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Data-driven methods for compact modeling of stochastic processes

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dc.contributor.authorJohnson, Mats S., author
dc.contributor.authorAristoff, David, advisor
dc.contributor.authorCheney, Margaret, committee member
dc.contributor.authorPinaud, Olivier, committee member
dc.contributor.authorKrapf, Diego, committee member
dc.date.accessioned2024-09-09T20:52:11Z
dc.date.available2024-09-09T20:52:11Z
dc.date.issued2024
dc.description.abstractStochastic dynamics are prevalent throughout many scientific disciplines where finding useful compact models is an ongoing pursuit. However, the simulations involved are often high-dimensional, complex problems necessitating vast amounts of data. This thesis addresses two approaches for handling such complications, coarse graining and neural networks. First, by combining Markov renewal processes with Mori-Zwanzig theory, coarse graining error can be eliminated when modeling the transition probabilities of the system. Second, instead of explicitly defining the low-dimensional approximation, using kernel approximations and a scaling matrix the appropriate subspace is uncovered through iteration. The algorithm, named the Fast Committor Machine, applies the recent Recursive Feature Machine of Radhakrishnan et al. to the committor problem using randomized numerical linear algebra. Both projects outline practical data-driven methods for estimating quantities of interest in stochastic processes that are tunable with only a few hyperparameters. The success of these methods is demonstrated numerically against standard methods on the biomolecule alanine dipeptide.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierJohnson_colostate_0053A_18514.pdf
dc.identifier.urihttps://hdl.handle.net/10217/239271
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2020-
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectcommittor
dc.subjectMarkov renewal process
dc.subjectrecursive feature machine
dc.subjectfeature machine
dc.subjectalanine dipeptide
dc.subjectMori-Zwanzig
dc.titleData-driven methods for compact modeling of stochastic processes
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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