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Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision.

ABSTRACT: Mesoscopic N-atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. A multiscale method for simulating these systems in the friction dominated regime from the underlying N-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate to coarse-grained variables constitute a stationary process on the time scale of coarse-grained dynamics. The method is demonstrated for lactoferrin, nudaurelia capensis omega virus, and human papillomavirus to assess its accuracy.

SUBMITTER: Abi Mansour A

PROVIDER: S-EPMC3985745 | biostudies-literature | 2014 Feb

REPOSITORIES: biostudies-literature

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Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision.

Abi Mansour Andrew A Ortoleva Peter J PJ

Journal of chemical theory and computation 20140109 2

Mesoscopic <i>N</i>-atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. A multiscale method for simulating these systems in the friction dominated regime from the underlying <i>N</i>-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate to coarse-grained variables constitute a stationary process on the time scale of coarse-gr ...[more]

PMID: 24803852

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Project description:Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.

Dataset Information

Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision.

Publications

Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision.

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