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Targeted Langevin Stabilization of Molecular Dynamics

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Targeted Langevin Stabilization of Molecular Dynamics

Qun (Marc) Ma and Jesús A. Izaguirre

Department of Computer Science and EngineeringUniversity of Notre Dame

CSE’03

February 9, 2003

Supported by:

NSF BIOCOMPLEXITY-IBN-0083653, and

NSF CAREER Award ACI-0135195

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

- Newton’s equations of motion:
- Atoms
- Molecules
- CHARMM potential(Chemistry at Harvard MolecularMechanics)
- Initial value problem
- Require correct statistics

Bonds, angles and torsions

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

- Fast/slow force splitting
- Bonded: “fast”
- Small periods

- Long range nonbonded: “slow”
- Large characteristic time

- Bonded: “fast”
- Evaluate slow forces less frequently
- Fast forces cheap
- Slow force evaluation expensive

Grubmüller,Heller, Windemuth and Schulten, 1991 Tuckerman, Berne and Martyna, 1992

- The impulse “train”

Fast impulses, t

Time, t

Slow impulses, t

How far apart can we stretch the impulse train?

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

- t ~ 100 fs if accuracy does not degenerate
- 1/10 of the characteristic time
MaIz, SIAM J. Multiscale Modeling and Simulation, 2003 (submitted)

- 1/10 of the characteristic time
- Resonances (let be the shortest period)
- Natural: t = n , n = 1, 2, 3, …
- Numerical:
- 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!

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

- Design multiscale integrators that are not limited by nonlinear and linear instabilities
- Allowing longer time steps
- Better sequential performance
- Better scaling

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

MaIz, 2003 ACM Symp. App. Comp. (SAC’03), 2002 (in press)

MaIz, SIAM J. Multiscale Modeling and Simulation, 2003 (submitted)

- TM = MOLLY + targeted Langevin coupling
- Mollified Impulse (MOLLY) to overcome linear instabilities
Izaguirre, Reich and Skeel, 1999

- Stochasticity to stabilize MOLLY
Izaguirre, Catarello, et al, 2001

- MOLLY (mollified Impulse)
- 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
- Averaging over certain time interval
- Needs analytical Hessians
- Step sizes up to 6 fs (50~100% speedup)

Vi

Vj

FRi, FDi

FRj = - FRiFDj = - FDi

- Langevin stabilization of MOLLY (LM)
Izaguirre, Catarello, et al, 2001

- 12 fs for flexible waters with correct dynamics

- Dissipative particle dynamics (DPD):
Pagonabarraga, Hagen and Frenkel, 1998

- Pair-wiseLangevin force on “particles”
- Time reversible if self-consistent

- Targeted at “trouble-making” pairs
- Bonds, angles
- Hydrogen bonds

- Stabilizing MOLLY
- Slow forces evaluated much less frequently

- Recovering correct dynamics
- Coupling coefficient small

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

- 16 fs for flexible waters
- Correct dynamics
- Self-diffusion coefficient, D.
- leapfrog w/ 1fs, D = 3.69+/-0.01
- TM w/ (16 fs, 2fs), D = 3.68+/-0.01

- Self-diffusion coefficient, D.
- Correct structure
- Radial distribution function (r.d.f.)

Fig. 4. Radial distribution function of O-H (left) and H-H (right) in flexible waters.

Front-end

libfrontend

Middle layer

libintegrators

back-end

libbase, libtopology

libparallel, libforces

Matthey, et al, ACM Tran. Math. Software (TOMS), submitted

Modular design of ProtoMol (Prototyping Molecular dynamics).

Available at http://www.cse.nd.edu/~lcls/protomol

- Background
- Classical molecular dynamics (MD)
- Multiple time stepping integrator
- Nonlinear instabilities

- Targeted MOLLY
- Objective statement
- Targeted Langevin coupling
- Results

- Acknowledgements

- People
- Dr. Jesus Izaguirre
- Dr. Robert Skeel, Univ. of Illinois at Urbana-Champaign
- Dr. Thierry Matthey, University of Bergen, Norway

- Resources
- Hydra and BOB clusters at ND
- Norwegian Supercomputing Center, Bergen, Norway

- Funding
- NSF BIOCOMPLEXITY-IBN-0083653, and
- NSF CAREER Award ACI-0135195

THE END. THANKS!

[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, Springer-Verlag, 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., 25:297-302, 1997

[8] J. A. Izaguirre, Justin M. Wozniak, Daniel P. Catarello, and Robert D. Skeel.Langevin Stabilization of Molecular Dynamics, J. Chem. Phys., 114(5):2090-2098, Feb. 1, 2001.

[9] T. Matthey and J. A. Izaguirre, ProtoMol: A Molecular Dynamics Framework with Incremental Parallelization, in Proc. of the Tenth SIAM Conf. on Parallel Processing for Scientific Computing, 2001.

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