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 language | English (US) |
|---|---|
| Pages (from-to) | 170-190 |
| Number of pages | 21 |
| Journal | Journal of Computational Physics |
| Volume | 380 |
| DOIs | |
| State | Published - Mar 1 2019 |
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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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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 journal › Article
TY - JOUR
T1 - Coarse-graining Langevin dynamics using reduced-order techniques
AU - Ma, Lina
AU - Li, Xiantao
AU - Liu, Chun
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.
UR - http://www.scopus.com/inward/record.url?scp=85060233527&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060233527&partnerID=8YFLogxK
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 -