Physics-informed neural networks for solving inverse problems in phase field models

The integration of materials science with Physics-Informed Neural Networks (PINNs) is critical for understanding and predicting material properties, especially through the study of inverse problems. However, much of the current research in materials science primarily focuses on applying PINNs to forward problems or improving prediction accuracy. This paper shifts the focus to inverse problems related to numerical simulation modeling, encompassing diffusion, flow, and phase transition problems through PINNs. By constructing a neural network that integrates data-driven and physics-driven modules, this study uncovers the underlying physical laws embedded within the data. More importantly, this work further validates the applicability of PINNs in the inversion of key anisotropic material parameters, with benchmark anisotropic function inversion results demonstrating a high degree of consistency between predicted and theoretical values. Additionally, this study extends the application of PINNs to multi-physics coupled systems by addressing inverse problems associated with the governing equations of phase field, temperature field, and flow field, thereby enabling parameter inversion under multi-physics conditions. This novel approach addressing inverse problems and the inversion of critical material parameters provides new perspectives, demonstrating the potential of integrating numerical simulation data and deep learning, further deepening the research on PINNs in material science.