The Quasi-Linear Geostatistical Approach is a method of inverse modeling to identify parameter fields, such as the hydraulic conductivity in heterogeneous aquifers, given observations of related quantities like hydraulic heads or arrival times of tracers. Derived in the Bayesian framework, it allows to rigorously quantify the uncertainty of the identified parameter field. Since inverse modeling...

The success of an Artificial Neural Network (ANN) strongly depends on its training process. Gradient-based techniques have been satisfactorily used in the ANN training. However, in many cases, these algorithms are very slow and susceptible to the local minimum problem. In our work, we implemented a hybrid learning algorithm that integrates Genetic Algorithms(GAs) and the LevenbergMarquardt(LM) ...

Globally convergent variants of the Gauss--Newton algorithm are often methods choice to tackle nonlinear least-squares problems. Among such frameworks, Levenberg--Marquardt and trust-region two well-established, similar paradigms. Both schemes have been studied when model is replaced by a random that only accurate with given probability. Trust-region also applied problems where objective value ...

Abstract A new Levenberg–Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM have been proposed, their main differences being in choice a damping parameter. In this paper, we propose rule updating parameter so as to achieve both global and local convergence even under presence constraint set. The key our results per...

The treatment planning software TRiP98 [1, 2, 3] is successfully used in the ion therapy project at GSI. A crucial part of the treatment planning is the particle number optimization in order to achieve a target dose distribution as close as possible to the prescribed biological dose distribution. The optimization task can be expressed mathematically by the minimization of a multidimensional obj...

This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the qu...

In this paper, we propose the block-diagonal matrix to approximate the Hessian matrix in the Levenberg Mar-quardt method in the training of neural networks. Two weight updating strategies, namely asynchronous and synchronous updating methods were investigated. Asyn-chronous method updates weights of one block at a time while synchronous method updates all weights at the same time. Variations of...

In this paper, we propose a new updating rule of the LevenbergMarquardt (LM) parameter for the LM method for nonlinear equations. We show that the global complexity bound of the new LM algorithm is O( −2), that is, it requires at most O( −2) iterations to derive the norm of the gradient of the merit function below the desired accuracy . Host: Jiawang Nie Wednesday, November 1, 2017 4:00 PM AP&M...