Uncertainty quantification in MD simulations. Part I: Forward propagation

Multiscale Modeling and Simulation

Volumn 10, Issue 4, 2012, Pages 1428-1459

  Rizzi, F ^a   Najm, H N ^b   Debusschere, B J ^b   Sargsyan, K ^b   Salloum, M ^b   Adalsteinsson, H ^b   Knio, O M ^a,c  

^a Johns Hopkins University   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

^c Duke University   (United States)

Author keywords

Adaptive sampling; Bayesian inference; Molecular dynamics; Polynomial chaos; TIP4P water; Uncertainty quantification

Indexed keywords

ADAPTIVE SAMPLING; AMBIENT CONDITIONS; ATOMISTIC SYSTEM; BAYESIAN INFERENCE; BULK WATER; FORWARD PROPAGATION; INTRINSIC NOISE; MD SIMULATION; MOLECULAR DYNAMICS SIMULATIONS; NON-INTRUSIVE; PARAMETER SPACES; PARAMETRIC UNCERTAINTIES; POLYNOMIAL CHAOS; SMOOTHNESS CONDITIONS; SPECTRAL PROJECTIONS; THERMAL FLUCTUATIONS; UNCERTAINTY QUANTIFICATIONS; UNIFORM RANDOM VARIABLES;

BAYESIAN NETWORKS; FORECASTING; INFERENCE ENGINES;

MOLECULAR DYNAMICS;

EID: 84871838673     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/110853169     Document Type: Article

References (49)

