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

Lu, Binghang; Moya, Christian; Lin, Guang

doi:10.3390/a16040194

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

Journal Article · Mon Apr 03 00:00:00 EDT 2023 · Algorithms

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

; Moya, Christian;

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.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0021142; SC0023161

OSTI ID:: 1968107

Journal Information:: Algorithms, Journal Name: Algorithms Journal Issue: 4 Vol. 16; ISSN ALGOCH; ISSN 1999-4893

Publisher:: MDPI AGCopyright Statement

Country of Publication:: Switzerland

Language:: English

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