A Fourier feature-embedded physics-informed neural network framework to investigate coupled heat and mass transfer characteristics of plant tissues during drying

This paper introduces a new computational framework for analysing heat and mass transfer during the drying of plant tissues, using Fourier Feature Embedded Physics-Informed Neural Networks (FFE-PINN). The proposed FFE-PINN framework enables direct communication between two physics-informed neural network-based models: PINN-MT for mass transfer and PINN HT for heat transfer, which are trained simultaneously to investigate heat and mass transfer characteristics. The novelty of this study is the integration of Fourier Feature Embedding (FFE) into the PINN framework to examine coupled heat and mass transfer during drying to significantly improve the accuracy and robustness of drying-kinetics-based predictions. The developed model demonstrates strong alignment with experimental data on moisture content variation and numerical results from Finite Element Analysis (FEA), with maximum deviations of 8.73% for moisture concentration and 4.51% for temperature predictions. The findings indicated that these differences are primarily due the distinct derivation techniques utilised in PINN and FEA, rather than any limitations of the proposed framework. Importantly, this study marks a significant milestone as the first to apply a PINN-based approach to analyse coupled heat and mass transfer in dried plant tissues over an extended 60-minute drying period, without relying on transfer learning, due to FFE introduction. The proposed FFE-PINN framework emerges as a promising computational tool, offering a physics-consistent approach to predict complex and nonlinear heat and mass transfer phenomena associated not only with drying, but further beyond.