NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training

This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed uses non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient algorithms (e.g., ADAM) escape local minima effectively. Additionally, NSGA-II enables satisfying initial and boundary conditions encoded into loss function during precisely. We demonstrate effectiveness our by applying NSGA-PINN several ordinary partial differential equation problems. In particular, we show that can handle challenging inverse problems with noisy data.