In the context of controlling a robot arm with multiple joints, the method of estimating the joint angles from the given end-effector coordinates is called inverse kinematics, which is a type of inverse problems. Network inversion has been proposed as a method for solving inverse problems by using a multilayer neural network. In this paper, network inversion is introduced as a method to solve t...

Recently, the metric of Ky Fan was successfully applied to assess uncertainty in linear inverse problems. In this work, we present an extension of these results to nonlinear problems. More precisely, we derive results on convergence and convergence rates for Tikhonov regularization applied to nonlinear stochastic ill-posed problems, and discuss strategies to extend these local convergence resul...

The weILposedr7ess of the problems is not always guaranteed in inverse problems, unlike the forward problems. Dnts, a number of methods for giving wellposedrjess hm?e been studied in mathematical fields. In the ,field qf neural! networks, the network inversion method. for solving inverse problems was proposed; it is useflll but does not dissolute the ill-posedness of inverse problems. To overco...

In this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical Lagrange finite elements. Th...

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties, and the principled way in which the set-up can be elaborated to encompass broader features of the context, such as measurement error, indirect observation, e...

In many ill-posed problems it can be assumed that the error in the data is dominated by noise which is independent identically normally distributed. Given this assumption the residual should also be normally distributed with similar mean and variance. This idea has been used to develop three statistical diagnostic tests to constrain the region of plausible solutions. This project aims to develo...