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Hyperparameter selection for physics-informed neural networks (PINNs) – Application to discontinuous heat conduction problems
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Llion Evans ,
Michelle Tindall ,
Perumal Nithiarasu
Numerical Heat Transfer, Part B: Fundamentals, Pages: 1 - 15
Swansea University Authors:
Prakhar Sharma , Llion Evans , Perumal Nithiarasu
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DOI (Published version): 10.1080/10407790.2023.2264489
Abstract
In recent years, physics-informed neural networks (PINNs) have emerged as an alternative to conventional numerical techniques to solve forward and inverse problems involving partial differential equations (PDEs). Despite its success in problems with smooth solutions, implementing PINNs for problems...
| Published in: | Numerical Heat Transfer, Part B: Fundamentals |
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| ISSN: | 1040-7790 1521-0626 |
| Published: |
Informa UK Limited
2023
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa64585 |
| Abstract: |
In recent years, physics-informed neural networks (PINNs) have emerged as an alternative to conventional numerical techniques to solve forward and inverse problems involving partial differential equations (PDEs). Despite its success in problems with smooth solutions, implementing PINNs for problems with discontinuous boundary conditions (BCs) or discontinuous PDE coefficients is a challenge. The accuracy of the predicted solution is contingent upon the selection of appropriate hyperparameters. In this work, we performed hyperparameter optimization of PINNs to find the optimal neural network architecture, number of hidden layers, learning rate, and activation function for heat conduction problems with a discontinuous solution. Our aim was to obtain all the settings that achieve a relative L2 error of 10% or less across all the test cases. Results from five different heat conduction problems show that the optimized hyperparameters produce a mean relative L2 error of 5.60%. |
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| Keywords: |
Discontinuous boundaries conditions, heat conduction, hyperparameter tuning, physics-informed neural networks, stiff partial differential equation |
| College: |
Faculty of Science and Engineering |
| Funders: |
This work is part-funded by the United Kingdom Atomic Energy Authority (UKAEA) and the Engineering and Physical Sciences Research Council (EPSRC) under the Grant Agreement Numbers EP/W006839/1, EP/T517987/1, and EP/R012091/1. We acknowledge the support of Supercomputing Wales and AccelerateAI projects, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government for giving us access to NVIDIA A100 40 GB GPUs for batch training. We also acknowledge the support of NVIDIA academic hardware grant for donating us NVIDIA RTX A5000 24 GB for local testing. |
| Start Page: |
1 |
| End Page: |
15 |