Coarse-graining Langevin dynamics using reduced-order techniques

Lina Ma, Xiantao Li, Chun Liu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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
StatePublished - Mar 1 2019

All Science Journal Classification (ASJC) codes

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


Dive into the research topics of 'Coarse-graining Langevin dynamics using reduced-order techniques'. Together they form a unique fingerprint.

Cite this