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Physics-Informed Neural Network based inverse framework for time-fractional differential equations for rheology by Thakur, Sukirt; Mitra, Harsa; Ardekani, Arezoo M. is a scholarly article available to read on EtoBox.

What is Physics-Informed Neural Network based inverse framework for time-fractional differential equations for rheology about?

Time-fractional differential equations offer a robust framework for capturing intricate phenomena characterized by memory effects, particularly in fields like biotransport and rheology. However, solving inverse problems involving fractional derivatives presents notable challenges, including issues related to stability and uniqueness. While Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving inverse problems, most existing PINN frameworks primarily focus on integer-ordered derivatives. In this study, we extend the application of PINNs to address inverse problems involving time-fractional derivatives, specifically targeting two problems: 1) anomalous diffusion and 2) fractional viscoelastic constitutive equation. Leveraging both numerically generated datasets and experimental data, we calibrate the concentration-dependent generalized diffusion coefficient and parameters for the fractional Maxwell model. We devise a tailored residual loss function that scales with the standard deviation of observed data. We rigorously test our framework's efficacy in handling anomalous diffusion. Even after introducing 25% Gaussian noise to the concentration dataset, o

Author

Thakur, Sukirt; Mitra, Harsa; Ardekani, Arezoo M.

Published

2024

Language

EN