Physics-Informed Neural Networks for Inversion of the Macroscopic Transport Parameters in Packed Bed

The effective permeability and effective thermal conductivity represent the macroscopic transport parameters crucial for characterizing fluid flow and heat transfer in packed beds. Accurately determining these parameters is essential for successful upscaling from the pore scale to the packed bed scale. In this study, a novel approach utilizing Physics-Informed Neural Networks (PINNs) is introduced to enhance the precision and efficiency in estimating these macroscopic transport parameters during the upscaling process. This approach treats the estimation of transport parameters as an inverse problem framed within the context of PINNs, where the network learns the underlying physical laws and outputs the desired macroscopic parameters. The minimization of discrepancies in pressure drops and temperature between the pore-scale and packed-bed scale models forms the basis of the objective function. The results demonstrate a high degree (relative deviations are within 1 %) of agreement between the pore-scale and packed-bed scale models in multi-physics fields, validating the effectiveness of the PINNs-based approach in accurately capturing the macroscopic transport parameters for packed beds. Macroscopic transport parameters of solid breeding blanket-packed beds in fusion reactors at different inlet velocities (0.05~0.25 m/s) and different inlet temperatures (300~900 K) are obtained.