binding free energy from computer simulations
journal, May 2005

  • Woo, H. -J.; Roux, B.
  • Proceedings of the National Academy of Sciences, Vol. 102, Issue 19
  • DOI: 10.1073/pnas.0409005102

Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science
journal, November 2008

Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
journal, October 2017

  • Li, Qianxiao; Dietrich, Felix; Bollt, Erik M.
  • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, Issue 10
  • DOI: 10.1063/1.4993854

Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
journal, April 2003

  • Donoho, D. L.; Grimes, C.
  • Proceedings of the National Academy of Sciences, Vol. 100, Issue 10
  • DOI: 10.1073/pnas.1031596100

Metadynamics with Discriminants: A Tool for Understanding Chemistry
journal, August 2018

  • Piccini, GiovanniMaria; Mendels, Dan; Parrinello, Michele
  • Journal of Chemical Theory and Computation, Vol. 14, Issue 10
  • DOI: 10.1021/acs.jctc.8b00634

A Computational Method to Extract Macroscopic Variables and Their Dynamics in Multiscale Systems
journal, January 2014

  • Froyland, Gary; Gottwald, Georg A.; Hammerlindl, Andy
  • SIAM Journal on Applied Dynamical Systems, Vol. 13, Issue 4
  • DOI: 10.1137/130943637

Markov State Models: From an Art to a Science
journal, February 2018

  • Husic, Brooke E.; Pande, Vijay S.
  • Journal of the American Chemical Society, Vol. 140, Issue 7
  • DOI: 10.1021/jacs.7b12191

Multiresolution Dynamic Mode Decomposition
journal, January 2016

  • Kutz, J. Nathan; Fu, Xing; Brunton, Steven L.
  • SIAM Journal on Applied Dynamical Systems, Vol. 15, Issue 2
  • DOI: 10.1137/15M1023543

Nonlinear Dimensionality Reduction by Locally Linear Embedding
journal, December 2000

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables
journal, December 2013

  • Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino
  • The Journal of Chemical Physics, Vol. 139, Issue 21
  • DOI: 10.1063/1.4830403

Everything you wanted to know about Markov State Models but were afraid to ask
journal, September 2010

Capabilities and limitations of time-lagged autoencoders for slow mode discovery in dynamical systems
journal, August 2019

  • Chen, Wei; Sidky, Hythem; Ferguson, Andrew L.
  • The Journal of Chemical Physics, Vol. 151, Issue 6
  • DOI: 10.1063/1.5112048

Hierarchical Time-Lagged Independent Component Analysis: Computing Slow Modes and Reaction Coordinates for Large Molecular Systems
journal, November 2016

  • Pérez-Hernández, Guillermo; Noé, Frank
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 12
  • DOI: 10.1021/acs.jctc.6b00738

Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9
journal, March 2013

  • Schwantes, Christian R.; Pande, Vijay S.
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 4
  • DOI: 10.1021/ct300878a

Time-Scale Separation from Diffusion-Mapped Delay Coordinates
journal, January 2013

  • Berry, T.; Cressman, J. R.; Gregurić-Ferenček, Z.
  • SIAM Journal on Applied Dynamical Systems, Vol. 12, Issue 2
  • DOI: 10.1137/12088183X

Rational design of patchy colloids via landscape engineering
journal, January 2018

  • Long, Andrew W.; Ferguson, Andrew L.
  • Molecular Systems Design & Engineering, Vol. 3, Issue 1
  • DOI: 10.1039/C7ME00077D

Density of States–Based Molecular Simulations
journal, July 2012

On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
journal, November 2017

Beating the Millisecond Barrier in Molecular Dynamics Simulations
journal, January 2015

Phase Transition for a Hard Sphere System
journal, November 1957

  • Alder, B. J.; Wainwright, T. E.
  • The Journal of Chemical Physics, Vol. 27, Issue 5
  • DOI: 10.1063/1.1743957

Graphite-diamond phase coexistence study employing a neural-network mapping of the ab initio potential energy surface
journal, March 2010

Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning
journal, September 2019

Stochastic Neural Network Approach for Learning High-Dimensional Free Energy Surfaces
journal, October 2017

The Protein-Folding Problem, 50 Years On
journal, November 2012

Nonlinear dimensionality reduction in molecular simulation: The diffusion map approach
journal, June 2011

  • Ferguson, Andrew L.; Panagiotopoulos, Athanassios Z.; Kevrekidis, Ioannis G.
  • Chemical Physics Letters, Vol. 509, Issue 1-3
  • DOI: 10.1016/j.cplett.2011.04.066

Systematic determination of order parameters for chain dynamics using diffusion maps
journal, July 2010

