Combining Fractional Derivatives and Machine Learning: A Review.

Area of Science:

• Applied Mathematics
• Data Science
• Machine Learning

Background:

• Fractional calculus models complex dynamics using non-integer derivatives, capturing spatiotemporal memory.
• Machine learning excels at pattern recognition and prediction from large datasets.
• Combining these fields offers novel approaches to data analysis and modeling.

Purpose of the Study:

• To review and contextualize past combined approaches of fractional calculus and machine learning.
• To identify and categorize existing techniques for integrating fractional derivatives into machine learning workflows.
• To motivate machine learning practitioners to adopt fractional calculus tools.

Main Methods:

• Literature review of combined fractional calculus and machine learning approaches.
• Categorization of existing methods into preprocessing, machine learning, and optimization.
• Analysis of fractional derivatives' contributions to machine learning.

Main Results:

• Fractional derivatives offer powerful preprocessing and feature augmentation.
• Integration improves physically informed machine learning models.
• Fractional calculus enhances hyperparameter optimization in machine learning.

Conclusions:

• Combined fractional calculus and machine learning approaches offer significant potential for data-based problems.
• Fractional derivatives provide valuable tools for enhancing machine learning techniques.
• This review highlights opportunities for advancing machine learning through fractional calculus.