Search results for "inverse problem"

Multilevel preconditioning and adaptive sparse solution of inverse problems

2012

Efficient Parallel Nash Genetic Algorithm for Solving Inverse Problems in Structural Engineering

2015

A parallel implementation of a game-theory based Nash Genetic Algorithm (Nash-GAs) is presented in this paper for solving reconstruction inverse problems in structural engineering. We compare it with the standard panmictic genetic algorithm in a HPC environment with up to eight processors. The procedure performance is evaluated on a fifty-five bar sized test case of discrete real cross-section types structural frame. Numerical results obtained on this application show a significant achieved increase of performance using the parallel Nash-GAs approach compared to the standard GAs or Parallel GAs.

Nonlinear Pulse Shaping in Optical Fibres with a Neural Network

2020

We use a supervised machine-learning model based on a neural network to solve the direct and inverse problems relating to the shaping of optical pulses that occurs upon nonlinear propagation in optical fibres.

A Meshfree Solver for the MEG Forward Problem

2015

Noninvasive estimation of brain activity via magnetoencephalography (MEG) involves an inverse problem whose solution requires an accurate and fast forward solver. To this end, we propose the Method of Fundamental Solutions (MFS) as a meshfree alternative to the Boundary Element Method (BEM). The solution of the MEG forward problem is obtained, via the Method of Particular Solutions (MPS), by numerically solving a boundary value problem for the electric scalar potential, derived from the quasi-stationary approximation of Maxwell’s equations. The magnetic field is then computed by the Biot-Savart law. Numerical experiments have been carried out in a realistic single-shell head geometry. The p…

Combining Biophysical Modeling and Machine Learning to Predict Location of Atrial Ectopic Triggers

2018

The search for focal ectopic activity in the atria triggered from non-standard regions can be time consuming. The use of body surface potential maps to plan the intervention can be helpful, but require an advance processing of the data, that usually involves to solve an ill-posed inverse problem. In addition, changes in maps due to pathological substrate such as fibrosis might affect the expected electrical patterns. In this work, we use a machine learning approach to relate ectopic focus activity in different atrial regions with body surface potential maps, and consider the effects of fibrosis in various densities and distributions. Results show that as fibrosis increases over 15% the syst…

Probabilistic interpretation of the Calderón problem

2017

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderon's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. This probabilistic interpretation comes in three equivalent formulations which open up novel perspectives on the classical question of unique determinability of conductivities from boundary data. We aim to make this work accessible to both readers with a background in stochastic process theory as well as researchers working on deterministic methods in inverse problems.

Optimisation non-lisse pour l'estimation de composants immunitaires cellulaires dans un environnement tumoral

2021

In this PhD proposal we will investigate new regularization methods of inverse problems that provide an absolute quantification of immune cell subpopulations. The mathematical aspect of this PhD proposal is two-fold. The first goal is to enhance the underlying linear model through a more refined construction of the expression matrix. The second goal is, given this linear model, to derive the best possible estimator. These two issues can be treated in a decoupled way, which is the standard for existing methods such as Cibersort, or as a coupled optimization problem (which is known as blind deconvolution in signal processing).

The polar method as a tool for solving inverse problems of the classical laminated plate theory

2000

Publisher Summary Fiber reinforced laminates are widely used in modem applications. For these kinds of structures, the Classical Laminated Plate Theory and its various extensions provide efficient methods for theoretical analysis, that is, when the stacking sequence, the orientations, and the properties of the individual laminas are known. For design of laminates, a very limited number of rules are available. For stiffriess design, two are currently known and used in practical applications: the Werren and Norris rule to get membrane isotropy, and the symmetrical sequence rule to suppress stretching/bending coupling. This chapter deals with the resolution of inverse problems of the Classical…

On real-time algorithms for the location search of discontinuous conductivities with one measurement

2008

We discuss, and compare, two simple methods that provide coordinates of a point in the vicinity of one inclusion within some object with homogeneous electrical properties. In the context of nondestructive testing such an inclusion may correspond to a material defect, whereas in medicine this may correspond to a lesion in the brain, to name only two possible applications. Both methods use only one pair of voltage/current measurements on the entire boundary of the object to determine a single pair of coordinates that is considered to be close to the center of the inclusion. The first method has been proposed previously by Kwon, Seo and Yoon; the second method, called here the effective dipole…

Sets of Efficiency in a Normed Space and Inner Product

1987

In a normed space X the distances to the points of a given set A being considered as the objective functions of a multicriteria optimization problem, we define four sets of efficiency (efficient, strictly efficient, weakly efficient and properly efficient points). Instead of studying properties of the sets of efficiency according to properties of the norm, we investigate an inverse problem: deduce properties of the norm of X from properties of the sets of efficiency, valid for every finite subset A of X.