PINN Method

Physics-informed neural networks (PINNs) are a class of deep learning methods designed to solve partial differential equations (PDEs) by incorporating the governing equations directly into the network's loss function. Current research focuses on improving PINN accuracy and efficiency, addressing challenges like stiffness, high dimensionality, and extrapolation failures through techniques such as hybrid methods (combining PINNs with finite element methods), spectral methods, improved network architectures (e.g., skip connections, separable networks), and ensemble methods. The ability of PINNs to solve complex PDEs with limited data, and their potential for real-time applications like constitutive model calibration and fluid flow simulation, makes them a significant tool for scientific computing and engineering.