Study of Burgers–Huxley Equation Using Neural Network Method

The study of non-linear partial differential equations is a complex task requiring sophisticated methods and techniques. In this context, we propose a neural network approach based on Lie series in Lie groups of differential equations (symmetry) for solving Burgers–Huxley nonlinear partial different...

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Bibliographic Details
Published in:Axioms 2023-04, Vol.12 (5), p.429
Main Authors: Wen, Ying, Chaolu, Temuer
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Approximation
Artificial neural networks
Burgers–Huxley equation
Deep learning
Differential equations, Partial
Exact solutions
Keywords
Lie groups
Lie series
Machine learning
Mathematical analysis
Mathematical research
neural network method
Neural networks
Nonlinear differential equations
Numerical analysis
optimization
Ordinary differential equations
Partial differential equations
Physics
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Summary:The study of non-linear partial differential equations is a complex task requiring sophisticated methods and techniques. In this context, we propose a neural network approach based on Lie series in Lie groups of differential equations (symmetry) for solving Burgers–Huxley nonlinear partial differential equations, considering initial or boundary value terms in the loss functions. The proposed technique yields closed analytic solutions that possess excellent generalization properties. Our approach differs from existing deep neural networks in that it employs only shallow neural networks. This choice significantly reduces the parameter cost while retaining the dynamic behavior and accuracy of the solution. A thorough comparison with its exact solution was carried out to validate the practicality and effectiveness of our proposed method, using vivid graphics and detailed analysis to present the results.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12050429