NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training
This addresses training difficulties in PINNs for solving differential equations, which is incremental as it builds on existing PINN and optimization methods.
The paper tackles the problem of training Physics-Informed Neural Networks (PINNs) by proposing NSGA-PINN, a multi-objective optimization framework that uses NSGA-II to help escape local minima and precisely satisfy initial and boundary conditions, demonstrating effectiveness on ordinary and partial differential equation problems, including challenging inverse problems with noisy data.
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.