PF-PINNs: Physics-informed neural networks for solving coupled Allen-Cahn and Cahn-Hilliard phase field equations

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.