PINN Model of Diffusion Coefficient Identification Problem in Fick's Laws.

This study tackles the complex task of determining diffusion coefficients in inverse problems, addressing the challenges of instability and computational demands. The primary objective is to introduce an efficient model for estimating diffusion coefficients under specific conditions. Through a unique fusion of Fick's laws and a Neural Network framework, a physics-informed neural network (PINN) is developed for the diffusion coefficient identification problem. The model accommodates scenarios where both diffusion flux and concentration gradient are known, where diffusion flux is known while the concentration gradient is unknown, and where diffusion flux is unknown while the concentration gradient is known. Results demonstrate the model's efficiency, obtaining diffusion coefficients in less than 1000, 2000, and 3000 iterations for the respective scenarios. Sensitivity analysis underscores the model's validity across conditions, highlighting the positive impact of a higher proportion of effective data on convergence and alignment with general diffusion coefficient patterns. In conclusion, the PINN model stands out as a powerful tool for accurately estimating diffusion coefficients under varying conditions.