Neural Fractional Differential Equations

To effectively predict and understand these complex systems, mathematical models are employed, allowing to gain insights into the system behaviour without the need for time-consuming or expensive experiments. Due to the inherent presence of continuous dynamics in these systems, Differential Equations (DEs) are commonly employed as mathematical models, accounting for the continuous evolution of the system's behaviour and offering the advantage of enabling predictions throughout the entire time domain and not only at specific points. With the emergence of Neural Networks (NNs) and their impressive performance in fitting mathematical models to data, numerous studies have focused on modelling realworld systems. However, conventional NNs are designed to model discrete functions and may not be able to accurately capture the continuous dynamics observed in several systems. To overcome this limitation, Chen et al. [1] introduced the Neural Ordinary Differential Equations (Neural ODEs), a NN architecture that adjusts an Ordinary Differential Equation (ODE) to the dynamics of a system.