https://doi.org/10.1140/epjp/s13360-024-04897-7
Regular Article
A new algorithm for solving nonlinear parabolic equations using extreme learning machine method with parameter retention
School of Mathematics and Statistics, Central South University, Lushan Road, 410083, Changsha, Hunan, China
Received:
11
October
2023
Accepted:
12
January
2024
Published online:
1
February
2024
This paper proposes a new iterative method using extreme learning machine (ELM) to solve nonlinear parabolic equations. Unlike feedforward neural networks, ELM does not require training a large number of parameters, but only needs to calculate the pseudo-inverse of the matrix, reducing a significant amount of computation time. The important step of the new iterative method is to first use supervised learning to obtain the initial conditions of the discretized partial differential equation and then continue to calculate the differential operator while retaining the parameters. Finally, the finite difference method is used for iterative solution in time. The key difference here is that the parameters of the ELM are retained throughout the entire process and do not need to be updated. The feasibility of our method is verified by applying it to two nonlinear parabolic equations.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.