Data-Driven Discrete Spatio-Temporal Models: Problems, Methods and an Arctic Sea Ice Application
Many natural phenomena are governed by forces on multiple spatial and temporal scales. Yet, it is often not a computationally feasible option to describe the intrinsically multiscale interactions via a deterministic model. Consequently, there is a need to go beyond purely deterministic modeling and...
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| Other Authors: | , , |
| Format: | Doctoral or Postdoctoral Thesis |
| Language: | English |
| Published: |
2015
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| Subjects: | |
| Online Access: | https://refubium.fu-berlin.de/handle/fub188/54 https://doi.org/10.17169/refubium-4258 https://nbn-resolving.org/urn:nbn:de:kobv:188-fudissthesis000000098296-3 |
| Summary: | Many natural phenomena are governed by forces on multiple spatial and temporal scales. Yet, it is often not a computationally feasible option to describe the intrinsically multiscale interactions via a deterministic model. Consequently, there is a need to go beyond purely deterministic modeling and to use stochastic processes to describe the unresolved scales of a system. Here the considered process is assumed to be Markovian, i.e., the state probability depends only on the previous state. Yet, the standard Markov model does not allow to incorporate external influences that drive the considered system. A modeling approach, addressing this issue, has been proposed by Illia Horenko who suggested a model ansatz that incorporates available influences and is applicable to identify time discrete Markov processes with a finite state space. The unknown model matrices can be identified by means of an available time-series via parametrization tools such as the FEM-BV clustering approach. As in most realistic applications not all relevant quantities are directly accessible; a central challenge is that such approaches are confronted with the problem of missing information from unresolved or unmeasured scales. Unfortunately, standard data-based analysis techniques often lack the option to take these missing factors into account, leading to biased and distorted results when confronted with this particular problem. As recently demonstrated by Illia Horenko in the context of modeling discrete processes, such systematically missing or implicit information can be taken into account via a non-stationary model. In this thesis, the existing Markov regression framework is extended for modeling of discrete stochastic processes with an additional spatial component. In that context, the general problem of finding an adequate data-based description of the considered spatio-temporal process in the absence of relevant information is addressed. In purely time-dependent cases, unresolved governing quantities lead to a non-stationary model ... |
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