Dissertation
High and infinite-dimensional filtering methods
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2020
DOI:
https://doi.org/10.17918/00001089
Abstract
This thesis covers two major methods in high and infinite-dimensional filtering. The first is an iterate averaged 3DVAR filter for solving ill-posed inverse problems. The second is an implementation of weighted ensemble filtering for molecular simulation. Our new iterate-averaged filter demonstrates similar convergence to the traditional Kalman filter but is numerically, much cheaper, being more closely related to the 3DVAR filter. We will derive convergence results in mean squared error. Weighted ensemble is a variance reduction and importance sampling method. We will cover some key results related to the algorithm and implement it to obtain mean first passage time results for the alanine dipeptide molecule. We will also provide exact variance estimates for a two-step, rare-event model.
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Details
- Title
- High and infinite-dimensional filtering methods
- Creators
- Felix Gleeson Edward Jones
- Contributors
- Gideon Simpson (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- ix, 131 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991014695235804721