scholarly journals Building Recurrent Neural Networks to Implement Multiple Attractor Dynamics Using the Gradient Descent Method

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Jun Namikawa ◽  
Jun Tani
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Recurrent Neural Network ◽  
Gradient Descent ◽  
Learning Algorithm ◽  
Transition Function ◽  
Descent Method ◽  
Van Der Pol Oscillator ◽  
Multiple Time ◽  
Gradient Descent Method

The present paper proposes a recurrent neural network model and learning algorithm that can acquire the ability to generate desired multiple sequences. The network model is a dynamical system in which the transition function is a contraction mapping, and the learning algorithm is based on the gradient descent method. We show a numerical simulation in which a recurrent neural network obtains a multiple periodic attractor consisting of five Lissajous curves, or a Van der Pol oscillator with twelve different parameters. The present analysis clarifies that the model contains many stable regions as attractors, and multiple time series can be embedded into these regions by using the present learning method.

scholarly journals Adaptive Natural Gradient Method for Learning of Stochastic Neural Networks in Mini-Batch Mode

2019 ◽  
Vol 9 (21) ◽  
pp. 4568
Author(s):  
Hyeyoung Park ◽  
Kwanyong Lee
Keyword(s):  
Neural Networks ◽  
Gradient Descent ◽  
Learning Algorithm ◽  
Descent Method ◽  
Benchmark Problems ◽  
Stochastic Neural Networks ◽  
Gradient Descent Method ◽  
Natural Gradient ◽  
Convergence Properties ◽  
Data Set

Gradient descent method is an essential algorithm for learning of neural networks. Among diverse variations of gradient descent method that have been developed for accelerating learning speed, the natural gradient learning is based on the theory of information geometry on stochastic neuromanifold, and is known to have ideal convergence properties. Despite its theoretical advantages, the pure natural gradient has some limitations that prevent its practical usage. In order to get the explicit value of the natural gradient, it is required to know true probability distribution of input variables, and to calculate inverse of a matrix with the square size of the number of parameters. Though an adaptive estimation of the natural gradient has been proposed as a solution, it was originally developed for online learning mode, which is computationally inefficient for the learning of large data set. In this paper, we propose a novel adaptive natural gradient estimation for mini-batch learning mode, which is commonly adopted for big data analysis. For two representative stochastic neural network models, we present explicit rules of parameter updates and learning algorithm. Through experiments on three benchmark problems, we confirm that the proposed method has superior convergence properties to the conventional methods.

scholarly journals A Pre-Trained Fuzzy Reinforcement Learning Method for the Pursuing Satellite in a One-to-One Game in Space

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2253
Author(s):  
Xiao Wang ◽  
Peng Shi ◽  
Yushan Zhao ◽  
Yue Sun
Keyword(s):  
Reinforcement Learning ◽  
Gradient Descent ◽  
Fuzzy Inference ◽  
Learning Algorithm ◽  
Control Policy ◽  
Descent Method ◽  
Gradient Descent Method ◽  
One To One ◽  
Inference Systems ◽  
First Time

In order to help the pursuer find its advantaged control policy in a one-to-one game in space, this paper proposes an innovative pre-trained fuzzy reinforcement learning algorithm, which is conducted in the x, y, and z channels separately. Compared with the previous algorithms applied in ground games, this is the first time reinforcement learning has been introduced to help the pursuer in space optimize its control policy. The known part of the environment is utilized to help the pursuer pre-train its consequent set before learning. An actor-critic framework is built in each moving channel of the pursuer. The consequent set of the pursuer is updated through the gradient descent method in fuzzy inference systems. The numerical experimental results validate the effectiveness of the proposed algorithm in improving the game ability of the pursuer.

scholarly journals IDENTIFICATION OF AREAS OF CORONAVIRUS COVID-19 INCIDENCE SPREADING BASED ON CLUSTER ANALYSIS METHOD

2021 ◽  
pp. 5-13
Author(s):  
Kseniia Bazilevych ◽  
Ievgen Meniailov ◽  
Dmytro Chumachenko
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Cluster Analysis ◽  
Data Analysis ◽  
Gradient Descent ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Adaptive Boosting ◽  
Software Product ◽  
Boosting Method

