{"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/graph-neural-networks-for-fast-electron","title":"Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids","arxiv_id":"2112.00652","date":"2021-12-01","proceeding":null,"authors":["Peter Bjørn Jørgensen","Arghya Bhowmik"],"abstract":"Electron density $\\rho(\\vec{r})$ is the fundamental variable in the calculation of ground state energy with density functional theory (DFT). Beyond total energy, features and changes in $\\rho(\\vec{r})$ distributions are often used to capture critical physicochemical phenomena in functional materials. We present a machine learning framework for the prediction of $\\rho(\\vec{r})$. The model is based on equivariant graph neural networks and the electron density is predicted at special query point vertices that are part of the message passing graph, but only receive messages. The model is tested across multiple data sets of molecules (QM9), liquid ethylene carbonate electrolyte (EC) and LixNiyMnzCo(1-y-z)O2 lithium ion battery cathodes (NMC). For QM9 molecules, the accuracy of the proposed model exceeds typical variability in $\\rho(\\vec{r})$ obtained from DFT done with different exchange-correlation functionals. The accuracy on all three datasets is beyond state of the art and the computation time is orders of magnitude faster than DFT.","url_abs":"https://arxiv.org/abs/2112.00652v2","url_pdf":"https://arxiv.org/pdf/2112.00652v2.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":"graph-neural-networks-for-fast-electron","repo_url":"https://github.com/peterbjorgensen/DeepDFT","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[{"slug":"ethylene-carbonate-molecular-dynamics","name":"Ethylene Carbonate Molecular Dynamics","full_name":""},{"slug":"nmc-li-ion-battery-cathode-energies-and","name":"NMC Li-ion Battery Cathode Energies and Charge Densities","full_name":""}],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2112.00652","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2112.00652"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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