Approximating selected non-dominant timescales by Markov state models
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We consider time-continuous, reversible Markov processes on large or continuous state space.For a practical analysis of such processes it is often necessary to construct low dimensional approximations, like Markov State Models (MSM).MSM have been used for this purpose in several applications, particularly in molecular dynamics; see [16] for an example.One of the main goals of MSMs is the correct approximation of slow processes in the system.Recently, it was possible to understand under which conditions a MSM inherits the most dominant timescales of the original Markov process [7,6].However, all rigorous statements known have yet been concerned with the approximation of the absolutely slowest processes in the system, i.e., its dominant timescales.In this article, we will show that it is also possible to design MSMs to reproduce selected non-dominant timescales and which approximation quality can be achieved.
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Selected dynamical processes of interest can be approximated to arbitrary accuracy.
“In addition, selected dynamical processes of interest can be approximated to arbitrary accuracy [9].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [9]
The Conclusion (page unavailable) says that specially designed Markov state models can approximate selected non-dominant timescales in principle. The Discussion and examples (page unavailable) makes the quality of that approximation conditional on how well an associated eigenvector can be represented; it does not establish arbitrary accuracy for selected dynamical processes generally. (LLM, conf=0.87)
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Cites
Robust Perron cluster analysis in conformation dynamics
Deuflhard, P., & Weber, M. (2005) · Linear Algebra and its Applications · doi:10.1016/j.laa.2004.10.026 · Cited by 506 · cited 1× · see citing works
“Markov State Models (MSM) have been used as finite Markov chain approximations for ergodic, time-continuous Markov processes for many years [20, 21, 22, 5, 24, 4].”
Coarse master equations for peptide folding dynamics
Buchete, N.-V., & Hummer, G. (2008) · The Journal of Physical Chemistry B · doi:10.1021/jp0761665 · Cited by 477 · see citing works
Markov state models based on milestoning
Schütte, C., Noé, F., Lu, J., Sarich, M., & Vanden-Eijnden, E. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3590108 · Cited by 228 · see citing works
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Research works printed but not linked: 7
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Markov state models of biomolecular conformational dynamics
Chodera, J. D., & Noé, F. (2014) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2014.04.002 · Cited by 776 · see citing works
Suárez, E., Wiewiora, R. P., Wehmeyer, C., Noé, F., Chodera, J. D., & Zuckerman, D. M. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c01154 · Cited by 65 · see citing works
- Authors
- Sarich, M., & Schütte, C.
- Affiliations
- Freie Universität Berlin (DE)
- ORCID
- Schütte, Christof
- Venue
- Communications in Mathematical Sciences
- Publisher
- International Press of Boston
- Published
- 2012
- Volume
- 10
- Issue
- 3
- Pages
- 1001-1013
- ISSN
- 1539-6746 (ISSN-L)
- 1945-0796
- OpenAlex
- W2033238191
- Cited by
- 17
- References
- 3
- Citations by year
- 2023: 1 · 2021: 2 · 2020: 1 · 2018: 1 · 2017: 1 · 2016: 2 · 2015: 3 · 2014: 3 · 2013: 2 · 2012: 1
- FWCI
- 2.18
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Communications in Mathematical Sciences (publishedVersion)
- Funders
- Deutsche Forschungsgemeinschaft
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Mathematical Modeling in Engineering
- Keywords
- Markov state models, slow processes, low-dimensional approximation, reversible Markov processes, continuous state spaces, molecular dynamics
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