Subject: the use of the mathematical apparatus of neural networks for the scientific substantiation of anti-epidemic measures in order to reduce the incidence of diseases when making effective management decisions. Purpose: to apply cluster analysis, based on a neural network, to solve the problem of identifying areas of incidence. Tasks: to analyze methods of data analysis to solve the clustering problem; to develop a neural network method for clustering the territory of Ukraine according to the nature of the epidemic process COVID-19; on the basis of the developed method, to implement a data analysis software product to identify the areas of incidence of the disease using the example of the coronavirus COVID-19. Methods: models and methods of data analysis, models and methods of systems theory (based on the information approach), machine learning methods, in particular the Adaptive Boosting method (based on the gradient descent method), methods for training neural networks. Results: we used the data of the Center for Public Health of the Ministry of Health of Ukraine distributed over the regions of Ukraine on the incidence of COVID-19, the number of laboratory examined persons, the number of laboratory tests performed by PCR and ELISA methods, the number of laboratory tests of IgA, IgM, IgG; the model used data from March 2020 to December 2020, the modeling did not take into account data from the temporarily occupied territories of Ukraine; for cluster analysis, a neural network of 60 input neurons, 100 hidden neurons with an activation Fermi function and 4 output neurons was built; for the software implementation of the model, the programming language Python was used. Conclusions: analysis of methods for constructing neural networks; analysis of training methods for neural networks, including the use of the gradient descent method for the Adaptive Boosting method; all theoretical information described in this work was used to implement a software product for processing test data for COVID-19 in Ukraine; the division of the regions of Ukraine into zones of infection with the COVID-19 virus was carried out and a map of this division was presented.

scholarly journals Evaluation of Neural Network Model for Estimating Pile Load Capacity

2021 ◽  
Vol 21 (5) ◽  
pp. 221-228
Author(s):  
Byungsik Lee
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Load Capacity ◽  
Absolute Error ◽  
Descent Method ◽  
Training Data ◽  
Gradient Descent Method ◽  
Neural Network Models ◽  
Data Set

Neural network models based on deep learning algorithms are increasingly used for estimating pile load capacities as supplements of bearing capacity equations and field load tests. A series of hyperparameter tuning is required to improve the performance and reliability of developing a neural network model. In this study, the number of hidden layers and neurons, the activation functions, the optimizing algorithms of the gradient descent method, and the learning rates were tuned. The grid search method was applied for the tuning, which is a hyperpameter optimizer supplied by the developing platform. The cross-validation method was applied to enhance reliability for model validation. An appropriate number of epochs was determined using the early stopping method to prevent the overfitting of the model to the training data. The performance of the tuned optimum model evaluated for the test data set revealed that the model could estimate pile load capacities approximately with an average absolute error of 3,000 kN and a coefficient of determinant of 0.5.

scholarly journals An Adaptive Neural Network Controller Based on PSO and Gradient Descent Method for PMSM Speed Drive

2018 ◽  
Vol 9 (3) ◽  
pp. 1412
Author(s):  
Zribi Ali ◽  
Zaineb Frijet ◽  
Mohamed Chtourou
Keyword(s):  
Neural Network ◽  
Gradient Descent ◽  
Control Method ◽  
Speed Control ◽  
Pso Algorithm ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Adaptive Neural Network ◽  
Neural Network Controller ◽  
Network Controller

In this paper, based on the combination of particle swarm optimization (PSO) algorithm and neural network (NN), a new adaptive speed control method for a permanent magnet synchronous motor (PMSM) is proposed. Firstly, PSO algorithm is adopted to get the best set of weights of neural network controller (NNC) for accelerating the convergent speed and preventing the problems of trapping in local minimum. Then, to achieve high-performance speed tracking despite of the existence of varying parameters in the control system, gradient descent method is used to adjust the NNC parameters. The stability of the proposed controller is analyzed and guaranteed from Lyapunov theorem. The robustness and good dynamic performance of the proposed adaptive neural network speed control scheme are verified through computer simulations.

