Application of Generalized Finite Difference Method and Radial Basis Function Neural Networks in Solving Inverse Problems of Surface Anomalous Diffusion
In this study, a new hybrid method based on the generalized finite difference method (GFDM) and radial basis function (RBF) neural network technologies is developed to solve the inverse problems of surface anomalous diffusion. Specifically, the GFDM is utilized to compute the time-fractional derivat...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/30/1/7 |
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| Summary: | In this study, a new hybrid method based on the generalized finite difference method (GFDM) and radial basis function (RBF) neural network technologies is developed to solve the inverse problems of surface anomalous diffusion. Specifically, the GFDM is utilized to compute the time-fractional derivative model on the surface, whereas RBF neural networks are employed to invert the diffusion coefficient, source term coefficient, and the fractional order within the anomalous diffusion equation governing the surface. The results of four examples show that for the three parameters of diffusion coefficient, source term coefficient, and fractional order, the errors of inversion results are in the order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> under different conditions. Therefore, this method can obtain the required parameters quickly and accurately under different conditions. |
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| ISSN: | 1300-686X 2297-8747 |