16,648 research outputs found
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
We introduce a derivative-free computational framework for approximating
solutions to nonlinear PDE-constrained inverse problems. The aim is to merge
ideas from iterative regularization with ensemble Kalman methods from Bayesian
inference to develop a derivative-free stable method easy to implement in
applications where the PDE (forward) model is only accessible as a black box.
The method can be derived as an approximation of the regularizing
Levenberg-Marquardt (LM) scheme [14] in which the derivative of the forward
operator and its adjoint are replaced with empirical covariances from an
ensemble of elements from the admissible space of solutions. The resulting
ensemble method consists of an update formula that is applied to each ensemble
member and that has a regularization parameter selected in a similar fashion to
the one in the LM scheme. Moreover, an early termination of the scheme is
proposed according to a discrepancy principle-type of criterion. The proposed
method can be also viewed as a regularizing version of standard Kalman
approaches which are often unstable unless ad-hoc fixes, such as covariance
localization, are implemented. We provide a numerical investigation of the
conditions under which the proposed method inherits the regularizing properties
of the LM scheme of [14]. More concretely, we study the effect of ensemble
size, number of measurements, selection of initial ensemble and tunable
parameters on the performance of the method. The numerical investigation is
carried out with synthetic experiments on two model inverse problems: (i)
identification of conductivity on a Darcy flow model and (ii) electrical
impedance tomography with the complete electrode model. We further demonstrate
the potential application of the method in solving shape identification
problems by means of a level-set approach for the parameterization of unknown
geometries
Living in an Irrational Society: Wealth Distribution with Correlations between Risk and Expected Profits
Different models to study the wealth distribution in an artificial society
have considered a transactional dynamics as the driving force. Those models
include a risk aversion factor, but also a finite probability of favoring the
poorer agent in a transaction. Here we study the case where the partners in the
transaction have a previous knowledge of the winning probability and adjust
their risk aversion taking this information into consideration. The results
indicate that a relatively equalitarian society is obtained when the agents
risk in direct proportion to their winning probabilities. However, it is the
opposite case that delivers wealth distribution curves and Gini indices closer
to empirical data. This indicates that, at least for this very simple model,
either agents have no knowledge of their winning probabilities, either they
exhibit an ``irrational'' behavior risking more than reasonable.Comment: 7 pages, 8 figure
Modelling exchange bias in core/shell nanoparticles
We present an atomistic model of a single nanoparticle with core/shell
structure that takes into account its lattice strucutre and spherical geometry,
and in which the values of microscopic parameters such as anisotropy and
exchange constants can be tuned in the core, shell and interfacial regions. By
means of Monte Carlo simulations of the hysteresis loops based on this model,
we have determined the range of microscopic parameters for which loop shifts
after field cooling can be observed. The study of the magnetic order of the
interfacial spins for different particles sizes and values of the interfacial
exchange coupling have allowed us to correlate the appearance of loop
asymmetries and vertical displacements to the existence of a fraction of
uncompensated spins at the shell interface that remain pinned during field
cycling, offering new insight on the microscopic origin of the experimental
phenomenology.Comment: 7 pages, 3 figures. Contribution presented at HMM 2007 held at Napoli
4-6 June 2007. To be published in J. Phys. Condens. Matte
Convective regularization for optical flow
We argue that the time derivative in a fixed coordinate frame may not be the
most appropriate measure of time regularity of an optical flow field. Instead,
for a given velocity field we consider the convective acceleration which describes the acceleration of objects moving according to
. Consequently we investigate the suitability of the nonconvex functional
as a regularization term for optical flow. We
demonstrate that this term acts as both a spatial and a temporal regularizer
and has an intrinsic edge-preserving property. We incorporate it into a
contrast invariant and time-regularized variant of the Horn-Schunck functional,
prove existence of minimizers and verify experimentally that it addresses some
of the problems of basic quadratic models. For the minimization we use an
iterative scheme that approximates the original nonlinear problem with a
sequence of linear ones. We believe that the convective acceleration may be
gainfully introduced in a variety of optical flow models
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