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.
@article{arxiv.2303.02219,
title = {NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training},
author = {Binghang Lu and Christian B. Moya and Guang Lin},
journal= {arXiv preprint arXiv:2303.02219},
year = {2023}
}