UniFIDES: Universal Fractional Integro-Differential Equation Solvers
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929412624089088 |
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| author | Saadat, Milad Mangal, Deepak Jamali, Safa |
| author_facet | Saadat, Milad Mangal, Deepak Jamali, Safa |
| contents | The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of 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 Equation Solvers (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 dynamical and complex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | UniFIDES: Universal Fractional Integro-Differential Equation Solvers Saadat, Milad Mangal, Deepak Jamali, Safa Machine Learning Computational Engineering, Finance, and Science The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of 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 Equation Solvers (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 dynamical and complex systems. |
| title | UniFIDES: Universal Fractional Integro-Differential Equation Solvers |
| topic | Machine Learning Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2407.01848 |