PF-PINNs: Physics-informed neural networks for solving coupled Allen-Cahn and Cahn-Hilliard phase field equations
Nanxi Chen, S. Lucarini, Rujin Ma, Airong Chen, Chuanjie Cui
Abstract
Physics-informed neural networks (PINNs) have emerged as a promising tool for effectively resolving diverse partial differential equations . Despite the numerous recent advances, PINNs often encounter significant challenges when dealing with complex nonlinear systems , such as the coupling Allen-Cahn (AC) and Cahn-Hilliard (CH) equations for phase field interfacial problems. In this work, we present an enhanced PINN framework, termed PF-PINNs, for the robust and efficient resolution of AC-CH coupled PDEs. Key features of the PF-PINNs framework include: (1) a normalisation and de-normalisation method to bridge the disparity in temporal and spatial scales in real-world physical problems, (2) an advanced sampling strategy designed to efficiently diffuse the initial interface and dynamically monitor its evolution throughout the training process, and (3) an NTK-based adaptive weighting strategy with random-batch method to balance the complex loss terms associated with phase field governing equations. We conduct extensive benchmarks on electrochemical corrosion , to showcase the accuracy and efficiency of the proposed PF-PINNs framework. The comparison of our results with reference solutions from FEniCS demonstrates that our PF-PINNs framework is a versatile and powerful tool for a wide range of AC-CH phase field applications.