{"paper":{"title":"Relationship Between Controllability Scoring and Optimal Experimental Design","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kazuhiro Sato","submitted_at":"2026-02-12T13:20:53Z","abstract_excerpt":"Controllability scores provide control-theoretic centrality measures that quantify the relative importance of state nodes in networked dynamical systems. We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED. This yields a direct correspondence between the volumetric controllability score (VCS) and D-optimality, and between the average energy controllabili"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The finite-time controllability Gramian admits an additive decomposition across nodes for linear networked systems, and source-like nodes without negative self-loops exhibit the stated long-horizon downweighting under AECS.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Finite-time controllability scoring matches approximate OED, with VCS corresponding to D-optimality and AECS to A-optimality, plus a unique optimizer and long-horizon node downweighting.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1bbded80f7d1900e126117841fcf8a2388b19da3ca651101566d85d9e8a360bb"},"source":{"id":"2602.11921","kind":"arxiv","version":3},"verdict":{"id":"02f8f3f8-d68a-471d-85e8-40a907cd2fe4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T02:43:37.956714Z","strongest_claim":"We establish a structural connection between finite-time controllability scoring and approximate optimal experimental design (OED): the finite-time controllability Gramian decomposes additively across nodes, yielding an affine matrix model of the same form as the information-matrix model in OED.","one_line_summary":"Finite-time controllability scoring matches approximate OED, with VCS corresponding to D-optimality and AECS to A-optimality, plus a unique optimizer and long-horizon node downweighting.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The finite-time controllability Gramian admits an additive decomposition across nodes for linear networked systems, and source-like nodes without negative self-loops exhibit the stated long-horizon downweighting under AECS.","pith_extraction_headline":"Finite-time controllability scores in linear networks match D- and A-optimality criteria from optimal experimental design via additive Gramian decomposition."},"references":{"count":16,"sample":[{"doi":"","year":2017,"title":"On the role of network centrality in the controllability of complex networks,","work_id":"2f6da2c5-36a2-4d5c-920c-666b87e26cbd","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Controllability of complex networks,","work_id":"3f283b0d-8a86-4ff6-afee-795316d4f26c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Controllability metrics, limitations and algorithms for complex networks,","work_id":"077e082e-3544-445f-aabc-7dc27c9b7b0b","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"On submodularity and controllability in complex dynamical networks,","work_id":"f17933db-9cb9-4a2c-a595-60eb940cd572","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Controllability of large-scale networks: The control energy exponents,","work_id":"3244ec8f-c2bd-4736-9910-06f63551aee4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":16,"snapshot_sha256":"b938f4b7b1dcca710ba41bbd433b82466a9ecbda4a9908775722961effe3b9f1","internal_anchors":1},"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"}