Customization of Loss Weights for Physics-Informed Neural Networks (PINNs) when solving Multiple Partial Differential Equations: A Case Study on Plant Cell Drying

Physics-informed Neural Networks (PINNs) have received significant attention across science and engineering research communities due to their capabilities of integrating physics with observational data [1]. The automatic differentiation feature of PINNs can compute derivatives in partial differential equations (PDEs) and solve them with no domain discretisation or particle interaction errors. In addition, a trained PINN for a given spatiotemporal domain can be exclusively utilised to obtain predictions for any interpolated or extrapolated domains without further re-training. Such additional benefits have attracted significant research efforts on PINNs for solving physics-based models, especially when traditional computational techniques are challenged [2]. In PINNs, residuals of governing PDEs and boundary conditions are integrated into the loss function. Equally-weighted loss terms, the popular option, have a tendency of failing to converge, impacting the overall performance of corresponding PINN frameworks. As a remedy, customised loss weights can be introduced, emphasising on specific objectives during the training process of multi-objective predictive frameworks [3]. Further, the impact of customised loss weights for coupled spatiotemporal variations of PINN-based soft matter modelling have not yet been widely investigated. Accordingly, in this study, we investigate the significance of customised loss weights to solve the mass transfer model for a plant cell during food drying. Fick’s law of diffusion can be utilised to establish moisture transport within the cell as caused by convective mass transfer at cell wall. The corresponding boundary conditions add further specificity to the overall problem when solving the relevant PINN-based predictive framework. Through this case study, we establish the significance of customised and optimised loss weights to reduce mean percentage error as low as 0.15% when predicting spatiotemporal mass loss for apple cell drying, compared to benchmark Finite-Element-Analysis-based results