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