scholarly journals The Fractional Differential Polynomial Neural Network for Approximation of Functions

Entropy ◽  
2013 ◽  
Vol 15 (12) ◽  
pp. 4188-4198 ◽  
Author(s):  
Rabha Ibrahim
Keyword(s):  
Neural Network ◽  
Differential Polynomial ◽  
Approximation Of Functions ◽  
Polynomial Neural Network ◽  
Fractional Differential

scholarly journals Recognition of Generalized Patterns by a Differential Polynomial Neural Network

2012 ◽  
Vol 2 (1) ◽  
pp. 167-172 ◽  
Author(s):  
L. Zjavka
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Differential Polynomial ◽  
Use Of Data ◽  
Polynomial Neural Network ◽  
Wide Range ◽  
Pattern Similarity ◽  
Generalized Patterns ◽  
Input Variables ◽  
Parametric Polynomials

A lot of problems involve unknown data relations, identification of which can serve as a generalization of their qualities. Relative values of variables are applied in this case, and not the absolute values, which can better make use of data properties in a wide range of the validity. This resembles more to the functionality of the brain, which seems to generalize relations of variables too, than a common pattern classification. Differential polynomial neural network is a new type of neural network designed by the author, which constructs and approximates an unknown differential equation of dependent variables using special type of root multi-parametric polynomials. It creates fractional partial differential terms, describing mutual derivative changes of some variables, likewise the differential equation does. Particular polynomials catch relations of given combinations of input variables. This type of identification is not based on a whole-pattern similarity, but only to the learned hidden generalized relations of variables.

An accurate full-dimensional potential energy surface for the reaction OH + SO → H + SO2

2021 ◽  
Vol 23 (1) ◽  
pp. 487-497
Author(s):  
Jie Qin ◽  
Jun Li
Keyword(s):  
Neural Network ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Invariant Polynomial ◽  
Network Approach ◽  
Neural Network Approach ◽  
Polynomial Neural Network

An accurate full-dimensional PES for the OH + SO ↔ H + SO2 reaction is developed by the permutation invariant polynomial-neural network approach.

scholarly journals Generalization of Patterns by Identification with Polynomial Neural Network

2010 ◽  
Vol 61 (2) ◽  
pp. 120-124 ◽  
Author(s):  
Ladislav Zjavka
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Functional Dependence ◽  
Polynomial Neural Network ◽  
New Type ◽  
Input Variables ◽  
The Brain ◽  
Functional Output ◽  
Simplified Form

Generalization of Patterns by Identification with Polynomial Neural Network Artificial neural networks (ANN) in general classify patterns according to their relationship, they are responding to related patterns with a similar output. Polynomial neural networks (PNN) are capable of organizing themselves in response to some features (relations) of the data. Polynomial neural network for dependence of variables identification (D-PNN) describes a functional dependence of input variables (not entire patterns). It approximates a hyper-surface of this function with multi-parametric particular polynomials forming its functional output as a generalization of input patterns. This new type of neural network is based on GMDH polynomial neural network and was designed by author. D-PNN operates in a way closer to the brain learning as the ANN does. The ANN is in principle a simplified form of the PNN, where the combinations of input variables are missing.

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