{"paper":{"title":"Dimensionless Policies based on the Buckingham $\\pi$ Theorem: Is This a Good Way to Generalize Numerical Results?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.RO","cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Alexandre Girard","submitted_at":"2023-07-29T00:51:26Z","abstract_excerpt":"The answer to the question posed in the title is yes if the context (the list of variables defining the motion control problem) is dimensionally similar. This article explores the use of the Buckingham $\\pi$ theorem as a tool to encode the control policies of physical systems into a more generic form of knowledge that can be reused in various situations. This approach can be interpreted as enforcing invariance to the scaling of the fundamental units in an algorithm learning a control policy. First, we show, by restating the solution to a motion control problem using dimensionless variables, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15852","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.15852/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}