Physics-Informed Neural Network based inverse framework for time-fractional differential equations for rheology

Simple Summary Modeling complex systems with memory-dependent behavior, such as anomalous diffusion and viscoelasticity, is often hindered by limited data and the computational challenges of inverse problems. Here, we developed a Physics-Informed Neural Network (PINN) framework that incorporates time-fractional derivatives to infer key physical parameters from sparse and noisy data. Despite the recognized potential of fractional models, we found that existing PINN methods largely overlook non-integer dynamics. Using synthetic data and experimental rheology measurements, we showed that our framework could accurately recover parameters such as the generalized diffusion coefficient and fractional orders—even under 25% Gaussian noise. Notably, while traditional models require extensive parameterization, our approach predicted relaxation behavior in biological tissues with fewer assumptions and less than 10% relative error. These results suggest that while fractional PINNs offer powerful tools for learning hidden dynamics, the benefits may be constrained when noise levels are extreme or when behavioral complexity exceeds the model structure.