Adaptive Hard-Soft Physics-Informed Neural Networks for Robust Boundary-Constrained PDE Solving (opens in new tab)

Physics-informed neural networks (PINNs) provide an effective way to solve partial differential equations (PDEs) by embedding physical principles into the learning process. However, the conventional PINN formulation, in which all constraints are imposed as soft penalty terms within a composite loss, often exhibits slow convergence, sensitivity to loss weight scaling, and inaccurate boundary enforcement due to poor conditioning of the optimizat...