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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.13228 |
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| _version_ | 1866929553875664896 |
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| author | Toscano, Juan Diego Oommen, Vivek Varghese, Alan John Zou, Zongren Daryakenari, Nazanin Ahmadi Wu, Chenxi Karniadakis, George Em |
| author_facet | Toscano, Juan Diego Oommen, Vivek Varghese, Alan John Zou, Zongren Daryakenari, Nazanin Ahmadi Wu, Chenxi Karniadakis, George Em |
| contents | Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Finally, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning Toscano, Juan Diego Oommen, Vivek Varghese, Alan John Zou, Zongren Daryakenari, Nazanin Ahmadi Wu, Chenxi Karniadakis, George Em Machine Learning Artificial Intelligence Computational Physics Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Finally, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications. |
| title | From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning |
| topic | Machine Learning Artificial Intelligence Computational Physics |
| url | https://arxiv.org/abs/2410.13228 |