Neural Fractional Differential Equations: Optimising the Order of the Fractional Derivative

• Type: Article in International Scientific Journal
• Date: 2024

Authors

Coelho, C (Author) Other; Costa, MFP (Author) Other; Ferrás, LL (Author) FEUP

Journal

The Journal is awaiting validation by the Administrative Services.

Title: FRACTAL AND FRACTIONAL

Vol. 8

Final page: 529

ISSN: 2504-3110

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-016-ZWK

DOI: 10.3390/fractalfract8090529

Abstract (EN): Neural Fractional Differential Equations (Neural FDEs) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represented by a fractional derivative, with a neural network component, forming an initial value problem. During the learning process, both the order of the derivative and the parameters of the neural network must be optimised. In this work, we investigate the non-uniqueness of the optimal order of the derivative and its interaction with the neural network component. Based on our findings, we perform a numerical analysis to examine how different initialisations and values of the order of the derivative (in the optimisation process) impact its final optimal value. Results show that the neural network on the right-hand side of the Neural FDE struggles to adjust its parameters to fit the FDE to the data dynamics for any given order of the fractional derivative. Consequently, Neural FDEs do not require a unique alpha value; instead, they can use a wide range of alpha values to fit data. This flexibility is beneficial when fitting to given data is required and the underlying physics is not known.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16