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

Journal Article · 03 April 2023 · Algorithms

DOI: https://doi.org/10.3390/a16040194 · OSTI ID:1968107

Lu, Binghang ; Moya, Christian; Lin, Guang

This paper presents NSGA-PINN, a multi-objective optimization framework for the 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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: 382247
• OSTI ID: 1968107
• Journal Information: Algorithms, Journal Name: Algorithms Vol. 16 Journal Issue: 4; ISSN 1999-4893
• Publisher: MDPI AGCopyright Statement
• Country of Publication: Switzerland
• Language: English