UniFIDES: Universal Fractional Integro-Differential Equation Solvers
<|reference_start|>UniFIDES: Universal Fractional Integro-Differential Equation Solvers: 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.<|reference_end|>
@article{saadat2024unifides:,
    title={UniFIDES: Universal Fractional Integro-Differential Equation Solvers},
    author={Milad Saadat, Deepak Mangal and Safa Jamali},
    journal={arXiv preprint arXiv:2407.01848},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.01848},
    primaryClass={cs.LG cs.CE}
}