A variational approach to modeling slow processes in stochastic\n dynamical systems

2012/11/29 by Frank Noé, Noé, Frank, Feliks Nüske +1 · 11 citations
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · #Chemical Physics (physics.chem-ph) #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Simulation Techniques and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1211.7103

openalex publication_date 2012/11/29 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

The slow processes of metastable stochastic dynamical systems are difficult\nto access by direct numerical simulation due the sampling problem. Here, we\nsuggest an approach for modeling the slow parts of Markov processes by\napproximating the dominant eigenfunctions and eigenvalues of the propagator. To\nthis end, a variational principle is derived that is based on the maximization\nof a Rayleigh coefficient. It is shown that this Rayleigh coefficient can be\nestimated from statistical observables that can be obtained from short\ndistributed simulations starting from different parts of state space. The\napproach forms a basis for the development of adaptive and efficient\ncomputational algorithms for simulating and analyzing metastable Markov\nprocesses while avoiding the sampling problem. Since any stochastic process\nwith finite memory can be transformed into a Markov process, the approach is\napplicable to a wide range of processes relevant for modeling complex\nreal-world phenomena.\n

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