Comparative study on the fractional rheology-informed neural networks for the time-dependent mechanical behavior of polymer solutions

In this paper, fractional rheology-informed neural networks (f-RhINNs) are established to predict the time-dependent mechanical behaviors of polymer solutions. Both constant-order and variable-order fractional constitutive models are derived and imposed as physical constraints within the f-RhINNs framework. To enhance training accuracy and robustness, a self-generating data method is also developed, producing expanded datasets via a forward-inverse problem loop. Next, the effectiveness of the proposed f-RhINNs is validated by the experimental data of polyacrylamide (PAAm) aqueous solutions under time-varying shear rates. It is demonstrated that under the balanced data and model weights, the variable-order f-RhINN (Vof-RhINN) captures the stress-shear rate relationship of PAAm solutions more accurately than the constant-order form, especially in the initial stress overshoot stage. Furthermore, the law of order function shows a consistent increase with the increase in strain rate at different concentrations, which proves that the Vof-RhINN reasonably reflects the physical mechanism that higher shear rates enhancing the flowability of PAAm solutions. Finally, the extrapolation prediction ability of the Vof-RhINN for the stress response at different concentrations outside the training data is verified. These findings highlight the potential of Vof-RhINN to provide rapid and accurate predictions for the rheological behaviors of polymer solutions with new formulations, which is of great significance in scientific research and engineering applications.