Physics-Informed Neural Networks for Solving Derivative-Constrained PDEs
This paper introduces Derivative-Constrained PINNs (DC-PINNs), a general framework that enhances Physics-Informed Neural Networks by embedding general nonlinear constraints on states and derivatives via automatic differentiation and self-adaptive loss balancing, thereby stabilizing training and ensuring physically admissible solutions for problems requiring derivative-based relations beyond standard PDE residuals.