Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations

DOI10.1007/S00500-019-03944-1zbMath1442.65441OpenAlexW2922646101WikidataQ128205549 ScholiaQ128205549MaRDI QIDQ780292

Jianshu Luo, Yunlei Yang, Futian Weng, Muzhou Hou, Hongli Sun, Tianle Zhang

Publication date: 15 July 2020

Published in: Soft Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00500-019-03944-1

zbMATH Keywords

Legendre polynomialsPDEsIELMLegendre neural network

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical methods for partial differential equations, boundary value problems (65N99)

Related Items (6)

DeLISA: deep learning based iteration scheme approximation for solving PDEs ⋮ A matrix-eigenvalue method to compute Sturm-Liouville polynomials ⋮ The LS-SVM algorithms for boundary value problems of high-order ordinary differential equations ⋮ Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations ⋮ A novel numerical scheme for fractional differential equations using extreme learning machine ⋮ Solving partial differential equation based on extreme learning machine

Cites Work

• A first approach in solving initial-value problems in ODEs by elliptic fitting methods
• Approximating a finite element model by neural network prediction for facility optimization in groundwater engineering
• Adaptive finite element mesh triangulation using self-organizing neural networks
• Forecasting time series with optimal neural networks using multi-objective optimization algorithm based on AICc
• Solving a parabolic PDE with nonlocal boundary conditions using the sinc method
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Neural network algorithm based on Legendre improved extreme learning machine for solving elliptic partial differential equations