UniFIDES: Universal fractional integro-differential equations solver
The development of data-driven approaches for solving differential equations has led to numerous applications in science and engineering across many disciplines and remains a central focus of active scientific inquiry. However, a large body of natural phenomena incorporates memory effects that are b...
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2025-03-01
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| Series: | APL Machine Learning |
| Online Access: | http://dx.doi.org/10.1063/5.0258122 |
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| author | Milad Saadat Deepak Mangal Safa Jamali |
| author_facet | Milad Saadat Deepak Mangal Safa Jamali |
| author_sort | Milad Saadat |
| collection | DOAJ |
| description | The development of data-driven approaches for solving differential equations has led to numerous applications in science and engineering across many disciplines and remains a central focus of active scientific inquiry. However, a large body of natural phenomena incorporates memory effects that are best described via fractional integro-differential equations (FIDEs), in which the integral or differential operators accept non-integer orders. Addressing the challenges posed by nonlinear FIDEs is a recognized difficulty, necessitating the application of generic methods with immediate practical relevance. This work introduces the Universal Fractional Integro-Differential Equations Solver (UniFIDES), a comprehensive machine learning platform designed to expeditiously solve a variety of FIDEs in both forward and inverse directions, without the need for ad hoc manipulation of the equations. The effectiveness of UniFIDES is demonstrated through a collection of integer-order and fractional problems in science and engineering. Our results highlight UniFIDES’ ability to accurately solve a wide spectrum of integro-differential equations and offer the prospect of using machine learning platforms universally for discovering and describing dynamic and complex systems. |
| format | Article |
| id | doaj-art-5db19103d7e24482a3ee7d05a0637a5f |
| institution | DOAJ |
| issn | 2770-9019 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Machine Learning |
| spelling | doaj-art-5db19103d7e24482a3ee7d05a0637a5f2025-08-20T03:04:26ZengAIP Publishing LLCAPL Machine Learning2770-90192025-03-0131016116016116-1110.1063/5.0258122UniFIDES: Universal fractional integro-differential equations solverMilad Saadat0Deepak Mangal1Safa Jamali2Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USADepartment of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USADepartment of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USAThe development of data-driven approaches for solving differential equations has led to numerous applications in science and engineering across many disciplines and remains a central focus of active scientific inquiry. However, a large body of natural phenomena incorporates memory effects that are best described via fractional integro-differential equations (FIDEs), in which the integral or differential operators accept non-integer orders. Addressing the challenges posed by nonlinear FIDEs is a recognized difficulty, necessitating the application of generic methods with immediate practical relevance. This work introduces the Universal Fractional Integro-Differential Equations Solver (UniFIDES), a comprehensive machine learning platform designed to expeditiously solve a variety of FIDEs in both forward and inverse directions, without the need for ad hoc manipulation of the equations. The effectiveness of UniFIDES is demonstrated through a collection of integer-order and fractional problems in science and engineering. Our results highlight UniFIDES’ ability to accurately solve a wide spectrum of integro-differential equations and offer the prospect of using machine learning platforms universally for discovering and describing dynamic and complex systems.http://dx.doi.org/10.1063/5.0258122 |
| spellingShingle | Milad Saadat Deepak Mangal Safa Jamali UniFIDES: Universal fractional integro-differential equations solver APL Machine Learning |
| title | UniFIDES: Universal fractional integro-differential equations solver |
| title_full | UniFIDES: Universal fractional integro-differential equations solver |
| title_fullStr | UniFIDES: Universal fractional integro-differential equations solver |
| title_full_unstemmed | UniFIDES: Universal fractional integro-differential equations solver |
| title_short | UniFIDES: Universal fractional integro-differential equations solver |
| title_sort | unifides universal fractional integro differential equations solver |
| url | http://dx.doi.org/10.1063/5.0258122 |
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