Fractional neural networks for constitutive modeling of complex fluids

Constitutive modeling of complex fluids' rheological behavior has always been of great interest to academics and industrial researchers alike, as these complex fluids find applications in many diverse. In general, the goal is to describe the complex and non-linear responses of the fluid to an applied deformation/stress with a limited number of model parameters. Fractional derivatives have been found very effective in representing such complex behavior in a compact mathematical format. These fractional derivative, replacing the classical spring and dash-pot elements in a concise representation, can be used to alleviate the complexity of viscoelastic models and reduce the parameter count, thus preventing the unnecessary complications often encountered in rheological modeling. However, an automatic platform for guiding the experimental rheologists in determining the exact exponents of the fractional derivatives is lacking. Here, we will utilize rheology-informed neural networks (RhINNs) to quantify the quasi-properties and the fractional derivative orders. Also, we will show that the proposed fractional RhINN platform can accurately capture the material responses to transient flow protocols over the entire accessible input space, i.e., shear rate and time.