Data-Driven Discovery of Time Fractional Differential Equations

Abstract

In the era of data abundance and machine learning technologies, we often encounter difficulties in learning data-driven discovery of hidden physics, that is, learning differential equations/fractional differential equations via data. In [1], Schaeffer proposed a machine learning algorithm to learn the differential equation via data discovery. We extend Schaeffer’s work in the case of time fractional differential equations and propose an algorithm to identify the fractional order α and discover the form of F. Furthermore, if we have prior information regarding the set in which parameters belong to have some advantages in terms of time complexity of the algorithm over Schaeffer’s work. Finally, we conduct various numerical experiments to verify the method’s robustness at different noise levels.