2,213 research outputs found

### Iterative Updating of Model Error for Bayesian Inversion

In computational inverse problems, it is common that a detailed and accurate
forward model is approximated by a computationally less challenging substitute.
The model reduction may be necessary to meet constraints in computing time when
optimization algorithms are used to find a single estimate, or to speed up
Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use
of an approximate model introduces a discrepancy, or modeling error, that may
have a detrimental effect on the solution of the ill-posed inverse problem, or
it may severely distort the estimate of the posterior distribution. In the
Bayesian paradigm, the modeling error can be considered as a random variable,
and by using an estimate of the probability distribution of the unknown, one
may estimate the probability distribution of the modeling error and incorporate
it into the inversion. We introduce an algorithm which iterates this idea to
update the distribution of the model error, leading to a sequence of posterior
distributions that are demonstrated empirically to capture the underlying truth
with increasing accuracy. Since the algorithm is not based on rejections, it
requires only limited full model evaluations.
We show analytically that, in the linear Gaussian case, the algorithm
converges geometrically fast with respect to the number of iterations. For more
general models, we introduce particle approximations of the iteratively
generated sequence of distributions; we also prove that each element of the
sequence converges in the large particle limit. We show numerically that, as in
the linear case, rapid convergence occurs with respect to the number of
iterations. Additionally, we show through computed examples that point
estimates obtained from this iterative algorithm are superior to those obtained
by neglecting the model error.Comment: 39 pages, 9 figure

### A Model for Granular Texture with Steric Exclusion

We propose a new method to characterize the geometrical texture of a granular
packing at the particle scale including the steric hindrance effect. This
method is based on the assumption of a maximum disorder (entropy) compatible
both with strain-induced anisotropy of the contact network and steric
exclusions. We show that the predicted statistics for the local configurations
is in a fairly agreement with our numerical data.Comment: 9 pages, 5 figure

### An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems

We study Bayesian inference methods for solving linear inverse problems,
focusing on hierarchical formulations where the prior or the likelihood
function depend on unspecified hyperparameters. In practice, these
hyperparameters are often determined via an empirical Bayesian method that
maximizes the marginal likelihood function, i.e., the probability density of
the data conditional on the hyperparameters. Evaluating the marginal
likelihood, however, is computationally challenging for large-scale problems.
In this work, we present a method to approximately evaluate marginal likelihood
functions, based on a low-rank approximation of the update from the prior
covariance to the posterior covariance. We show that this approximation is
optimal in a minimax sense. Moreover, we provide an efficient algorithm to
implement the proposed method, based on a combination of the randomized SVD and
a spectral approximation method to compute square roots of the prior covariance
matrix. Several numerical examples demonstrate good performance of the proposed
method

### Electromagnetic penguin operators and direct CP violation in K --> pi l^+ l^-

Supersymmetric extensions of the Standard Model predict a large enhancement
of the Wilson coefficients of the dimension-five electromagnetic penguin
operators affecting the direct CP violation in K_L --> pi^0 e^+ e^- and the
charge asymmetry in K^\pm --> pi^\pm l^+ l^-.
Here we compute the relevant matrix elements in the chiral quark model and
compare these with the ones given by lattice calculationsComment: 12 pages, JHEP style, gluonic corrections to B_T adde

### An approach to enhance efficiency of DEM modelling of soils with crushable grains

In this study oedometric compression tests of hydrocarbon coke, Fontainebleau sand and silica sand are simulated in three dimensions using breakable particles. The method adapts a rigorous breakage criterion for elasto-brittle spheres to represent failure of grains isolated between platens or within granular masses. The breakage criterion allows for the effect of particle bulk and contact properties to be treated separately. A discrete fragmentation multigenerational approach is applied as a spawning procedure. The number of particles quickly increases during the simulation, but is kept manageable by systematic fine exclusion and upscaling. Fine exclusion leads to mass losses between generations, but that loss is accounted for outside the mechanical model. Sensitivity analysis shows that it is enough to keep 53% of the crushed particle mass within the mechanical model to correctly reproduce experimental macroscopic behaviour. Practical upscaling rules are proposed for (a) contact stiffness, (b) breakage criteria and (c) grain size distribution, and validated simulating the same test, reducing by half the initial number of particles. The results are promising as both the mechanical and grading evolution are well captured with two orders of magnitude savings in computing efficiency

### Cone penetration tests in a virtual calibration chamber

A virtual calibration chamber was built using a threedimensional model based on the discrete-element method. The chamber was then filled with a scaled granular equivalent of Ticino sand, the material properties of which were selected by curve-fitting triaxial tests. Cone penetration tests were then performed under different initial densities and isotropic stresses. Penetration resistance in the virtual calibration chamber was affected by the same cone/chamber size effect that affects physical calibration chambers and was corrected accordingly. The corrected cone resistance obtained from the virtual calibration chamber cone penetration tests shows good quantitative agreement with correlations that summarise previous physical results

### A process-based framework for digital building logbooks

Digital building logbooks (DBLs), as repositories of building lifecycle data, can contribute to improving the performance of and decisions about buildings. However, for DBL concept, its required data and the roles of various stakeholders. These are all aspects that need to be investigated. We thus propose a process-based DBL framework integrating data and stakeholder roles. This fulfils key DBL requirements and supports digitalisation of building objects. The research uses a literature review, process mapping, and a focus group to develop and validate the framework. This proposal contributes to the priority actions 1 and 2 of the European Commission’s DBL report

### Fast Gibbs sampling for high-dimensional Bayesian inversion

Solving ill-posed inverse problems by Bayesian inference has recently
attracted considerable attention. Compared to deterministic approaches, the
probabilistic representation of the solution by the posterior distribution can
be exploited to explore and quantify its uncertainties. In applications where
the inverse solution is subject to further analysis procedures, this can be a
significant advantage. Alongside theoretical progress, various new
computational techniques allow to sample very high dimensional posterior
distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior
sampler was developed for linear inverse problems with $\ell_1$-type priors. In
this article, we extend this single component Gibbs-type sampler to a wide
range of priors used in Bayesian inversion, such as general $\ell_p^q$ priors
with additional hard constraints. Besides a fast computation of the
conditional, single component densities in an explicit, parameterized form, a
fast, robust and exact sampling from these one-dimensional densities is key to
obtain an efficient algorithm. We demonstrate that a generalization of slice
sampling can utilize their specific structure for this task and illustrate the
performance of the resulting slice-within-Gibbs samplers by different computed
examples. These new samplers allow us to perform sample-based Bayesian
inference in high-dimensional scenarios with certain priors for the first time,
including the inversion of computed tomography (CT) data with the popular
isotropic total variation (TV) prior.Comment: submitted to "Inverse Problems

### The anisotropy of granular materials

The effect of the anisotropy on the elastoplastic response of two dimensional
packed samples of polygons is investigated here, using molecular dynamics
simulation. We show a correlation between fabric coefficients, characterizing
the anisotropy of the granular skeleton, and the anisotropy of the elastic
response. We also study the anisotropy induced by shearing on the subnetwork of
the sliding contacts. This anisotropy provides an explanation to some features
of the plastic deformation of granular media.Comment: Submitted to PR

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