5 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
The sparse Polynomial Chaos expansion: a fully Bayesian approach with joint priors on the coefficients and global selection of terms
Polynomial chaos expansion (PCE) is a versatile tool widely used in
uncertainty quantification and machine learning, but its successful application
depends strongly on the accuracy and reliability of the resulting PCE-based
response surface. High accuracy typically requires high polynomial degrees,
demanding many training points especially in high-dimensional problems through
the curse of dimensionality. So-called sparse PCE concepts work with a much
smaller selection of basis polynomials compared to conventional PCE approaches
and can overcome the curse of dimensionality very efficiently, but have to pay
specific attention to their strategies of choosing training points.
Furthermore, the approximation error resembles an uncertainty that most
existing PCE-based methods do not estimate. In this study, we develop and
evaluate a fully Bayesian approach to establish the PCE representation via
joint shrinkage priors and Markov chain Monte Carlo. The suggested Bayesian PCE
model directly aims to solve the two challenges named above: achieving a sparse
PCE representation and estimating uncertainty of the PCE itself. The embedded
Bayesian regularizing via the joint shrinkage prior allows using higher
polynomial degrees for given training points due to its ability to handle
underdetermined situations, where the number of considered PCE coefficients
could be much larger than the number of available training points. We also
explore multiple variable selection methods to construct sparse PCE expansions
based on the established Bayesian representations, while globally selecting the
most meaningful orthonormal polynomials given the available training data. We
demonstrate the advantages of our Bayesian PCE and the corresponding
sparsity-inducing methods on several benchmarks
A computational approach to identifiability analysis for a model of the propagation and control of COVID-19 in Chile
A computational approach is adapted to analyze the parameter identifiability of a compartmental model. The model is intended to describe the progression of the COVID-19 pandemic in Chile during the initial phase in early 2020 when government declared quarantine measures. The computational approach to analyze the structural and practical identifiability is applied in two parts, one for synthetic data and another for some Chilean regional data. The first part defines the identifiable parameter sets when these recover the true parameters used to create the synthetic data. The second part compares the results derived from synthetic data, estimating the identifiable parameter sets from regional Chilean epidemic data. Experiments provide evidence of the loss of identifiability if some initial conditions are estimated, the period of time used to fit is before the peak, and if a significant proportion of the population is involved in quarantine periods
Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage
Benchmark datasets and executables of the paper "Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario