Parameter-independent model reduction of transient groundwater flow models: Application to inverse problems |
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| Institution: | 1. Department of Mathematics, Jilin University, Changchun, Jilin 130023, PR China;2. Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, Arkansas 72204, United States;1. Engineered and Geosystems Analysis, Institute for Environment, Health and Safety, Belgian Nuclear Research Centre, Belgium;2. UNIROUEN, UNIHAVRE, INSA Rouen, Normandie Université, LITIS, Rouen 76000, France;3. IREC/MIRO and ICTEAM/MLG, Université catholique de Louvain, Louvain-la-Neuve, Belgium;4. Applied and Environmental Geophysics Group, Institute of Earth Sciences, University of Lausanne, Lausanne, Switzerland |
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| Abstract: | A new methodology is proposed for the development of parameter-independent reduced models for transient groundwater flow models. The model reduction technique is based on Galerkin projection of a highly discretized model onto a subspace spanned by a small number of optimally chosen basis functions. We propose two greedy algorithms that iteratively select optimal parameter sets and snapshot times between the parameter space and the time domain in order to generate snapshots. The snapshots are used to build the Galerkin projection matrix, which covers the entire parameter space in the full model. We then apply the reduced subspace model to solve two inverse problems: a deterministic inverse problem and a Bayesian inverse problem with a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is validated with a conceptual one-dimensional groundwater flow model. We then apply the methodology to a basin-scale, conceptual aquifer in the Oristano plain of Sardinia, Italy. Using the methodology, the full model governed by 29,197 ordinary differential equations is reduced by two to three orders of magnitude, resulting in a drastic reduction in computational requirements. |
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| Keywords: | Model reduction Proper orthogonal decomposition Inverse problem Markov Chain Monte Carlo Greedy algorithm Snapshot selection |
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