From {\tt Ferminet} to PINN. Connections between neural network-based algorithms for high-dimensional Schrödinger Hamiltonian
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912127548129280 |
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| author | Khan, Mashhood Lorin, Emmanuel |
| author_facet | Khan, Mashhood Lorin, Emmanuel |
| contents | In this note, we establish some connections between standard (data-driven) neural network-based solvers for PDE and eigenvalue problems developed on one side in the applied mathematics and engineering communities (e.g. Deep-Ritz and Physics Informed Neural Networks (PINN)), and on the other side in quantum chemistry (e.g. Variational Monte Carlo algorithms, {\tt Ferminet} or {\tt Paulinet} following the pioneer work of {\it Carleo et. al}. In particular, we re-formulate a PINN algorithm as a {\it fitting} problem with data corresponding to the solution to a standard Diffusion Monte Carlo algorithm initialized thanks to neural network-based Variational Monte Carlo. Connections at the level of the optimization algorithms are also established. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_09177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From {\tt Ferminet} to PINN. Connections between neural network-based algorithms for high-dimensional Schrödinger Hamiltonian Khan, Mashhood Lorin, Emmanuel Computational Physics Quantum Physics In this note, we establish some connections between standard (data-driven) neural network-based solvers for PDE and eigenvalue problems developed on one side in the applied mathematics and engineering communities (e.g. Deep-Ritz and Physics Informed Neural Networks (PINN)), and on the other side in quantum chemistry (e.g. Variational Monte Carlo algorithms, {\tt Ferminet} or {\tt Paulinet} following the pioneer work of {\it Carleo et. al}. In particular, we re-formulate a PINN algorithm as a {\it fitting} problem with data corresponding to the solution to a standard Diffusion Monte Carlo algorithm initialized thanks to neural network-based Variational Monte Carlo. Connections at the level of the optimization algorithms are also established. |
| title | From {\tt Ferminet} to PINN. Connections between neural network-based algorithms for high-dimensional Schrödinger Hamiltonian |
| topic | Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2410.09177 |