Higher-Order Neural Networks for Efficient Physics-Informed Solutions of Partial Differential Equations

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21220%2F25%3A00386097" target="_blank" >RIV/68407700:21220/25:00386097 - isvavai.cz</a>
Výsledek na webu
<a href="https://compmech.kme.zcu.cz/info_sborniky.php" target="_blank" >https://compmech.kme.zcu.cz/info_sborniky.php</a>
DOI - Digital Object Identifier
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Jazyk výsledku
angličtina
Název v původním jazyce
Higher-Order Neural Networks for Efficient Physics-Informed Solutions of Partial Differential Equations
Popis výsledku v původním jazyce
Present contribution deals with an alternative method for solving partial differential equations based on physics-informed neural networks (PINNs). A number of shallow neural networks consisting of standard perceptron network are tested and compared to networks with higher order synaptic operations (HONNs). Viscous Burgers equation is chosen as a representative example. It turns out that HONNs are able to solve the problem with order of magnitude less optimizable parameters and furthermore with higher accuracy of the solution.
Název v anglickém jazyce
Higher-Order Neural Networks for Efficient Physics-Informed Solutions of Partial Differential Equations
Popis výsledku anglicky
Present contribution deals with an alternative method for solving partial differential equations based on physics-informed neural networks (PINNs). A number of shallow neural networks consisting of standard perceptron network are tested and compared to networks with higher order synaptic operations (HONNs). Viscous Burgers equation is chosen as a representative example. It turns out that HONNs are able to solve the problem with order of magnitude less optimizable parameters and furthermore with higher accuracy of the solution.

Rok uplatnění
2025
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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