In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as paramete...

A large number of researchers spend a lot time searching for the most efficient neural network to solve given problem. The procedure configuration, training, testing, and comparison expected performance is applied each experimental network. configuration parameters—training methods, transfer functions, hidden layers, neurons, epochs, tolerable error—have multiple possible values. Setting guidel...

Quasi-Newton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paper gives conditions under which these approximations can be proved to converge globally to the true Hessian matrix, in the case where the Symmetric Rank One update formula is used. The rate of convergence ...

We consider the problem of solving linear systems of equations with limited-memory members of the restricted Broyden class and symmetric rank-one matrices. In this paper, we present various methods for solving these linear systems, and propose a new approach based on a practical implementation of the compact representation for the inverse of these limited-memory matrices. Using the proposed app...

The preconditioned conjugate gradient (CG) method is becoming accepted as a powerful tool for solving the linear systems of equations resulting from the application of the finite element method. Applications of the non-linear algorithm are mainly confined to the diagonally scaled CG. In this study the coupling of preconditioning techniques with non-linear versions of the conjugate gradient and ...

In the article, we present the best possible parameters [Formula: see text] and [Formula: see text] on the interval [Formula: see text] such that the double inequality [Formula: see text] holds for any [Formula: see text] and all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic, geometric and special quasi-ar...

Recurrent Neural Networks (RNNs) are powerful models that achieve unparalleled performance on several pattern recognition problems. However, training of RNNs is a computationally difficult task owing to the well-known “vanishing/exploding” gradient problems. In recent years, several algorithms have been proposed for training RNNs. These algorithms either: exploit no (or limited) curvature infor...

In this paper, some meshless methods based on the local Newton basis functions are used to solve some time dependent partial differential equations. For stability reasons, used variably scaled radial kernels for constructing Newton basis functions. In continuation, with considering presented basis functions as trial functions, approximated solution functions in the event of spatial variable wit...

one of the problems that sometimes occur in gas allocation optimization is instability phenomenon. this phenomenon reduces the oil production and damages downhole and surface facilities. different works have studied the stability and suggested some solutions to override it, but most of them (such as making the well intelligent) are very expensive and thus they are not applicable to many cases. ...