Constructing General Partial Differential Equations using Polynomial and Neural Networks

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F16%3A86095964" target="_blank" >RIV/61989100:27240/16:86095964 - isvavai.cz</a>

Alternative codes found

RIV/61989100:27730/16:86095964

Result on the web

<a href="http://www.sciencedirect.com/science/article/pii/S0893608015001999" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0893608015001999</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.neunet.2015.10.001" target="_blank" >10.1016/j.neunet.2015.10.001</a>

Result language

angličtina

Original language name

Constructing General Partial Differential Equations using Polynomial and Neural Networks

Original language description

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

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Project

<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Neural Networks

ISSN

0893-6080

e-ISSN

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Volume of the periodical

73

Issue of the periodical within the volume

jaro

Country of publishing house

GB - UNITED KINGDOM

Number of pages

12

Pages from-to

"58-69"

UT code for WoS article

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EID of the result in the Scopus database

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