Solving polynomial systems using a fast adaptive back propagation-type neural network algorithm

2017 ◽  
Vol 29 (2) ◽  
pp. 301-337 ◽  
Author(s):  
K. GOULIANAS ◽  
A. MARGARIS ◽  
I. REFANIDIS ◽  
K. DIAMANTARAS
Keyword(s):  
Neural Network ◽  
Adaptive Learning ◽  
Linear Equations ◽  
Back Propagation ◽  
Polynomial Systems ◽  
Optimization Techniques ◽  
Back Propagation Algorithm ◽  
Network Activation ◽  
Non Linear ◽  
Non Linear Equations

This paper proposes a neural network architecture for solving systems of non-linear equations. A back propagation algorithm is applied to solve the problem, using an adaptive learning rate procedure, based on the minimization of the mean squared error function defined by the system, as well as the network activation function, which can be linear or non-linear. The results obtained are compared with some of the standard global optimization techniques that are used for solving non-linear equations systems. The method was tested with some well-known and difficult applications (such as Gauss–Legendre 2-point formula for numerical integration, chemical equilibrium application, kinematic application, neuropsychology application, combustion application and interval arithmetic benchmark) in order to evaluate the performance of the new approach. Empirical results reveal that the proposed method is characterized by fast convergence and is able to deal with high-dimensional equations systems.

Longitudinal Control for AUV with Self-Adaptive Learning Law

2013 ◽  
Vol 819 ◽  
pp. 259-265
Author(s):  
Xiu Jun Sun ◽  
Yan Yang
Keyword(s):  
Neural Network ◽  
Adaptive Learning ◽  
Attitude Control ◽  
Autonomous Underwater Vehicle ◽  
Linear Equations ◽  
Back Propagation ◽  
Mathematic Model ◽  
Back Propagation Algorithm ◽  
Neural Network Controller ◽  
Self Adaptive

A mini AUV (Autonomous Underwater Vehicle) with cross shaped rudders and one single thruster is presented, which features high maneuverability due to the intelligent control algorithm. A single variable PID neural network controller is also proposed, which is utilized to maintain attitude for the vehicle. In order to testify feasibility of the control methodology, a spatial motion mathematic model is constructed and linear equations that indicate the relation between attitude angles of vehicle and deflection angles of rudders is deduced firstly. Subsequently, the neural network PID controller is developed according to the deduced equations and the attitude control simulation of the vehicle with this controller is conducted. Taking actual and desired attitude angles of the vehicle as input and deflection angles of the rudders as output, this controller performs self-adaptive update for 9 synaptic weights through back-propagation algorithm and employs the converged weights to calculate the appropriate deflection angle of each rudder.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

scholarly journals Deep neural networks using a single neuron: folded-in-time architecture using feedback-modulated delay loops

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Florian Stelzer ◽  
André Röhm ◽  
Raul Vicente ◽  
Ingo Fischer ◽  
Serhiy Yanchuk
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Neural Network ◽  
Single Neuron ◽  
Deep Neural Networks ◽  
Back Propagation ◽  
Local Network ◽  
Multiple Time ◽  
Learning Tools ◽  
Back Propagation Algorithm

AbstractDeep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with multiple time-delayed feedback loops. This single-neuron deep neural network comprises only a single nonlinearity and appropriately adjusted modulations of the feedback signals. The network states emerge in time as a temporal unfolding of the neuron’s dynamics. By adjusting the feedback-modulation within the loops, we adapt the network’s connection weights. These connection weights are determined via a back-propagation algorithm, where both the delay-induced and local network connections must be taken into account. Our approach can fully represent standard Deep Neural Networks (DNN), encompasses sparse DNNs, and extends the DNN concept toward dynamical systems implementations. The new method, which we call Folded-in-time DNN (Fit-DNN), exhibits promising performance in a set of benchmark tasks.

scholarly journals Influence of hinge length and distribution number on the camber and cornering properties of a non-pneumatic tire

2020 ◽  
Vol 12 (12) ◽  
pp. 168781402098468
Author(s):  
Xianbin Du ◽  
Youqun Zhao ◽  
Yijiang Ma ◽  
Hongxun Fu
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Adaptive Learning ◽  
High Speed ◽  
Back Propagation ◽  
Lateral Force ◽  
Learning Ability ◽  
Vehicle Performance ◽  
Neural Network Theory ◽  
Bp Neural Network Model

The camber and cornering properties of the tire directly affect the handling stability of vehicles, especially in emergencies such as high-speed cornering and obstacle avoidance. The structural and load-bearing mode of non-pneumatic mechanical elastic (ME) wheel determine that the mechanical properties of ME wheel will change when different combinations of hinge length and distribution number are adopted. The camber and cornering properties of ME wheel with different hinge lengths and distributions were studied by combining finite element method (FEM) with neural network theory. A ME wheel back propagation (BP) neural network model was established, and the additional momentum method and adaptive learning rate method were utilized to improve BP algorithm. The learning ability and generalization ability of the network model were verified by comparing the output values with the actual input values. The camber and cornering properties of ME wheel were analyzed when the hinge length and distribution changed. The results showed the variation of lateral force and aligning torque of different wheel structures under the combined conditions, and also provided guidance for the matching of wheel and vehicle performance.

