Allen Cahn Equation

The Allen-Cahn equation is a partial differential equation modeling phase separation and interface dynamics, primarily used in materials science and other fields requiring the simulation of evolving interfaces. Current research focuses on developing efficient and accurate numerical solutions, particularly using machine learning techniques such as physics-informed neural networks (PINNs) with various architectures (e.g., hybrid residual networks, convolutional recurrent networks, and densely multiplied PINNs) and incorporating strategies like adversarial training and transfer learning to improve robustness and accuracy. These advancements offer significant potential for accelerating simulations and enhancing the predictive capabilities of models in diverse scientific and engineering applications.