{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/deep-neural-network-solution-of-the","title":"Deep neural network solution of the electronic Schrödinger equation","arxiv_id":"1909.08423","date":"2019-09-16","proceeding":null,"authors":["Jan Hermann","Zeno Schätzle","Frank Noé"],"abstract":"[New and updated results were published in Nature Chemistry, doi:10.1038/s41557-020-0544-y.] The electronic Schr\\\"odinger equation describes fundamental properties of molecules and materials, but can only be solved analytically for the hydrogen atom. The numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo is a possible way out: it scales well to large molecules, can be parallelized, and its accuracy has, as yet, only been limited by the flexibility of the used wave function ansatz. Here we propose PauliNet, a deep-learning wave function ansatz that achieves nearly exact solutions of the electronic Schr\\\"odinger equation. PauliNet has a multireference Hartree-Fock solution built in as a baseline, incorporates the physics of valid wave functions, and is trained using variational quantum Monte Carlo (VMC). PauliNet outperforms comparable state-of-the-art VMC ansatzes for atoms, diatomic molecules and a strongly-correlated hydrogen chain by a margin and is yet computationally efficient. We anticipate that thanks to the favourable scaling with system size, this method may become a new leading method for highly accurate electronic-strucutre calculations on medium-sized molecular systems.","url_abs":"https://arxiv.org/abs/1909.08423v5","url_pdf":"https://arxiv.org/pdf/1909.08423v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"deep-neural-network-solution-of-the","repo_url":"https://github.com/deepqmc/deepqmc","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1909.08423","atlas_url":"https://app.syntology.ai/?focus=1909.08423","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}