Hybrid acceleration techniques for the physics-informed neural networks: a comparative analysis

Physics-informed neural networks (PINN) has emerged as a promising approach for solving partial differential equations (PDEs). However, the training process for PINN can be computationally expensive, limiting its practical applications. To address this issue, we investigate several acceleration tech...

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Bibliographic Details
Published in:Machine learning 2024-06, Vol.113 (6), p.3675-3692
Main Authors: Buzaev, Fedor, Gao, Jiexing, Chuprov, Ivan, Kazakov, Evgeniy
Format: Article
Language:English
Subjects:
Artificial Intelligence
Boundary conditions
Comparative analysis
Computer Science
Control
Efficiency
Inverse problems
Machine Learning
Mechatronics
Natural Language Processing (NLP)
Neural networks
Operators
Partial differential equations
Physics
Robotics
Simulation and Modeling
Special Issue of the ACML 2023
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Summary:Physics-informed neural networks (PINN) has emerged as a promising approach for solving partial differential equations (PDEs). However, the training process for PINN can be computationally expensive, limiting its practical applications. To address this issue, we investigate several acceleration techniques for PINN that combine Fourier neural operators, separable PINN, and first-order PINN. We also propose novel acceleration techniques based on second-order PINN and Koopman neural operators. We evaluate the efficiency of these techniques on various PDEs, and our results show that the hybrid models can provide much more accurate results than classical PINN under time constraints for the training, making PINN a more viable option for practical applications. The proposed methodology in the manuscript is generic and can be extended on a larger set of problems including inverse problems.
ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-023-06442-6