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

Area of Science:

• Computational physics
• Materials science
• Chemical engineering

Background:

• Determining diffusion coefficients is crucial in many scientific fields.
• Inverse problems involving diffusion coefficients present challenges like instability and high computational cost.
• Existing methods may lack efficiency and accuracy under varying conditions.

Purpose of the Study:

• To develop an efficient and accurate model for estimating diffusion coefficients in inverse problems.
• To address the challenges of instability and computational demands in diffusion coefficient determination.
• To create a versatile model applicable to different scenarios of known/unknown diffusion flux and concentration gradients.

Main Methods:

• A physics-informed neural network (PINN) framework was developed by integrating Fick's laws.
• The PINN model was designed to handle three distinct scenarios based on the availability of diffusion flux and concentration gradient data.
• Sensitivity analysis was performed to validate the model's performance and robustness.

Main Results:

• The PINN model achieved efficient estimation of diffusion coefficients in under 1000, 2000, and 3000 iterations for the three considered scenarios.
• Sensitivity analysis confirmed the model's validity and highlighted the positive influence of effective data proportion on convergence.
• The model demonstrated alignment with general diffusion coefficient patterns.

Conclusions:

• The developed PINN model is a powerful and efficient tool for accurately estimating diffusion coefficients.
• The model offers a robust solution for inverse problems related to diffusion, overcoming previous limitations.
• This approach provides a significant advancement in the field of diffusion coefficient identification.