{"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/representations-of-molecules-and-materials","title":"Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning","arxiv_id":"2003.12081","date":"2020-03-26","proceeding":null,"authors":["Marcel F. Langer","Alex Goeßmann","Matthias Rupp"],"abstract":"Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry, and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, often by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We comprehensively review and discuss current representations and relations between them, using a unified mathematical framework based on many-body functions, group averaging, and tensor products. For selected state-of-the-art representations, we compare energy predictions for organic molecules, binary alloys, and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method, and hyper-parameter optimization.","url_abs":"https://arxiv.org/abs/2003.12081v2","url_pdf":"https://arxiv.org/pdf/2003.12081v2.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":"representations-of-molecules-and-materials","repo_url":"https://gitlab.com/qmml/qmmlpack","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"representations-of-molecules-and-materials","repo_url":"https://github.com/sirmarcel/cmlkit","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"representations-of-molecules-and-materials","repo_url":"https://gitlab.com/repbench/repbench-datasets","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"representations-of-molecules-and-materials","repo_url":"https://gitlab.com/repbench/repbench-results","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"representations-of-molecules-and-materials","repo_url":"https://gitlab.com/sirmarcel/mortimer","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"representations-of-molecules-and-materials","repo_url":"https://gitlab.com/sirmarcel/skrrt","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2003.12081","atlas_url":"https://app.syntology.ai/?focus=2003.12081","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2003.12081"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/sirmarcel/cmlkit","reach":{"status":"ok","spdx":"MIT"}},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://gitlab.com/sirmarcel/skrrt","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://gitlab.com/sirmarcel/mortimer","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://gitlab.com/qmml/qmmlpack","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://gitlab.com/repbench/repbench-datasets","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://gitlab.com/repbench/repbench-results","reach":null}],"summary":{"ran":7},"by_repo_kind":{"official":{"samples":7,"ran":7,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"90abda60e89b501d","entry":"compute_incidence","repo":"sirmarcel/cmlkit","repo_kind":"official","path":"cmlkit/dataset/dataset.py","file_url":"https://github.com/sirmarcel/cmlkit/blob/HEAD/cmlkit/dataset/dataset.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"90abda60e89b501d"}},{"code_sha256_prefix":"e4d1a706c87ee250","entry":"compute_mask","repo":"sirmarcel/cmlkit","repo_kind":"official","path":"cmlkit/dataset/dataset.py","file_url":"https://github.com/sirmarcel/cmlkit/blob/HEAD/cmlkit/dataset/dataset.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e4d1a706c87ee250"}},{"code_sha256_prefix":"ca795ca1e0c0af42","entry":"float_representer","repo":"sirmarcel/cmlkit","repo_kind":"official","path":"cmlkit/engine/inout.py","file_url":"https://github.com/sirmarcel/cmlkit/blob/HEAD/cmlkit/engine/inout.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ca795ca1e0c0af42"}},{"code_sha256_prefix":"0ac4bf46d288d0ee","entry":"int_representer","repo":"sirmarcel/cmlkit","repo_kind":"official","path":"cmlkit/engine/inout.py","file_url":"https://github.com/sirmarcel/cmlkit/blob/HEAD/cmlkit/engine/inout.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0ac4bf46d288d0ee"}},{"code_sha256_prefix":"1ae6182454e233e4","entry":"is_config","repo":"sirmarcel/cmlkit","repo_kind":"official","path":"cmlkit/engine/configparse.py","file_url":"https://github.com/sirmarcel/cmlkit/blob/HEAD/cmlkit/engine/configparse.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1ae6182454e233e4"}},{"code_sha256_prefix":"98cb7ad30bd3497c","entry":"parse_config","repo":"sirmarcel/cmlkit","repo_kind":"official","path":"cmlkit/engine/configparse.py","file_url":"https://github.com/sirmarcel/cmlkit/blob/HEAD/cmlkit/engine/configparse.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"98cb7ad30bd3497c"}},{"code_sha256_prefix":"928c58ef178d35e9","entry":"sequence_representer","repo":"sirmarcel/cmlkit","repo_kind":"official","path":"cmlkit/engine/inout.py","file_url":"https://github.com/sirmarcel/cmlkit/blob/HEAD/cmlkit/engine/inout.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"928c58ef178d35e9"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}