13,533 research outputs found
Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario
A variety of methods is available to quantify uncertainties arising with\-in
the modeling of flow and transport in carbon dioxide storage, but there is a
lack of thorough comparisons. Usually, raw data from such storage sites can
hardly be described by theoretical statistical distributions since only very
limited data is available. Hence, exact information on distribution shapes for
all uncertain parameters is very rare in realistic applications. We discuss and
compare four different methods tested for data-driven uncertainty
quantification based on a benchmark scenario of carbon dioxide storage. In the
benchmark, for which we provide data and code, carbon dioxide is injected into
a saline aquifer modeled by the nonlinear capillarity-free fractional flow
formulation for two incompressible fluid phases, namely carbon dioxide and
brine. To cover different aspects of uncertainty quantification, we incorporate
various sources of uncertainty such as uncertainty of boundary conditions, of
conceptual model definitions and of material properties. We consider recent
versions of the following non-intrusive and intrusive uncertainty
quantification methods: arbitary polynomial chaos, spatially adaptive sparse
grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The
performance of each approach is demonstrated assessing expectation value and
standard deviation of the carbon dioxide saturation against a reference
statistic based on Monte Carlo sampling. We compare the convergence of all
methods reporting on accuracy with respect to the number of model runs and
resolution. Finally we offer suggestions about the methods' advantages and
disadvantages that can guide the modeler for uncertainty quantification in
carbon dioxide storage and beyond
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
We propose new compressive parameter estimation algorithms that make use of
polar interpolation to improve the estimator precision. Our work extends
previous approaches involving polar interpolation for compressive parameter
estimation in two aspects: (i) we extend the formulation from real non-negative
amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch
between the manifold described by the parameters and its polar approximation.
To quantify the improvements afforded by the proposed extensions, we evaluate
six algorithms for estimation of parameters in sparse translation-invariant
signals, exemplified with the time delay estimation problem. The evaluation is
based on three performance metrics: estimator precision, sampling rate and
computational complexity. We use compressive sensing with all the algorithms to
lower the necessary sampling rate and show that it is still possible to attain
good estimation precision and keep the computational complexity low. Our
numerical experiments show that the proposed algorithms outperform existing
approaches that either leverage polynomial interpolation or are based on a
conversion to a frequency-estimation problem followed by a super-resolution
algorithm. The algorithms studied here provide various tradeoffs between
computational complexity, estimation precision, and necessary sampling rate.
The work shows that compressive sensing for the class of sparse
translation-invariant signals allows for a decrease in sampling rate and that
the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal
Processing; minor edits and correction
A Multiscale Pyramid Transform for Graph Signals
Multiscale transforms designed to process analog and discrete-time signals
and images cannot be directly applied to analyze high-dimensional data residing
on the vertices of a weighted graph, as they do not capture the intrinsic
geometric structure of the underlying graph data domain. In this paper, we
adapt the Laplacian pyramid transform for signals on Euclidean domains so that
it can be used to analyze high-dimensional data residing on the vertices of a
weighted graph. Our approach is to study existing methods and develop new
methods for the four fundamental operations of graph downsampling, graph
reduction, and filtering and interpolation of signals on graphs. Equipped with
appropriate notions of these operations, we leverage the basic multiscale
constructs and intuitions from classical signal processing to generate a
transform that yields both a multiresolution of graphs and an associated
multiresolution of a graph signal on the underlying sequence of graphs.Comment: 16 pages, 13 figure
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