Linear programming algorithm for neural networks

A fast and robust algorithm for training feedforward neural networks (FNNs) by using a variable forgetting factor and U-D factorization-based recursive prediction error (RPE) method is proposed. In comparison with the backpropagation (BP) and RPE based learning algorithms, the proposed algorithm, called UD-RPE, can provide much more accurate learning results in fewer iterations with fewer hidden nodes and improve convergence rate and numerical stability (robustness). In addition, it is less sensitive to start-up parameters, such as initial weights and initial covariance matrix, and the randomness in the observed data. It also has good generalization ability and needs less learning time. Simulation results of nonlinear dynamic system modeling and identification show that the algorithm proposed here is an effective and efficient learning algorithm for FNNs.

In order to solve the problem that the traditional long-term high-speed traffic forecasting algorithm is affected by the approximation ability of the function and easy to fall into the local mass value, we wrote a multivariate-based highway traffic forecasting algorithm scaling and convolutional networks. Because the feedforward wavelet neural network algorithm predicts the short-term traffic flow in different areas, it is necessary to examine the ability to predict the difference between different models. From the standard feedforward wavelet neural network algorithm using global optimization capabilities, we improve the wolf pack algorithm, improve the search accuracy of the algorithm, get the best solution of the estimated value of the work according to the search results when completing the research objectives, and get the ability to predict the work of the model. Feedforward neural network algorithm: we develop and obtain the best short-term high-speed traffic forecast values. The results are as follows: after using the author’s algorithm, the processing time increases by 1.5 seconds, but the average percentage of errors decreases by more than 50%, in fact the error and the root mean square error decreased by about 30%, and the smoothing coefficient increased by about 1%. The prediction of the author’s algorithm for short-term high-speed traffic is better than the wavelet neural network prediction algorithm, and the prediction accuracy and stability of the author’s algorithm are higher.

This paper presents the development of several efficient learning algorithms for neural networks (ELEANNE). The ELEANNE 1 and ELEANNE 2 are two recursive least-squares learning algorithms, proposed for training single-layered neural networks with analog output. This paper also proposes a new optimization strategy for training single-layered neural networks, which provides the basis for the development of a variety of efficient learning algorithms. This optimization strategy is the source of the ELEANNE 3, a second-order learning algorithm for training single-layered neural networks with binary output. A simplified version of this algorithm, called ELEANNE 4, is also derived on the basis of some simplifying but reasonable assumptions. The two algorithms developed for single-layered neural networks provide the basis for the derivation of ELEANNE 5 and ELEANNE 6, which are proposed for training multilayered neural networks with binary output. The ELEANNE 7 is an efficient algorithm developed for training multilayered neural networks with either binary or analog output. >

A new fast learning algorithm for a multilayer feedforward neural network is presented. The new algorithm, based on an innovative variable step size and gradient averaging, has excellent properties to overcome major drawbacks of the backpropagation algorithm and shows high convergence speed. The improved performance of the new algorithm in comparison with other algorithms is verified via computer simulations.

The unsteady recovery of oil and gas prices in early 2017 led to an increase in drilling and hydraulic fracturing operations in North America liquid-rich shale plays. The increasing number of producing wells, in addition to re-fractured wells, impose the need for optimizing field development strategies and shale gas supply chain networks that maximize profitability. Moreover, operators must account for undulating natural gas demands both locally and externally in a persistently low oil price environment. In this paper, we adopt supervised machine learning approaches to forecast local natural gas demand as well as guide well re-frac candidature. Both serve as critical inputs for maximizing the net present value of any shale gas field development project. An optimized water management structure is also incorporated in the proposed framework to account for associated produced-water recycling. Considering a shale gas network in the Marcellus play, supply chain optimization was achieved using a mixed integer non-linear programming formulation. The Strategic Planning model relies on at least 4 major efforts including reservoir simulation, which in turn relies on output from a feed forward Neural Network (NN) algorithm. The trained NN algorithm was deemed suitable for recommending re-frac candidates, necessary decision variables for multiphase reservoir simulation. Finally, NPV optimization relied on a four-layer Long Short-Term Memory (LSTM) recurrent neural network, developed for forecasting local shale gas demand. Both neural network algorithms were scripted using python. 17 non-redundant parameters were mined for 250 wells in the case study. The t-Distributed Stochastic Neighbor Embedding technique was used to visualize related low dimensional manifolds within the high-dimensional data set, and a NN algorithm was used to obtain probabilities of misclassification. The well-pads in the case study superstructure are modeled using compositional reservoir simulation. Each reservoir model is tuned by history matching production and pressure data for designated producing wells. Alternative field development strategies (including re-fracturing) are then simulated for a 10-year planning horizon to generate gas and water rate decline profiles. Using the LSTM developed, local gas demand is forecasted using data sets created from multivariate time-dependent local and global variables affecting shale gas demand. The LSTM algorithm is derived by convolving some features from the raw data set, with fined-tuned weights, with the objective of minimizing a pre-defined demand error function. The results obtained show that application of this integrated approach can give operators a calculated advantage, preventing erroneous feedback of project profitability but allowing early time decision-making that maximizes shale asset NPV.

