{"id":"W4390784262","doi":"10.48550/arxiv.2401.04328","title":"Underdetermined Fourier Extensions for Surface Partial Differential Equations","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Partial differential equation; Sobolev space; Mathematical analysis; Surface (topology); Smoothness; Fourier transform; Applied mathematics; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00178158,0.0008674428,0.0007211104,0.0006084551,0.0003616363,0.001083734,0.0006809945,0.001171474,0.001209472],"category_scores_gemma":[0.005374317,0.0002978437,0.0007986485,0.0003542212,0.001591424,0.001638896,0.001845206,0.001649232,0.0002595997],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004146342,"about_ca_system_score_gemma":0.0005548027,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009642532,"about_ca_topic_score_gemma":0.0008198723,"domain_scores_codex":[0.9994043,0.0002777661,0.00001869972,0.00006631777,0.0001888535,0.00004409803],"domain_scores_gemma":[0.997915,0.001322341,0.0002353988,0.0001551567,0.0002792125,0.00009292208],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0000778445,0.00009564796,0.001420585,0.0001871282,0.00004655977,0.0003640769,0.0002641217,0.6218877,0.01220657,0.3293554,0.001074431,0.03301983],"study_design_scores_gemma":[0.000003398481,0.00001471919,0.00007271333,0.000006530858,0.000001917728,0.00003877327,0.00001386171,0.9777375,0.0006648455,0.02087916,0.0005607409,0.000005846903],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03905758,0.0001936104,0.9576188,0.0001985885,0.00003481032,0.0000326493,0.00002377585,0.00007277207,0.002767414],"genre_scores_gemma":[0.6310351,0.0007253028,0.3574412,0.0002130991,0.0001603283,0.0001828306,0.0001634628,0.0002149652,0.009863769],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00178158,"threshold_uncertainty_score":0.009422004,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1458499147464527,"score_gpt":0.25638197306664,"score_spread":0.1105320583201873,"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."}}