{"id":"W4410619129","doi":"10.1142/s0219530525500307","title":"Deep operator network approximation rates for Lipschitz operators","year":2025,"lang":"en","type":"article","venue":"Analysis and Applications","topic":"Numerical methods in inverse problems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council","keywords":"Mathematics; Lipschitz continuity; Operator (biology); Lipschitz domain; Mathematical analysis; Applied mathematics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004470447,0.0001125915,0.0002940402,0.0001257012,0.0003325942,0.00008702804,0.0001354724,0.00006402133,0.00003541369],"category_scores_gemma":[0.0001605378,0.00009633478,0.0001302164,0.001577421,0.00005059232,0.00005891619,0.00004957699,0.00006782605,0.000004843007],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001898613,"about_ca_system_score_gemma":0.00001945631,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001068741,"about_ca_topic_score_gemma":0.00002325669,"domain_scores_codex":[0.9991081,0.00006014817,0.0003183424,0.000283995,0.00006915206,0.0001602975],"domain_scores_gemma":[0.9987695,0.0006348702,0.00008843702,0.0003308585,0.0001234199,0.00005287467],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000004666685,0.00008185446,0.002994892,0.00007396617,0.0007971597,2.900735e-8,0.00006383047,0.001126158,0.0002766276,0.9582189,0.001564426,0.03479753],"study_design_scores_gemma":[0.0002228218,0.00001270957,0.0002645825,0.00001288144,0.001776942,1.741148e-7,0.0001097013,0.1239977,0.001148453,0.8426239,0.02965417,0.0001759201],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.001836089,0.0002436517,0.9950576,0.0004609217,0.00002316214,0.0006973061,0.000007305342,0.00005531342,0.001618616],"genre_scores_gemma":[0.05818581,0.00009014768,0.9375192,0.0004885829,0.0001176304,0.002744189,0.00004206342,0.0000152781,0.000797089],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.1228716,"threshold_uncertainty_score":0.3928418,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03254134380852547,"score_gpt":0.3812606273612025,"score_spread":0.348719283552677,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}