Comptes Rendus
Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects
Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 479-503.

We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [1]. We focus here on test cases of physical interest where the dynamics of the system is modelled by the Langevin equation and is simulated using the molecular dynamics software LAMMPS. In this work, the parareal algorithm uses a family of machine-learning spectral neighbor analysis potentials (SNAP) as fine, reference, potentials and embedded-atom method potentials (EAM) as coarse potentials. We consider a self-interstitial atom in a tungsten lattice and compute the average residence time of the system in metastable states. Our numerical results demonstrate significant computational gains using the adaptive parareal algorithm in comparison to a sequential integration of the Langevin dynamics. We also identify a large regime of numerical parameters for which statistical accuracy is reached without being a consequence of trajectorial accuracy.

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DOI: 10.5802/crmeca.220
Keywords: Parallel-in-time simulation, Molecular dynamics, Adaptive algorithm, Statistical accuracy
Olga Gorynina 1, 2; Frédéric Legoll 3, 2; Tony Lelièvre 1, 2; Danny Perez 4

1 CERMICS, École des Ponts, Marne-La-Vallée, France
2 MATHERIALS project-team, Inria, Paris, France
3 Navier, École des Ponts, Univ Gustave Eiffel, CNRS, Marne-La-Vallée, France
4 Theoretical Division T-1, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects},
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Olga Gorynina; Frédéric Legoll; Tony Lelièvre; Danny Perez. Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 479-503. doi : 10.5802/crmeca.220. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.220/

[1] F. Legoll; T. Lelièvre; U. Sharma An adaptive parareal algorithm: application to the simulation of molecular dynamics trajectories, SIAM J. Sci. Comput., Volume 44 (2022) no. 1, p. B146-B176 | DOI | MR | Zbl

[2] T. Lelièvre; M. Rousset; G. Stoltz Free Energy Computations. A mathematical perspective, Imperial College Press, 2010 | DOI | Zbl

[3] B. P. Uberuaga; D. Perez Computational methods for long-timescale atomistic simulations, Handbook of Materials Modeling: Method: Theory and Modeling (W. Andreoni; S. Yip, eds.), Springer, 2020, pp. 683-688 | DOI

[4] R. J. Zamora; D. Perez; E. Martinez; B. P. Uberuaga; A. F. Voter Accelerated molecular dynamics methods in a massively parallel world, Handbook of Materials Modeling: Methods: Theory and Modeling (W. Andreoni; S. Yip, eds.), Springer, 2020, pp. 745-772 | DOI

[5] J.-L. Lions; Y. Maday; G. Turinici Résolution d’EDP par un schéma en temps pararéel (A “parareal” in time discretization of PDE’s), C. R. Acad. Sci. Paris Sér. I Math., Volume 332 (2001) no. 7, pp. 661-668 | DOI | Zbl

[6] F. Legoll; T. Lelièvre; G. Samaey A micro-macro parareal algorithm: application to singularly perturbed ordinary differential equations, SIAM J. Sci. Comput., Volume 35 (2013) no. 4, p. A1951-A1986 | DOI | MR | Zbl

[7] A. P. Thompson; H. M. Aktulga; R. Berger; D. S. Bolintineanu; W. M. Brown; P. S. Crozier; P. J. in’t Veld; A. Kohlmeyer; S. G. Moore; T. D. Nguyen; R. Shan; M. J. Stevens; J. Tranchida; C. R. Trott; S. J. Plimpton LAMMPS – a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun., Volume 271 (2022), 108171 | DOI | Zbl

[8] A. P. Thompson; L. P. Swiler; C. R. Trott; S. M. Foiles; G. J. Tucker Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials, J. Comput. Phys., Volume 285 (2015), pp. 316-330 | DOI | MR | Zbl

[9] M. S. Daw; M. I. Baskes Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B, Volume 29 (1984) no. 12, pp. 6443-6453 | DOI

[10] A. Brünger; C. L. Brooks III; M. Karplus Stochastic boundary conditions for molecular dynamics simulations of ST2 water, Chem. Phys. Lett., Volume 105 (1984) no. 5, pp. 495-500 | DOI

[11] G. Bal; Y. Maday A parareal time discretization for nonlinear PDE’s with application to the pricing of an American put, Recent developments in domain decomposition methods (L. F. Pavarino; A. Toselli, eds.) (Lecture Notes in Computational Science and Engineering), Volume 23, Springer, 2002, pp. 189-202 | DOI | Zbl

