Architectural Strategies for the optimization of Physics-Informed Neural Networks
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929234264457216 |
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| author | Saratchandran, Hemanth Chng, Shin-Fang Lucey, Simon |
| author_facet | Saratchandran, Hemanth Chng, Shin-Fang Lucey, Simon |
| contents | Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their remarkable empirical success, PINNs have garnered a reputation for their notorious training challenges across a spectrum of PDEs. In this work, we delve into the intricacies of PINN optimization from a neural architecture perspective. Leveraging the Neural Tangent Kernel (NTK), our study reveals that Gaussian activations surpass several alternate activations when it comes to effectively training PINNs. Building on insights from numerical linear algebra, we introduce a preconditioned neural architecture, showcasing how such tailored architectures enhance the optimization process. Our theoretical findings are substantiated through rigorous validation against established PDEs within the scientific literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02711 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Architectural Strategies for the optimization of Physics-Informed Neural Networks Saratchandran, Hemanth Chng, Shin-Fang Lucey, Simon Machine Learning Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their remarkable empirical success, PINNs have garnered a reputation for their notorious training challenges across a spectrum of PDEs. In this work, we delve into the intricacies of PINN optimization from a neural architecture perspective. Leveraging the Neural Tangent Kernel (NTK), our study reveals that Gaussian activations surpass several alternate activations when it comes to effectively training PINNs. Building on insights from numerical linear algebra, we introduce a preconditioned neural architecture, showcasing how such tailored architectures enhance the optimization process. Our theoretical findings are substantiated through rigorous validation against established PDEs within the scientific literature. |
| title | Architectural Strategies for the optimization of Physics-Informed Neural Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.02711 |