Recent Advances in Fractal Interpolation Functions and Their Applications in AI

Dear Colleagues,

To date, Artificial Intelligence (AI) has been used for classification, prediction, and optimization. However, there is still room for improving the application of AI in many fields. In situations where the problem to be modelled is too intricate, the approach of incorporating AI can lead to promising results. There is a consistent body of literature demonstrating that AI-based methods provide greater reliability, accuracy, and predictability, while helping to detect hidden nonlinear chaotic patterns in big data applications. To this end, AI methods are often used to complement traditional classical methods in many fields, especially in complicated hybrid chaotic systems.

Although many studies in recent years have used AI in applied mathematics, the application of AI methods to fractal theory is less common. Fractal, fractional calculus, and wavelets have been the most widely-used methods in approximation theory and signal processing. Combining AI methods and fractal-based analysis is a new direction of research area.

Fractal-AI allows for the derivation of new mathematical tools that are designed to provide efficient solutions to problems in which many entities are interconnected. Fractal-AI is also used to extract hidden information from the dynamics of complicated systems and speed up experiments by performing massive data analysis.

In this special issue, the focus will be on recent developments of fractal functions and their applications in AI and data science, including theoretical and numerical aspects. The purpose is to develop the research area of differential equations, integral equations, approximation theory, wavelets, curve fitting, and reproducing kernel Hilbert spaces. We also aim to extend applications of fractal functions in machine learning and data modelling. Applications of AI in fractal functions are also welcome to this special issue.

Prof. Dr. Da-Chin Lour
Dr. Liang-Yu Hsieh 
Prof. Dr. María Antonia Navascués
Dr. Vasileios Drakopoulos
Guest Editors

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