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arXiv · 2303.02219

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

Binghang Lu·Christian B. Moya·Guang Lin
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Abstract

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.

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Binghang Lu, Christian B. Moya, Guang Lin. 2023-03-03. NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training. https://arxiv.org/abs/2303.02219

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