Constructing General Partial Differential Equations using Polynomial and Neural Networks

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/61989100:27730/16:86095964

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Constructing General Partial Differential Equations using Polynomial and Neural Networks

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Constructing General Partial Differential Equations using Polynomial and Neural Networks

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Neural Networks

ISSN

0893-6080

e-ISSN

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Svazek periodika

73

Číslo periodika v rámci svazku

jaro

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

"58-69"

Kód UT WoS článku

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EID výsledku v databázi Scopus

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