Coupled Partial Differential Equation

Coupled partial differential equations (PDEs) model complex systems where multiple physical processes interact, requiring simultaneous solution of multiple equations. Current research focuses on developing efficient and accurate numerical methods, particularly leveraging deep learning architectures like Physics-Informed Neural Networks (PINNs) and evolutional deep neural networks (EDNNs), often employing strategies like domain decomposition or multiwavelet decomposition to handle the complexity of coupled systems. These advancements are crucial for tackling challenging multiphysics problems in diverse fields such as materials science, fluid dynamics, and geomechanics, enabling more accurate simulations and potentially leading to improved designs and predictions.