Browsing by Author "Leube, Philipp Christoph"

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Open Access
Methods for physically-based model reduction in time : analysis, comparison of methods and application
(2013) Leube, Philipp Christoph; Nowak, Wolfgang (Jun.-Prof. Dr.-Ing.)
Model reduction techniques are essential tools to control the overburdening costs of complex models. One branch of such techniques is the reduction of the time dimension. Major contributions to solve this task have been based on integral transformation. They have the elegant property that by choosing suitable base functions, e.g., the monomials that lead to the so-called temporal moments (TM), the dynamic model can be simulated via steady-state equations. TM allow to maintain the required accuracy of hydro(geo)logical applications (e.g., forward predictions, model calibration or parameter estimation) at a reasonably high level whilst controlling the computational demand, or, alternatively, to admit more conceptual complexity, finer resolutions or larger domains at the same computational costs, or to make brute force optimization tasks more feasible. In comparison to classical approaches of model reduction that involve orthogonal base functions, however, the base functions that lead to TM are non-orthogonal. Also, most applications involving TM used only lower-degree TM without providing reasons for their choice. This led to a number of open research questions: - Does non-orthogonality impair the quality and efficiency of TM? - Can other temporal base functions more efficiently reduce dynamic systems than the monomials that lead to TM? - How can compression efficiency associated with temporal model reduction methods be quantified and how efficiently can information be compressed? - What is the value of temporal model reduction in competition with the computational demand of other discretized or reduced model dimensions, e.g., repetitive model runs through Monte-Carlo (MC) simulations? In this work, I successfully developed tools to analyze and assess existing techniques that reduce hydro(geo)logical models in time, and answered the questions posed above. As an overall conclusion, I found that there is no way of temporal model reduction for dynamic systems based on arbitrary integral transforms with (non-)polynomial base functions that is better than the monomials leading to TM. However, the order of TM as opposed to other model dimensions (e.g., number of MC realizations) should be carefully determined prior the model evaluation. TM can help to improve highly complex systems through upscaling. Based on my findings, I hope to encourage more studies to work with the concept of TM. Especially because the number of studies found in the literature that employ TM with real data is small, more improved tests on existing data sets should be performed as proof of concept for practical applications in real world scenarios. Also, I hope to encourage those who limited their TM applications to only lower-order TM to consider a longer moment sequence. My study results specifically provide valuable advice for hydraulic tomography studies under transient conditions to use TM up to the fourth order. This might potentially alleviate the loss of accuracy used as argument against TM by certain authors.