{"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/wavelet-scattering-regression-of-quantum","title":"Wavelet Scattering Regression of Quantum Chemical Energies","arxiv_id":"1605.04654","date":"2016-05-16","proceeding":null,"authors":["Matthew Hirn","Stéphane Mallat","Nicolas Poilvert"],"abstract":"We introduce multiscale invariant dictionaries to estimate quantum chemical\nenergies of organic molecules, from training databases. Molecular energies are\ninvariant to isometric atomic displacements, and are Lipschitz continuous to\nmolecular deformations. Similarly to density functional theory (DFT), the\nmolecule is represented by an electronic density function. A multiscale\ninvariant dictionary is calculated with wavelet scattering invariants. It\ncascades a first wavelet transform which separates scales, with a second\nwavelet transform which computes interactions across scales. Sparse scattering\nregressions give state of the art results over two databases of organic planar\nmolecules. On these databases, the regression error is of the order of the\nerror produced by DFT codes, but at a fraction of the computational cost.","url_abs":"http://arxiv.org/abs/1605.04654v3","url_pdf":"http://arxiv.org/pdf/1605.04654v3.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":"wavelet-scattering-regression-of-quantum","repo_url":"https://github.com/matthew-hirn/ScatNet-QM-2D","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1605.04654","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}