Data-Driven Discovery of Time Fractional Differential Equations

Abhishek Kumar Singh; Mani Mehra; Anatoly A. Alikhanov

doi:10.1007/978-3-031-08754-7_8

Data-Driven Discovery of Time Fractional Differential Equations

Abhishek Kumar Singh
, Mani Mehra^*
, Anatoly A. Alikhanov

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

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.

Original language	English
Title of host publication	Computational Science - ICCS 2022, 22nd International Conference, Proceedings
Editors	Derek Groen, Clélia de Mulatier, Valeria V. Krzhizhanovskaya, Peter M.A. Sloot, Maciej Paszynski, Jack J. Dongarra
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	56-63
Number of pages	8
ISBN (Print)	9783031087530
DOIs	https://doi.org/10.1007/978-3-031-08754-7_8
State	Published - 2022
Externally published	Yes
Event	22nd Annual International Conference on Computational Science, ICCS 2022 - London, United Kingdom Duration: 21 Jun 2022 → 23 Jun 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13351 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	22nd Annual International Conference on Computational Science, ICCS 2022
Country/Territory	United Kingdom
City	London
Period	21/06/22 → 23/06/22

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Differential evolution
Fractional differential equations
Machine learning
Sparse optimization

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-08754-7_8

Cite this

Singh, A. K., Mehra, M., & Alikhanov, A. A. (2022). Data-Driven Discovery of Time Fractional Differential Equations. In D. Groen, C. de Mulatier, V. V. Krzhizhanovskaya, P. M. A. Sloot, M. Paszynski, & J. J. Dongarra (Eds.), Computational Science - ICCS 2022, 22nd International Conference, Proceedings (pp. 56-63). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13351 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-08754-7_8

Singh, Abhishek Kumar ; Mehra, Mani ; Alikhanov, Anatoly A. / Data-Driven Discovery of Time Fractional Differential Equations. Computational Science - ICCS 2022, 22nd International Conference, Proceedings. editor / Derek Groen ; Clélia de Mulatier ; Valeria V. Krzhizhanovskaya ; Peter M.A. Sloot ; Maciej Paszynski ; Jack J. Dongarra. Springer Science and Business Media Deutschland GmbH, 2022. pp. 56-63 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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{\textquoteright}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{\textquoteright}s work. Finally, we conduct various numerical experiments to verify the method{\textquoteright}s robustness at different noise levels.",

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author = "Singh, \{Abhishek Kumar\} and Mani Mehra and Alikhanov, \{Anatoly A.\}",

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Singh, AK, Mehra, M & Alikhanov, AA 2022, Data-Driven Discovery of Time Fractional Differential Equations. in D Groen, C de Mulatier, VV Krzhizhanovskaya, PMA Sloot, M Paszynski & JJ Dongarra (eds), Computational Science - ICCS 2022, 22nd International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13351 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 56-63, 22nd Annual International Conference on Computational Science, ICCS 2022, London, United Kingdom, 21/06/22. https://doi.org/10.1007/978-3-031-08754-7_8

Data-Driven Discovery of Time Fractional Differential Equations. / Singh, Abhishek Kumar; Mehra, Mani; Alikhanov, Anatoly A.
Computational Science - ICCS 2022, 22nd International Conference, Proceedings. ed. / Derek Groen; Clélia de Mulatier; Valeria V. Krzhizhanovskaya; Peter M.A. Sloot; Maciej Paszynski; Jack J. Dongarra. Springer Science and Business Media Deutschland GmbH, 2022. p. 56-63 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13351 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

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Y2 - 21 June 2022 through 23 June 2022

ER -

Singh AK, Mehra M, Alikhanov AA. Data-Driven Discovery of Time Fractional Differential Equations. In Groen D, de Mulatier C, Krzhizhanovskaya VV, Sloot PMA, Paszynski M, Dongarra JJ, editors, Computational Science - ICCS 2022, 22nd International Conference, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 56-63. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-08754-7_8