Variational Approach to Molecular Kinetics.

By Feliks Nuske, Bettina G. Keller, G. Pérez-Hernández, A. Mey, Frank No'e. Journal of Chemical Theory and Computation, 2014

300 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/e512d983c0c05e1559a28b8f8f99af4a6b6aa93c

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In Atomic and Molecular Physics, and Optics

In Molecular Biology

Citations in the corpus

Variational Approach for Learning Markov Processes from Time Series Data (2017, methodology): “…operator is equivalent to the eigenvalue decomposition when the Markov process is time-reversible and stationary with ρ0 = ρ1, and therefore the variational principle presented here is a generalization of that developed for reversible conformation dynamics (Noé and Nüske 2013; Nüske et al. 2014).”
Data-Driven Model Reduction and Transfer Operator Approximation (2017, methodology): “2 motivates the variational approach developed in [10, 51] to maximize the Rayleigh trace restricted to some fixed space of ansatz functions: Proposition 4.”
VAMPnets for deep learning of molecular kinetics (2017, background): “In the special case where the dynamics are reversible with respect to equilibrium distribution then the theorem above specializes to variational principle for reversible Markov processes [17, 18].”
Error bounds for kernel-based approximations of the Koopman operator (2023, methodology): “Koopman methods have found widespread application in system identification [4], control [24, 42, 25, 17, 49], sensor placement [31], molecular dynamics [50, 44, 35, 36, 18, 56], and many other fields.”
Markov state models of biomolecular conformational dynamics (2014, background): “[15] discusses differences and similarities to quantum-mechanical approaches that may be exploited and applies the variational principle to the approximation of the peptide dynamics via Gaussian basis sets.”
Unsupervised Learning Methods for Molecular Simulation Data (2021, background): “142 Basis sets designed to be variationally optimized have also been developed, 330,331 and a deep learning approach to optimize this loss function was reported in ref 332.”
Constructing Markov State Models to elucidate the functional conformational changes of complex biomolecules (2018, background): “We note that MSM can also be derived from the framework of the variational principle.(57) As the kinetics of a system can be modeled by many different MSMs, one often needs to assess the quality of an MSM and select the one that best represents the original kinetics.”
Data-driven approximation of the Koopman generator: Model reduction, system identification, and control (2019, methodology): “Similar methods, developed mainly for reversible molecular dynamics problems, have been proposed in [15].”
Kinetic distance and kinetic maps from molecular dynamics simulation. (2015, methodology): “The first question has been answered: building on conformation dynamics theory [29, 28, 24, 15] it has been shown that the eigenfunctions of the backward Markov propagator underlying the MD are the optimal reaction coordinates: Projecting the dynamics upon these eigenfunctions will give rise to a ma”
On the numerical approximation of the Perron-Frobenius and Koopman operator (2015, methodology): “A similar technique has been developed in [42, 43].”