scholarly journals Using Artificial Neural Networks in Predicting the Level of Stress among Military Conscripts

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 626
Author(s):  
Svajone Bekesiene ◽  
Rasa Smaliukiene ◽  
Ramute Vaicaitiene
Keyword(s):  
Neural Network ◽  
Transfer Functions ◽  
Back Propagation ◽  
Armed Forces ◽  
Activation Function ◽  
Optimal Number ◽  
Ann Model ◽  
Back Propagation Algorithm ◽  
Classification Rate ◽  
Artificial Neural

The present study aims to elucidate the main variables that increase the level of stress at the beginning of military conscription service using an artificial neural network (ANN)-based prediction model. Random sample data were obtained from one battalion of the Lithuanian Armed Forces, and a survey was conducted to generate data for the training and testing of the ANN models. Using nonlinearity in stress research, numerous ANN structures were constructed and verified to limit the optimal number of neurons, hidden layers, and transfer functions. The highest accuracy was obtained by the multilayer perceptron neural network (MLPNN) with a 6-2-2 partition. A standardized rescaling method was used for covariates. For the activation function, the hyperbolic tangent was used with 20 units in one hidden layer as well as the back-propagation algorithm. The best ANN model was determined as the model that showed the smallest cross-entropy error, the correct classification rate, and the area under the ROC curve. These findings show, with high precision, that cohesion in a team and adaptation to military routines are two critical elements that have the greatest impact on the stress level of conscripts.

COMPUTING AN ADAPTIVE MESH IN FLUID PROBLEMS USING NEURAL NETWORK AND GENETIC ALGORITHM WITH ADAPTIVE RELAXATION

2008 ◽  
Vol 17 (06) ◽  
pp. 1089-1108 ◽  
Author(s):  
NAMEER N. EL. EMAM ◽  
RASHEED ABDUL SHAHEED
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Numerical Experiments ◽  
Back Propagation ◽  
Adaptive Mesh ◽  
Learning System ◽  
Back Propagation Algorithm ◽  
Adaptive Smoothing ◽  
Different Types ◽  
Optimal Values

A method based on neural network with Back-Propagation Algorithm (BPA) and Adaptive Smoothing Errors (ASE), and a Genetic Algorithm (GA) employing a new concept named Adaptive Relaxation (GAAR) is presented in this paper to construct learning system that can find an Adaptive Mesh points (AM) in fluid problems. AM based on reallocation scheme is implemented on different types of two steps channels by using a three layer neural network with GA. Results of numerical experiments using Finite Element Method (FEM) are discussed. Such discussion is intended to validate the process and to demonstrate the performance of the proposed learning system on three types of two steps channels. It appears that training is fast enough and accurate due to the optimal values of weights by using a few numbers of patterns. Results confirm that the presented neural network with the proposed GA consistently finds better solutions than the conventional neural network.

Study on the Generalized Holo-Factors Mathematical Model of Dimension-Error and Shape-Error for Sheet Metal in Stamping Based on the Back Propagation (BP) Neural Network

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Lizhi Gu ◽  
Tianqing Zheng
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Sheet Metal ◽  
Bp Neural Network ◽  
Back Propagation ◽  
Shape Error ◽  
Back Propagation Algorithm ◽  
Minor Strain ◽  
Major Strain ◽  
Forming Precision

Precision improvement in sheet metal stamping has been the concern that the stamping researchers have engaged in. In order to improve the forming precision of sheet metal in stamping, this paper devoted to establish the generalized holo-factors mathematical model of dimension-error and shape-error for sheet metal in stamping based on BP neural network. Factors influencing the forming precision of stamping sheet metal were divided, altogether ten factors, and the generalized holo-factors mathematical model of dimension-error and shape-error for sheet metal in stamping was established using the back-propagation algorithm of error based on BP neural network. The undetermined coefficients of the model previously established were soluble according to the simulation data of sheet punching combined with the specific shape based on the BP neural network. With this mathematical model, the forecast data compared with the validate data could be obtained, so as to verify the fine practicability that the previously established mathematical model had, and then, it was shown that the generalized holo-factors mathematical model of size error and shape-error had fine practicality and versatility. Based on the generalized holo-factors mathematical model of error exemplified by the cylindrical parts, a group of process parameters could be selected, in which forming thickness was between 0.713 mm and 1.335 mm, major strain was between 0.085 and 0.519, and minor strain was between −0.596 and 0.319 from the generalized holo-factors mathematical model prediction, at the same time, the forming thickness, the major strain, and the minor strain were in good condition.

Sign in / Sign up

Export Citation Format

Share Document