Reg PINNs

Regression-based Physics-Informed Neural Networks (Reg-PINNs) enhance traditional Physics-Informed Neural Networks (PINNs) by incorporating empirical models alongside differential equations to improve accuracy and generalization in solving partial differential equations (PDEs). Current research focuses on improving PINN training efficiency and accuracy through architectural innovations like transformers and variable-scaling methods, as well as addressing challenges such as handling stiff PDEs and improving interpretability via influence functions. Reg-PINNs are proving valuable across diverse scientific domains, from fluid dynamics and robotics to medical image analysis and materials science, offering faster and more accurate solutions to complex problems compared to traditional numerical methods.