Transcript Verlet-I/r-RESPA/Impulse is Limited by Nonlinear Instabilty

Targeted Langevin Stabilization
of Molecular Dynamics
Qun (Marc) Ma and Jesús A. Izaguirre
Department of Computer Science and Engineering
University of Notre Dame
CSE’03
February 9, 2003
Supported by:
NSF BIOCOMPLEXITY-IBN-0083653, and
NSF CAREER Award ACI-0135195
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Overview
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Background
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Targeted MOLLY
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Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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Overview
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Background
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Targeted MOLLY
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Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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Classical molecular dynamics
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Newton’s equations of motion:
Mq ''  U (q)  F(q). - - - (1)
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Atoms
Molecules
CHARMM potential
(Chemistry at Harvard Molecular Mechanics)
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Initial value problem
Require correct statistics
Bonds, angles and torsions
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Overview
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Background
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Targeted MOLLY
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Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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Multiple time stepping
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Fast/slow force splitting
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Bonded: “fast”
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Long range nonbonded: “slow”
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Small periods
Large characteristic time
Evaluate slow forces less frequently
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Fast forces cheap
Slow force evaluation expensive
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The Impulse integrator
Grubmüller,Heller, Windemuth and Schulten, 1991
Tuckerman, Berne and Martyna, 1992
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The impulse “train”
Fast impulses, t
Time, t
Slow impulses, t
How far apart can we stretch the impulse train?
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Overview
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Background
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Targeted MOLLY
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Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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Stretching slow impulses
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t ~ 100 fs if accuracy does not degenerate
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1/10 of the characteristic time
MaIz, SIAM J. Multiscale Modeling and Simulation, 2003 (submitted)
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Resonances (let  be the shortest period)
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Natural: t = n , n = 1, 2, 3, …
Numerical:
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Linear: t = /2
Nonlinear: t = /3
MaIS_a, SIAM J. on Sci. Comp. (SISC), 2002 (in press)
MaIS_b, 2003 ACM Symp. App. Comp. (SAC’03), 2002 (in press)
MTS limited by instabilities, not acuracy!
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Overview
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Background
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Targeted MOLLY
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Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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Objective statement
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Design multiscale integrators that are
not limited by nonlinear and linear
instabilities
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Allowing longer time steps
Better sequential performance
Better scaling
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Overview
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Background
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Targeted MOLLY
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Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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Targeted MOLLY (TM)
MaIz, 2003 ACM Symp. App. Comp. (SAC’03), 2002 (in press)
MaIz, SIAM J. Multiscale Modeling and Simulation, 2003 (submitted)
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TM = MOLLY + targeted Langevin coupling
Mollified Impulse (MOLLY) to overcome
linear instabilities
Izaguirre, Reich and Skeel, 1999
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Stochasticity to stabilize MOLLY
Izaguirre, Catarello, et al, 2001
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Mollified Impulse (MOLLY)
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MOLLY (mollified Impulse)
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Slow potential at time averaged positions, A(x)
Averaging using only fastest forces
Mollified slow force = Ax(x) F(A(x))
Equilibrium and B-spline
B-spline MOLLY
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Averaging over certain time interval
Needs analytical Hessians
Step sizes up to 6 fs (50~100% speedup)
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Introducing stochasticity
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Langevin stabilization of MOLLY (LM)
Izaguirre, Catarello, et al, 2001
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12 fs for flexible waters with correct dynamics
Dissipative particle dynamics (DPD):
Pagonabarraga, Hagen and Frenkel, 1998
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Pair-wise Langevin force on “particles”
Time reversible if self-consistent
Vi
FRi, FDi
Vj
FRj = - FRi
FDj = - FDi
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Targeted Langevin coupling
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Targeted at “trouble-making” pairs
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Stabilizing MOLLY
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Bonds, angles
Hydrogen bonds
Slow forces evaluated much less frequently
Recovering correct dynamics
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Coupling coefficient small
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Overview
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Background
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Targeted MOLLY
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Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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TM: main results
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16 fs for flexible waters
Correct dynamics
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Self-diffusion coefficient, D.
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leapfrog w/ 1fs,
D = 3.69+/-0.01
TM w/ (16 fs, 2fs), D = 3.68+/-0.01
Correct structure
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Radial distribution function (r.d.f.)
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TM: correct r.d.f.
Fig. 4. Radial distribution function of O-H (left) and H-H (right) in flexible waters.
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ProtoMol: the framework for MD
Matthey, et al, ACM Tran. Math. Software (TOMS), submitted
Front-end
Middle layer
back-end
libfrontend
libintegrators
libbase, libtopology
libparallel, libforces
Modular design of ProtoMol (Prototyping Molecular dynamics).
Available at http://www.cse.nd.edu/~lcls/protomol
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Overview

Background




Targeted MOLLY




Classical molecular dynamics (MD)
Multiple time stepping integrator
Nonlinear instabilities
Objective statement
Targeted Langevin coupling
Results
Acknowledgements
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Acknowledgements
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People
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Resources
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Dr. Jesus Izaguirre
Dr. Robert Skeel, Univ. of Illinois at Urbana-Champaign
Dr. Thierry Matthey, University of Bergen, Norway
Hydra and BOB clusters at ND
Norwegian Supercomputing Center, Bergen, Norway
Funding
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NSF BIOCOMPLEXITY-IBN-0083653, and
NSF CAREER Award ACI-0135195
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THE END.
THANKS!
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Key references
[1] J. A. Izaguirre, Q. Ma, T. Matthey, et al. Overcoming instabilities in Verlet-I/r-RESPA
with the mollified impulse method. In T. Schlick and H. H. Gan, editors, Proceedings of
the 3rd International Workshop on Algorithms for Macromolecular Modeling, Vol. 24
of Lecture Notes in Computational Science and Engineering, pages 146-174, SpringerVerlag, Berlin, New York, 2002
[2] Q. Ma, J. A. Izaguirre, and R. D. Skeel. Verlet-I/r-RESPA/Impulse is limited by
nonlinear instability. Accepted by the SIAM Journal on Scientific Computing, 2002.
Available at http://www.nd.edu/~qma1/publication_h.html.
[3] Q. Ma and J. A. Izaguirre. Targeted mollified impulse method for molecular dynamics.
Submitted to the SIAM Journal on Multiscale Modeling and Simulation, 2003.
[4] T. Matthey, T. Cickovski, S. Hampton, A. Ko, Q. Ma, T. Slabach and J. Izaguirre.
PROTOMOL, an object-oriented framework for prototyping novel applications of
molecular dynamics. Submitted to the ACM Transactions on Mathematical Software
(TOMS), 2003.
[5] Q. Ma, J. A. Izaguirre, and R. D. Skeel. Nonlinear instability in multiple time stepping
molecular dynamics. Accepted by the 2003 ACM Symposium on Applied Computing
(SAC’03). Melborne, Florida. March 2003
[6] Q. Ma and J. A. Izaguirre. Long time step molecular dynamics using targeted Langevin
Stabilization. Accepted by the 2003 ACM Symposium on Applied Computing (SAC’03).
Melborne, Florida. March 2003
[7] M. Zhang and R. D. Skeel. Cheap implicit symplectic integrators. Appl. Num. Math.,
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Other references
[8] J. A. Izaguirre, Justin M. Wozniak, Daniel P. Catarello, and Robert D. Skeel. Langevin
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Computing, 2001.
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Other references (cont.)
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analysis and applications to Newtonian and Langevin dynamics. J. Chem. Phys., 1997.
[17] I. Pagonabarraga, M. H. J. Hagen and D. Frenkel. Self-consistent dissipative particle dynamics
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