TY - JOUR
T1 - Coarse-graining Langevin dynamics using reduced-order techniques
AU - Ma, Lina
AU - Li, Xiantao
AU - Liu, Chun
N1 - Funding Information:
The research of Li is supported by NSF Grant DMS-1522617 and DMS-1619661. The research of Liu is supported by NSF Grant DMS-1759535 and DMS-1759536.
Funding Information:
The research of Li is supported by NSF Grant DMS-1522617 and DMS-1619661 . The research of Liu is supported by NSF Grant DMS-1759535 and DMS-1759536 .
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - 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.
AB - 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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U2 - 10.1016/j.jcp.2018.11.035
DO - 10.1016/j.jcp.2018.11.035
M3 - Article
AN - SCOPUS:85060233527
VL - 380
SP - 170
EP - 190
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -