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https://dspace.ncfu.ru/handle/20.500.12258/21540
Title: | Data-Driven Discovery of Time Fractional Differential Equations |
Authors: | Alikhanov, A. A. Алиханов, А. А. |
Keywords: | Differential evolution;Fractional differential equations;Machine learning;Sparse optimization |
Issue Date: | 2022 |
Publisher: | Springer Science and Business Media Deutschland GmbH |
Citation: | Singh, A.K., Mehra, M., Alikhanov, A.A. Data-Driven Discovery of Time Fractional Differential Equations // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2022. - Том 13351 LNCS. - Стр.: 56 - 63. - DOI10.1007/978-3-031-08754-7_8 |
Series/Report no.: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
Abstract: | In the era of data abundance and machine learning technologies, we often encounter difficulties in learning data-driven discovery of hidden physics, that is, learning differential equations/fractional differential equations via data. In [1], Schaeffer proposed a machine learning algorithm to learn the differential equation via data discovery. We extend Schaeffer’s work in the case of time fractional differential equations and propose an algorithm to identify the fractional order α and discover the form of F. Furthermore, if we have prior information regarding the set in which parameters belong to have some advantages in terms of time complexity of the algorithm over Schaeffer’s work. Finally, we conduct various numerical experiments to verify the method’s robustness at different noise levels. |
URI: | http://hdl.handle.net/20.500.12258/21540 |
Appears in Collections: | Статьи, проиндексированные в SCOPUS, WOS |
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