Power-Based Normalization of Loss Terms to Improve the Performance of Physics-Informed Neural Networks (PINNs)

A novel approach is developed to improve the convergence of Physics-Informed Neural Networks (PINNs), aiming to employ them as real-time computational models within the framework of the digital twin for manufacturing processes. This method entails the weighting of physical equations, boundary conditions, and initial conditions to ensure their comparable magnitudes, with power being the chosen quantity in this study. The approach is applied to thermal problems, which are crucial for predicting manufacturing part defects. Different configurations, including complex boundary conditions and complex physics, were tested to assess the model’s robustness. The W-PINN demonstrates good predictions and strong stability compared to the classical PINN.