کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4967890 | 1449387 | 2016 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A Bayesian approach to multiscale inverse problems with on-the-fly scale determination
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کلمات کلیدی
بیزی، مدل سازی چند بعدی، مشکلات معکوس، موجک، تجزیه و تحلیل چندگانه، سلسله مراتبی مونت کارلو توزیع، جریان دارسی نفوذپذیری، سازگاری جریان آب زیرزمینی بیضویان بیضوی،
Elliptic PDEs - PDE های بیضویBayesian - بیزیMulti-resolution analysis - تجزیه و تحلیل چند رزولوشنSequential Monte Carlo - تصادفی مونت کارلوGroundwater flow - جریان آب زیرزمینیDarcy flow - جریان دارسیAdaptive - سازگاریHierarchical - سلسله مراتبیMultiscale modeling - مدل سازی چند بعدیInverse problems - مسایل معکوسWavelet - موجکPermeability - نفوذپذیری
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
A Bayesian computational approach is presented to provide a multi-resolution estimate of an unknown spatially varying parameter from indirect measurement data. In particular, we are interested in spatially varying parameters with multiscale characteristics. In our work, we consider the challenge of not knowing the characteristic length scale(s) of the unknown a priori, and present an algorithm for on-the-fly scale determination. Our approach is based on representing the spatial field with a wavelet expansion. Wavelet basis functions are hierarchically structured, localized in both spatial and frequency domains and tend to provide sparse representations in that a large number of wavelet coefficients are approximately zero. For these reasons, wavelet bases are suitable for representing permeability fields with non-trivial correlation structures. Moreover, the intra-scale correlations between wavelet coefficients form a quadtree, and this structure is exploited to identify additional basis functions to refine the model. Bayesian inference is performed using a sequential Monte Carlo (SMC) sampler with a Markov Chain Monte Carlo (MCMC) transition kernel. The SMC sampler is used to move between posterior densities defined on different scales, thereby providing a computationally efficient method for adaptive refinement of the wavelet representation. We gain insight from the marginal likelihoods, by computing Bayes factors, for model comparison and model selection. The marginal likelihoods provide a termination criterion for our scale determination algorithm. The Bayesian computational approach is rather general and applicable to several inverse problems concerning the estimation of a spatially varying parameter. The approach is demonstrated with permeability estimation for groundwater flow using pressure sensor measurements.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 326, 1 December 2016, Pages 115-140
Journal: Journal of Computational Physics - Volume 326, 1 December 2016, Pages 115-140
نویسندگان
Louis Ellam, Nicholas Zabaras, Mark Girolami,