Physics-informed neural networks for solving functional renormalization group on a lattice
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909276881027072 |
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| author | Yokota, Takeru |
| author_facet | Yokota, Takeru |
| contents | Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even on lattices. We leverage physics-informed neural networks (PINNs) as a state-of-the-art machine learning method for solving high-dimensional partial differential equations to overcome this challenge. In a zero-dimensional O($N$) model, we numerically demonstrate the construction of an effective action on an $N$-dimensional configuration space, extending up to $N=100$. Our results underscore the effectiveness of PINN approximation, even in scenarios lacking small parameters such as a small coupling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16038 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Physics-informed neural networks for solving functional renormalization group on a lattice Yokota, Takeru Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even on lattices. We leverage physics-informed neural networks (PINNs) as a state-of-the-art machine learning method for solving high-dimensional partial differential equations to overcome this challenge. In a zero-dimensional O($N$) model, we numerically demonstrate the construction of an effective action on an $N$-dimensional configuration space, extending up to $N=100$. Our results underscore the effectiveness of PINN approximation, even in scenarios lacking small parameters such as a small coupling. |
| title | Physics-informed neural networks for solving functional renormalization group on a lattice |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.16038 |