Learning parameters of a system of variable order fractional differential equations

We introduce a machine learning framework that uses the differential evolution algorithm in combination with Adam–Bashforth–Moulton method to learn the parameters in a system of variable order fractional differential equations. In this work, we present out developments with regards to taking care of...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2023-05, Vol.39 (3), p.1962-1976
Main Authors: Singh, Abhishek Kumar, Mehra, Mani, Gulyani, Samarth
Format: Article
Language:English
Subjects:
Adam–Bashforth–Moulton method
Differential equations
differential evolution method
Ebola outbreak
Evolutionary algorithms
Evolutionary computation
Fractional calculus
Machine learning
Mathematical models
Parameters
SEIR epidemic model
variable order fractional differential equations
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Summary:We introduce a machine learning framework that uses the differential evolution algorithm in combination with Adam–Bashforth–Moulton method to learn the parameters in a system of variable order fractional differential equations. In this work, we present out developments with regards to taking care of a class of problem: data‐driven discovery of system of variable order fractional differential equations. The main advantage of the proposed framework is that it works even if data corresponding to only one of the variables in the system of equations is given. We illustrate the working of our framework on several Examples including modeling the 2014–15 Ebola outbreak in Africa via fractional SEIR (susceptible, exposed, infected, removed) model.
ISSN:0749-159X
1098-2426
DOI:10.1002/num.22796