  • Ferguson, A. L.; Panagiotopoulos, A. Z.; Debenedetti, P. G.
  • Proceedings of the National Academy of Sciences, Vol. 107, Issue 31
  • DOI: 10.1073/pnas.1003293107

Deflation reveals dynamical structure in nondominant reaction coordinates
journal, August 2019

  • Husic, Brooke E.; Noé, Frank
  • The Journal of Chemical Physics, Vol. 151, Issue 5
  • DOI: 10.1063/1.5099194

Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction
journal, June 2006

  • Das, P.; Moll, M.; Stamati, H.
  • Proceedings of the National Academy of Sciences, Vol. 103, Issue 26
  • DOI: 10.1073/pnas.0603553103

Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
journal, June 2018

  • Wehmeyer, Christoph; Noé, Frank
  • The Journal of Chemical Physics, Vol. 148, Issue 24
  • DOI: 10.1063/1.5011399

Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification
journal, May 2013

  • Röblitz, Susanna; Weber, Marcus
  • Advances in Data Analysis and Classification, Vol. 7, Issue 2
  • DOI: 10.1007/s11634-013-0134-6

Discovery Through the Computational Microscope
journal, October 2009

PotentialNet for Molecular Property Prediction
journal, November 2018

Recent advances in machine learning towards multiscale soft materials design
journal, March 2019

  • Jackson, Nicholas E.; Webb, Michael A.; de Pablo, Juan J.
  • Current Opinion in Chemical Engineering, Vol. 23
  • DOI: 10.1016/j.coche.2019.03.005

On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation
journal, July 2015

Dynamic mode decomposition for large and streaming datasets
journal, November 2014

  • Hemati, Maziar S.; Williams, Matthew O.; Rowley, Clarence W.
  • Physics of Fluids, Vol. 26, Issue 11
  • DOI: 10.1063/1.4901016

Girsanov reweighting for path ensembles and Markov state models
journal, June 2017

  • Donati, L.; Hartmann, C.; Keller, B. G.
  • The Journal of Chemical Physics, Vol. 146, Issue 24
  • DOI: 10.1063/1.4989474

Relations Between two sets of Variates
journal, December 1936

Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses
journal, April 2012

  • Chen, Kevin K.; Tu, Jonathan H.; Rowley, Clarence W.
  • Journal of Nonlinear Science, Vol. 22, Issue 6, p. 887-915
  • DOI: 10.1007/s00332-012-9130-9

Extensions to the likelihood maximization approach for finding reaction coordinates
journal, July 2007

  • Peters, Baron; Beckham, Gregg T.; Trout, Bernhardt L.
  • The Journal of Chemical Physics, Vol. 127, Issue 3
  • DOI: 10.1063/1.2748396

Separation of a mixture of independent signals using time delayed correlations
journal, June 1994

Escaping free-energy minima
journal, September 2002

  • Laio, A.; Parrinello, M.
  • Proceedings of the National Academy of Sciences, Vol. 99, Issue 20
  • DOI: 10.1073/pnas.202427399

Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
journal, May 2005

  • Coifman, R. R.; Lafon, S.; Lee, A. B.
  • Proceedings of the National Academy of Sciences, Vol. 102, Issue 21
  • DOI: 10.1073/pnas.0500334102

Folding a small protein using harmonic linear discriminant analysis
journal, November 2018

  • Mendels, Dan; Piccini, Giovannimaria; Brotzakis, Z. Faidon
  • The Journal of Chemical Physics, Vol. 149, Issue 19
  • DOI: 10.1063/1.5053566

Tensor-based dynamic mode decomposition
journal, June 2018

Unsupervised Learning of Image Manifolds by Semidefinite Programming
journal, May 2006

  • Weinberger, Kilian Q.; Saul, Lawrence K.
  • International Journal of Computer Vision, Vol. 70, Issue 1
  • DOI: 10.1007/s11263-005-4939-z

De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets
journal, April 2017

  • Hemati, Maziar S.; Rowley, Clarence W.; Deem, Eric A.
  • Theoretical and Computational Fluid Dynamics, Vol. 31, Issue 4
  • DOI: 10.1007/s00162-017-0432-2

Adaptive biasing force method for scalar and vector free energy calculations
journal, April 2008

  • Darve, Eric; Rodríguez-Gómez, David; Pohorille, Andrew
  • The Journal of Chemical Physics, Vol. 128, Issue 14
  • DOI: 10.1063/1.2829861

Identification of slow molecular order parameters for Markov model construction
journal, July 2013

  • Pérez-Hernández, Guillermo; Paul, Fabian; Giorgino, Toni
  • The Journal of Chemical Physics, Vol. 139, Issue 1
  • DOI: 10.1063/1.4811489

Machine Learning of Coarse-Grained Molecular Dynamics Force Fields
journal, April 2019

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