NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training
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., A...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-04-01
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| Series: | Algorithms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1999-4893/16/4/194 |
| _version_ | 1797606684552593408 |
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| author | Binghang Lu Christian Moya Guang Lin |
| author_facet | Binghang Lu Christian Moya Guang Lin |
| author_sort | Binghang Lu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T05:18:33Z |
| format | Article |
| id | doaj.art-116b7b20e74a4533b40a0cf965a273ee |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-11T05:18:33Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-116b7b20e74a4533b40a0cf965a273ee2023-11-17T17:59:05ZengMDPI AGAlgorithms1999-48932023-04-0116419410.3390/a16040194NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network TrainingBinghang Lu0Christian Moya1Guang Lin2Department of Computer Science, Purdue University, West Lafayette, IN 47906, USADepartment of Mathematics, Purdue University, West Lafayette, IN 47906, USADepartment of Mathematics and School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USAThis 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.https://www.mdpi.com/1999-4893/16/4/194machine learningdata-driven scientific computingmulti-objective optimization |
| spellingShingle | Binghang Lu Christian Moya Guang Lin NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training Algorithms machine learning data-driven scientific computing multi-objective optimization |
| title | NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training |
| title_full | NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training |
| title_fullStr | NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training |
| title_full_unstemmed | NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training |
| title_short | NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training |
| title_sort | nsga pinn a multi objective optimization method for physics informed neural network training |
| topic | machine learning data-driven scientific computing multi-objective optimization |
| url | https://www.mdpi.com/1999-4893/16/4/194 |
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