Coarse-graining Langevin dynamics using reduced-order techniques

Research output: Contribution to journalArticle

Abstract

This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The reduced models can then be directly obtained from a Galerkin projection to appropriately defined Krylov subspaces. The equivalence to a moment-matching procedure, previously implemented in [32], is proved. A particular emphasis is placed on the reduction of the stochastic noise, which is absent in many order-reduction problems. In particular, for order less than six we can show the reduced model obtained from the subspace projection automatically satisfies the fluctuation-dissipation theorem. Details for the implementations, including a bi-orthogonalization procedure and the minimization of the number of matrix multiplications, will be discussed as well.

Original languageEnglish (US)
Pages (from-to)170-190
Number of pages21
JournalJournal of Computational Physics
Volume380
DOIs
StatePublished - Mar 1 2019

Fingerprint

Langevin Dynamics
Coarse-graining
Reduced Model
Projection
Moment Matching
Reduced-order Modeling
Fluctuation-dissipation Theorem
Order Reduction
Orthogonalization
Krylov Subspace
projection
Matrix multiplication
Langevin Equation
Galerkin
Subspace
multiplication
Equivalence
equivalence
dissipation
theorems

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

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title = "Coarse-graining Langevin dynamics using reduced-order techniques",
abstract = "This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The reduced models can then be directly obtained from a Galerkin projection to appropriately defined Krylov subspaces. The equivalence to a moment-matching procedure, previously implemented in [32], is proved. A particular emphasis is placed on the reduction of the stochastic noise, which is absent in many order-reduction problems. In particular, for order less than six we can show the reduced model obtained from the subspace projection automatically satisfies the fluctuation-dissipation theorem. Details for the implementations, including a bi-orthogonalization procedure and the minimization of the number of matrix multiplications, will be discussed as well.",
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Coarse-graining Langevin dynamics using reduced-order techniques. / Ma, Lina; Li, Xiantao; Liu, Chun.

In: Journal of Computational Physics, Vol. 380, 01.03.2019, p. 170-190.

Research output: Contribution to journalArticle

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