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Neural Fractional Differential Equations
March 6, 2024, 5:41 a.m. | C. Coelho, M. Fernanda P. Costa, L. L. Ferr\'as
cs.LG updates on arXiv.org arxiv.org
Abstract: Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise representation of processes characterised by non-local and memory-dependent behaviours.
This property is useful in systems where variables do not respond to changes instantaneously, but instead exhibit a strong memory of past interactions.
Having this in mind, and drawing inspiration from Neural Ordinary Differential Equations …
abstract arxiv complex systems concepts cs.ce cs.lg cs.na differential differentiation enabling engineering integration math.na memory modelling orders processes property representation science systems tools type variables
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