scholarly journals Vessel Track Prediction Based on Fractional Gradient Recurrent Neural Network with Maneuvering Behavior Identification

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Han Xue ◽  
Tian Chai
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Traffic Management ◽  
Descent Method ◽  
Gradient Descent Method ◽  
Ship Maneuvering ◽  
Marine Traffic ◽  
Training Error ◽  
Fractional Orders ◽  
And Training

To improve the accuracy of ship track prediction, a fractional-order gradient descent method is adopted into a recurrent neural network (RNN). The convergence of the proposed algorithm is proved. Identification of ship maneuvering behavior, atmospheric information, and oceanographic information is considered in vessel tack prediction. The ship track of Xiamen Port is predicted using the new algorithm. Error analysis is made with different factional orders and traffic busy degrees. Results show that the testing and training error differs with different fractional orders. The predicted track results can not only improve the efficiency of marine traffic management but also prevent and warn the safety accidents, so as to avoid accidents.

Wireless Brain Wave Classification for Alzheimer’s Patients via Efficient Neural Network Computation

2018 ◽  
Vol 10 (03) ◽  
pp. 1850004
Author(s):  
Grant Sheen
Keyword(s):  
Neural Network ◽  
Gradient Descent ◽  
Descent Method ◽  
Stochastic Gradient Descent ◽  
Normal Person ◽  
Gradient Descent Method ◽  
Step Size ◽  
Brain Wave ◽  
Proposed Model ◽  
Wireless Recording

Wireless recording and real time classification of brain waves are essential steps towards future wearable devices to assist Alzheimer’s patients in conveying their thoughts. This work is concerned with efficient computation of a dimension-reduced neural network (NN) model on Alzheimer’s patient data recorded by a wireless headset. Due to much fewer sensors in wireless recording than the number of electrodes in a traditional wired cap and shorter attention span of an Alzheimer’s patient than a normal person, the data is much more restrictive than is typical in neural robotics and mind-controlled games. To overcome this challenge, an alternating minimization (AM) method is developed for network training. AM minimizes a nonsmooth and nonconvex objective function one variable at a time while fixing the rest. The sub-problem for each variable is piecewise convex with a finite number of minima. The overall iterative AM method is descending and free of step size (learning parameter) in the standard gradient descent method. The proposed model, trained by the AM method, significantly outperforms the standard NN model trained by the stochastic gradient descent method in classifying four daily thoughts, reaching accuracies around 90% for Alzheimer’s patient. Curved decision boundaries of the proposed model with multiple hidden neurons are found analytically to establish the nonlinear nature of the classification.

Data-Driven Approach for Equipment Reliability Prediction Using Neural Network

2011 ◽  
Vol 411 ◽  
pp. 563-566 ◽  
Author(s):  
Feng Ding ◽  
Xing Ben Han
Keyword(s):  
Neural Network ◽  
Bp Neural Network ◽  
Gradient Descent ◽  
Optimization Theory ◽  
Descent Method ◽  
Numerical Control ◽  
Data Driven ◽  
Gradient Descent Method ◽  
Training Algorithm ◽  
Cnc Machine

BP neural network based data-driven method is proposed to predict reliability in this paper. The BP neural network prediction using Gradient Descent Method (GDM), Additional Momentum Gradient Descent Method (AMGDM) and Levenberg-Marquardt Method(L-M) based on numerical optimization theory of training algorithm are compared with different neuron number. The proposed approach is validated via age data collected from computer numerical control (CNC) machine tool in the field. The results from the proposed method show that perfect predicting performance is achieved under considering selecting suitable number of the hidden neurons and training algorithm. Remarks are outlined regarding the fact that BP neural network based on data-driven method is feasible, effective and adequate predicting accuracy can be obtained.

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