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Modified Optimal Prediction and its Application to a Particle-Method Problem

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Abstract

The paper is concerned with system reduction by statistical methods and, in particular, by the optimal prediction method introduced in (Chorin, A.J., Hald, O.H., Kupferman, R., Optimal prediction with memory, Phys. D 166:239–257, 2002). The optimal prediction method deals with problems that possess large and small scales and uses the conditional expectation to model the influence of the small scales on the large ones.

In the current paper, we develop a different variant of the optimal prediction method as well as introduce and compare several approximations of this method. We apply the original and modified optimal prediction methods to a system of ODEs obtained from a particle method discretization of a hyperbolic PDE and demonstrate their performance in a number of numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Alina Chertock

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    David Gottlieb & Alex Solomonoff

Authors
  1. Alina Chertock
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  2. David Gottlieb
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  3. Alex Solomonoff
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Correspondence to Alina Chertock.

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Chertock, A., Gottlieb, D. & Solomonoff, A. Modified Optimal Prediction and its Application to a Particle-Method Problem. J Sci Comput 37, 189–201 (2008). https://doi.org/10.1007/s10915-008-9242-4

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  • DOI: https://doi.org/10.1007/s10915-008-9242-4

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