[12] M. J. Gander; S. Vandewalle Analysis of the parareal time-parallel time-integration method, SIAM J. Sci. Comput., Volume 29 (2007), pp. 556-578 | DOI | MR | Zbl

[13] M. J. Gander; T. Lunet; D. Ruprecht; R. Speck A unified analysis framework for iterative parallel-in-time algorithms, SIAM J. Sci. Comput., Volume 45 (2023) no. 5, p. A2275-A2303 | DOI | MR | Zbl

[14] M. J. Gander 50 years of time parallel time integration, Multiple Shooting and Time Domain Decomposition Methods (T. Carraro; M. Geiger; S. Körkel; R. Rannacher, eds.) (Contributions in Mathematical and Computational Sciences), Volume 9, Springer, 2015, pp. 69-114 | DOI | MR | Zbl

[15] A. Blouza; L. Boudin; S.-M. Kaber Parallel in time algorithms with reduction methods for solving chemical kinetics, Commun. Appl. Math. Comput. Sci., Volume 5 (2010) no. 2, pp. 241-263 | DOI | MR | Zbl

[16] Y. Maday Parareal in time algorithm for kinetic systems based on model reduction, High-dimensional partial differential equations in science and engineering (A. Bandrauk; M. C. Delfour; C. Le Bris, eds.) (CRM Proceedings & Lecture Notes), Volume 41, American Mathematical Society, 2007, pp. 183-194 | MR | Zbl

[17] S. Engblom Parallel in time simulation of multiscale stochastic chemical kinetics, Multiscale Model. Simul., Volume 8 (2009), pp. 46-68 | DOI | MR | Zbl

[18] X. Dai; C. Le Bris; F. Legoll; Y. Maday Symmetric parareal algorithms for Hamiltonian systems, ESAIM, Math. Model. Numer. Anal., Volume 47 (2013) no. 3, pp. 717-742 | DOI | Numdam | MR | Zbl

[19] X. Dai; Y. Maday Stable parareal in time method for first- and second-order hyperbolic systems, SIAM J. Sci. Comput., Volume 35 (2013) no. 1, p. A52-A78 | DOI | MR | Zbl

[20] G. Bal Parallelization in time of (stochastic) ordinary differential equations (Preprint available at https://www.stat.uchicago.edu/~guillaumebal/PAPERS/paralleltime.pdf)

[21] G. Pagès; O. Pironneau; G. Sall The parareal algorithm for American options, C. R. Acad. Sci. Paris Sér. I Math., Volume 354 (2016) no. 11, pp. 1132-1138 | DOI | Numdam | MR | Zbl

[22] F. Legoll; T. Lelièvre; K. Myerscough; G. Samaey Parareal computation of stochastic differential equations with time-scale separation: a numerical convergence study, Comput. Vis. Sci., Volume 23 (2020), 9 | DOI | MR | Zbl

[23] I. Garrido; M. Espedal; G. Fladmark A convergent algorithm for time parallelization applied to reservoir simulation, Domain decomposition methods in science and engineering (R. Kornhuber; R. Hoppe; J. Périaux; O. Pironneau; O. Widlund; J. Xu, eds.) (Lecture Notes in Computational Science and Engineering), Volume 40, Springer, 2005, pp. 469-476 | DOI | MR | Zbl

[24] C. Farhat; M. Chandesris Time-decomposed parallel time-integrators: theory and feasibility studies for fluid, structure, and fluid–structure applications, Int. J. Numer. Methods Eng., Volume 58 (2003) no. 9, pp. 1397-1434 | DOI | MR | Zbl

[25] M. Gaja; O. Gorynina Parallel in time algorithms for nonlinear iterative methods, ESAIM, Proc. Surv., Volume 63 (2018), pp. 248-257 | DOI | MR | Zbl

[26] Y. Maday; O. Mula An adaptive parareal algorithm, J. Comput. Appl. Math., Volume 377 (2020), 112915 | DOI | MR | Zbl

[27] P. L’Ecuyer; D. Munger; B. Oreshkin; R. Simard Random numbers for parallel computers: Requirements and methods, with emphasis on GPUs, Math. Comput. Simul., Volume 135 (2017), pp. 3-17 | DOI | MR | Zbl

[28] A. Stukowski Visualization and analysis of atomistic simulation data with OVITO – the Open Visualization Tool, Model. Simul. Mat. Sci. Eng., Volume 18 (2010) no. 1, 015012 | DOI

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