In this paper a general class of fast learning algorithms for feedforward neural networks is introduced and described. The approach exploits the separability of each layer into linear and nonlinear blocks and consists of two steps. The first step is the descent of the error functional in the space of the outputs of the linear blocks (descent in the neuron space), which can be performed using any preferred optimization strategy. In the second step, each linear block is optimized separately by using a least squares (LS) criterion. To demonstrate the effectiveness of the new approach, a detailed treatment of a gradient descent in the neuron space is conducted. The main properties of this approach are the higher speed of convergence with respect to methods that employ an ordinary gradient descent in the weight space backpropagation (BP), better numerical conditioning, and lower computational cost compared to techniques based on the Hessian matrix. The numerical stability is assured by the use of robust LS linear system solvers, operating directly on the input data of each layer. Experimental results obtained in three problems are described, which confirm the effectiveness of the new method.

The convergence of a class of stochastic pseudo-gradient algorithms driven by correlated data sequences is considered in this paper. The obtained results are applied to a learning algorithm for feedforward neural networks and sufficient conditions for its convergence are determined.

Extreme learning machine (ELM) is a learning algorithm for single-hidden layer feedforward neural networks. In theory, this algorithm is able to provide good generalization capability at extremely fast learning speed. Comparative studies of benchmark function approximation problems revealed that ELM can learn thousands of times faster than conventional neural network (NN) and can produce good generalization performance in most cases. Unfortunately, the research on damage localization using ELM is limited in the literature. In this chapter, the ELM is extended to the domain of damage localization of plate structures. Its effectiveness in comparison with typical neural networks such as back-propagation neural network (BPNN) and least squares support vector machine (LSSVM) is illustrated through experimental studies. Comparative investigations in terms of learning time and localization accuracy are carried out in detail. It is shown that ELM paves a new way in the domain of plate structure health monitoring. Both advantages and disadvantages of using ELM are discussed.

Investigates linear separability in feature space from Tietze extension theorem and function approximation theory, and kernel technique is motivated theoretically. Two kernel-based algorithms are presented. One of them is a general learning algorithm for feedforward neural networks, and they can solve large-scale classification problems.

In this paper, the terminal attractor based back propagation learning algorithms for feedforward neural networks are examined. Through a rigorous mathematical analysis, a condition to guarantee the convergence of the algorithms is given. A simulation study is presented to demonstrate the effectiveness of the analysis.

A fast and robust learning algorithm for feedforward neural networks

Davidon least squares-based learning algorithm for feedforward neural networks

This paper presents an efficient learning algorithm for complex-valued feedforward neural networks with application to classification problems. It simplifies complex-valued neural networks learning by using the forward-only computation rather than traditional forward and backward computations. By incorporating the forward-only computation, the complex-valued Levenberg-Marquardt algorithm becomes more efficient. Comparison results of computation cost show that the proposed forward-only complex-valued learning algorithm can be faster than the traditional implementation of the Levenberg-Marquardt algorithm.

Many real scenarios in machine learning are non-stationary. These challenges forces to develop new algorithms that are able to deal with changes in the underlying problem to be learnt. These changes can be gradual or abrupt. As the dynamics of the changes can be different, the existing machine learning algorithms exhibit difficulties to cope with them. In this work we propose a new method, that is based in the introduction of a forgetting function in an incremental online learning algorithm for two-layer feedforward neural networks. This forgetting function gives a monotonically crescent importance to new data. Due to this fact, the network forgets in presence of changes while maintaining a stable behavior when the context is stationary. The theoretical basis for the method is given and its performance is illustrated by evaluating its behavior. The results confirm that the proposed method is able to work in evolving environments.

Presents an algorithm of dynamic node creation and weights learning for a hybrid feedforward neural network (HFNN) which consists of a linear model and a multilayer neural network. The algorithm is only based on linear least squares, and no iterative learning process is needed. According to the demand of model precision, the algorithm determines the best weights of network and the minimal number of hidden nodes automatically. Compared with the well-known backpropagation network, simulation results show that the new learning algorithm for the HFNN is efficient in model precision, rate of convergence and generalization ability.