Jacobi Neural Network Method for Solving Linear Differential-Algebraic Equations with Variable Coefficients

A novel Jacobi neural network method is proposed for solving linear differential-algebraic equations (DAEs) in the paper. First, Jacobi neural network is applied to derive the approximate solutions form of DAEs, and the loss function is constructed for DAEs based on single hidden layer Jacobi neural...

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Veröffentlicht in:Neural processing letters Jg. 53; H. 5; S. 3357 - 3374
Hauptverfasser: Liu, Hongliang, Liu, Huini, Xu, Jie, Li, Lijuan, Song, Jingwen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.10.2021
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Approximation
Artificial Intelligence
Artificial neural networks
Chebyshev approximation
Complex Systems
Computational Intelligence
Computer Science
Differential equations
Machine learning
Methods
Neural networks
Numerical analysis
Numerical methods
Ordinary differential equations
Partial differential equations
Jacobi polynomials
Neural network
Differential-algebraic equations
Extreme learning machine algorithm
Convergence
ISSN:1370-4621, 1573-773X
Online-Zugang:Volltext
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Zusammenfassung:A novel Jacobi neural network method is proposed for solving linear differential-algebraic equations (DAEs) in the paper. First, Jacobi neural network is applied to derive the approximate solutions form of DAEs, and the loss function is constructed for DAEs based on single hidden layer Jacobi neural network structure. Then, we get the optimal output weights of Jacobi neural network by applying extreme learning machine algorithm. In particular, Legendre neural network method and Chebyshev neural network method which have been widely used by scholars are special cases of Jacobi neural network method, and the numerical results of the proposed method are better than these of Legendre neural network method and Chebyshev neural network method. Furthermore, Jacobi neural network method has higher accuracy compared with the approximate analytical methods, the numerical comparison results further show the feasibility and effectiveness of the proposed method for solving the DAEs.
Bibliographie:ObjectType-Article-1
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ISSN:1370-4621
1573-773X
DOI:10.1007/s11063-021-10543-5