1. H. Adalsteinsson, B. J. Debusschere, K. R. Long, and H. N. Najm, Components for atomistic-to-continuum multiscale modeling of flow in micro-and nanofluidic systems, Sci. Program., 16 (2008), pp. 297-313.
2. C. Andrieu and E. Moulines, On the ergodicity properties of some adaptive MCMC algorithms, Ann. Appl. Probab., 16 (2006), pp. 1462-1505.
3. Y. F. Atchadé and J. S. Rosenthal, On adaptive Markov chain Monte Carlo algorithms, Bernoulli, 11 (2005), pp. 815-828.
4. H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, The missing term in effective pair potentials, J. Phys. Chem., 91 (1987), pp. 6269-6271.
5. J. F. Bourgat, P. Le Tallec, and M. Tidriri, Coupling Boltzmann and Navier-Stokes equations by friction, J. Comput. Phys., 127 (1996), pp. 227-245.
6. K. A. Dill and S. Bromberg, Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology, Garland Science, New York, 2003.
7. A. Donev, J. B. Bell, A. L. Garcia, and B. J. Alder, A hybrid particle-continuum method for hydrodynamics of complex fluids, Multiscale Model. Simul., 8 (2010), pp. 871-911.
8. A. Einstein, Investigations on the Theory of the Brownian Movement, Dover, New York, 1956.
9. L. Fejér, On the infinite sequences arising in the theories of harmonic analysis, of interpola-tion, and of mechanical quadratures, Bull. Amer. Math. Soc., 39 (1933), pp. 521-534.
10. R. G. Ghanem and A. Doostan, On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data, J. Comput. Phys., 217 (2006), pp. 63-81.
11. R. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York, 1991.
12. H. Haario, E. Saksman, and J. Tamminen, An adaptive Metropolis algorithm, Bernoulli, 7 (2001), pp. 223-242.
13. N. Hadjiconstantinou and A. T. Patera, Heterogeneous atomistic-continuum representation for dense fluid systems, Int. J. Mod. Phys., C8 (1997), pp. 967-976.
14. N. G. Hadjiconstantinou, Hybrid atomistic-continuum formulations and the moving contactline problem, J. Comput. Phys., 154 (1999), pp. 245-265.
15. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles, Taylor & Francis, New York, 1989.
16. W. G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A (3), 31 (1985), pp. 1695-1697.
17. H. W. Horn, W. C. Swope, and J. W. Pitera, Characterization of the TIP4P-Ew water model: Vapor pressure and boiling point, J. Chem. Phys., 123 (2005), 194504.
18. H. W. Horn, W. C. Swope, J. W. Pitera, J. D. Madura, T. J. Dick, G. L. Hura, and T. H. Gordon, Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew, J. Chem. Phys., 120 (2004), pp. 9665-9678.
19. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, Comparison of simple potential functions for simulating liquid water, J. Chem. Phys., 79 (1983), pp. 926-935.
20. W. L. Jorgensen and J. D. Madura, Temperature and size dependence for Monte Carlo simulations of TIP4P water, Mol. Phys., 56 (1985), pp. 1381-1392.
21. LAMMPS (Large-Scale Atomic/Molecular Massively Parallel Simulator), http://lammps. sandia.gov.
22. O. P. Le Maître and O. M. Knio, Spectral Methods for Uncertainty Quantification, Springer, New York, 2010.
23. O. P. Le Maître, M. T. Reagan, H. N. Najm, R. G. Ghanem, and O. M. Knio, A stochastic projection method for fluid flow. II. Random process, J. Comput. Phys., 181 (2002), pp. 9-44.
24. J. Li, D. Liao, and S. Yip, Coupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator, Phys. Rev. E (3), 57 (1998), pp. 7259-7267.
25. J. Liu, S. Chen, X. Nie, and M. O. Robbins, A continuum-atomistic simulation of heat transfer in micro-and nano-flows, J. Comput. Phys., 227 (2007), pp. 279-291.
26. M.W. Mahoney and W. L. Jorgensen, A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions, J. Chem. Phys., 112 (2000), pp. 8910-8922.
27. K. M. Mohamed and A. A. Mohamad, A review of the development of hybrid atomisticcontinuum methods for dense fluids, Microfluid. Nanofluid., 8 (2010), pp. 283-302.
28. X. B. Nie, S. Y. Chen, W. N. E, and M. O. Robbins, A continuum and molecular dynamics hybrid method for micro-and nano-fluid flow, J. Fluid Mech., 500 (2004), pp. 55-64.
29. S. Nosé, A molecular dynamics method for simulations in the canonical ensemble, Mol. Phys., 52 (1984), pp. 255-268.
30. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys., 81 (1984), pp. 511-519.
31. S. T. O'Connell and P. A. Thompson, Molecular dynamics-continuum hybrid computations: A tool for studying complex fluid flows, Phys. Rev. E (3), 52 (1995), pp. R5792-R5795.
32. M. Parrinello and A. Rahman, Crystal structure and pair potentials: A molecular-dynamics study, Phys. Rev. Lett., 45 (1980), pp. 1196-1199.
33. M. Parrinello and A. Rahman, Polymorphic transitions in single crystals: A new molecular dynamics method, J. Appl. Phys., 52 (1981), pp. 7182-7190.
34. R. K. Pathria, Statistical Mechanics, Elsevier, Amsterdam, 1996.
35. S. J. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys., 117 (1995), pp. 1-19.
36. M. T. Reagan, H. N. Najm, R. G. Ghanem, and O. M. Knio, Uncertainty quantification in reacting flow simulations through non-intrusive spectral projection, Combust. Flame, 132 (2003), pp. 545-555.
37. J. R. Reimers, R. O. Watts, and M. L. Klein, Intermolecular potential functions and the properties of water, Chem. Phys., 64 (1982), pp. 95-114.
38. S. W. Rick, S. J. Stuart, and B. J. Berne, Dynamical fluctuating charge force fields: Application to liquid water, J. Chem. Phys., 101 (1994), pp. 6141-6156.
39. G. O. Roberts and J. S. Rosenthal, Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms, J. Appl. Probab., 44 (2007), pp. 458-475.
40. G. O. Roberts and J. S. Rosenthal, Examples of adaptive MCMC, J. Comput. Graph. Statist., 18 (2009), pp. 349-367.
41. R. E. Rudd and J. Q. Broughton, Concurrent coupling of length scales in solid state systems, Phys. Status Solidi (B), 217 (2000), pp. 251-291.
42. M. Salloum, K. Sargsyan, R. Jones, B. Debusschere, H. N. Najm, and H. Adalsteinsson, A stochastic multiscale coupling scheme to account for sampling noise in atomistic-tocontinuum simulations, Multiscale Model. Simul., 10 (2012), pp. 550-584.
43. K. Sargsyan, B. Debusschere, H. N. Najm, and Y. Marzouk, Bayesian inference of spectral expansions for predictability assessment in stochastic reaction networks, J. Comput. Theor. Nanosci., 6 (2009), pp. 2283-2297.
44. D. S. Sivia, Data Analysis: A Bayesian Tutorial, Oxford Sci. Publ., Oxford University Press, Oxford, UK, 2006.
45. S. Tiwari, Coupling of the Boltzmann and Euler equations with automatic domain decomposition, J. Comput. Phys., 144 (1998), pp. 710-726.
46. M. Von Smoluchowski, Zur kinetischen theorie der brownschen molekularbewegung und der suspensionen, Ann. der Physik, 326 (1906), pp. 756-780.
47. N. Wiener, The homogeneous chaos, Amer. J. Math., 60 (1938), pp. 897-936.
48. H. S. Wijesinghe, R. D. Hornung, A. L. Garcia, and N. G. Hadjiconstantinou, Threedimensional hybrid continuum-atomistic simulations for multiscale hydrodynamics, J. Fluid Eng., 126 (2004), pp. 768-777.
49. D. Xiu and G. E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24 (2002), pp. 619-644.