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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2511.18512 |
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| _version_ | 1866917100103139328 |
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| author | Csirik, Mihály A. Laestadius, Andre Oster, Mathias |
| author_facet | Csirik, Mihály A. Laestadius, Andre Oster, Mathias |
| contents | Density functional theory is one of the most efficient and widely used computational methods of quantum mechanics, especially in fields such as solid state physics and quantum chemistry. From the theoretical perspecive, its central object is the universal density functional which contains all intrinsic information about the quantum system in question. Once the external potential is provided, in principle one can obtain the exact ground-state energy via a simple minimization. However, the universal density functional is a very complicated mathematical object and almost always it is replaced with its approximate variants. So far, no ``first principles'', mathematically consistent and convergent approximation procedure has been devised that has general applicability. In this paper, we propose such a procedure by first applying Moreau--Yosida regularization to make the exact functionals continuous (even differentiable) and then approximate the regularized functional by a neural network. The resulting neural network preserves the positivity and convexity of the exact functionals. More importantly, it is differentiable, so it can be directly used in a Kohn--Sham calculation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neural network approximation of regularized density functionals Csirik, Mihály A. Laestadius, Andre Oster, Mathias Chemical Physics Disordered Systems and Neural Networks Numerical Analysis Mathematical Physics Quantum Physics 81Q05, 68T07, 41A65 Density functional theory is one of the most efficient and widely used computational methods of quantum mechanics, especially in fields such as solid state physics and quantum chemistry. From the theoretical perspecive, its central object is the universal density functional which contains all intrinsic information about the quantum system in question. Once the external potential is provided, in principle one can obtain the exact ground-state energy via a simple minimization. However, the universal density functional is a very complicated mathematical object and almost always it is replaced with its approximate variants. So far, no ``first principles'', mathematically consistent and convergent approximation procedure has been devised that has general applicability. In this paper, we propose such a procedure by first applying Moreau--Yosida regularization to make the exact functionals continuous (even differentiable) and then approximate the regularized functional by a neural network. The resulting neural network preserves the positivity and convexity of the exact functionals. More importantly, it is differentiable, so it can be directly used in a Kohn--Sham calculation. |
| title | Neural network approximation of regularized density functionals |
| topic | Chemical Physics Disordered Systems and Neural Networks Numerical Analysis Mathematical Physics Quantum Physics 81Q05, 68T07, 41A65 |
| url | https://arxiv.org/abs/2511.18512 |