{"id":"W4416889706","doi":"10.1093/imanum/draf109","title":"Underdetermined Fourier extensions for surface partial differential equations","year":2025,"lang":"en","type":"article","venue":"IMA Journal of Numerical Analysis","topic":"Advanced Numerical Methods in Computational Mathematics","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Hilbert space; Partial differential equation; Surface (topology); Fourier transform; Basis function; Function space; Numerical partial differential equations; Exponential integrator; Domain (mathematical analysis)","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001826382,0.000155829,0.0005823009,0.0002824209,0.00009397016,0.00003818906,0.000205727,0.00005870945,0.00007992083],"category_scores_gemma":[0.0008562251,0.0001313463,0.0005713332,0.001235879,0.00004824492,0.0001118915,0.00003170543,0.0001848891,0.000003128441],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008180384,"about_ca_system_score_gemma":0.00003477879,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001242261,"about_ca_topic_score_gemma":4.258389e-7,"domain_scores_codex":[0.9986004,0.00006904811,0.0007341701,0.0001238753,0.0002660663,0.0002064992],"domain_scores_gemma":[0.9967834,0.002420024,0.0001910466,0.0001738603,0.0003188412,0.0001128626],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003432645,0.0001085175,0.00009368906,0.00003464937,0.001859113,0.000004092274,0.00004710751,0.9804202,0.001428259,0.002455996,0.000519659,0.01299444],"study_design_scores_gemma":[0.0003555756,0.00004915278,0.0003214105,0.00002121373,0.001628039,0.000003817726,0.00004032913,0.9714026,0.0006019003,0.02473869,0.0007085034,0.0001287633],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01201623,0.000186196,0.986736,0.0004591191,0.0003811938,0.00008612793,0.0000126829,0.00004252494,0.00007990161],"genre_scores_gemma":[0.5937802,0.00001095362,0.4059692,0.00005980728,0.00008298432,0.000004266493,0.000003265131,0.00001290219,0.00007642458],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5817639,"threshold_uncertainty_score":0.5356147,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02936527012265179,"score_gpt":0.3435679131901175,"score_spread":0.3142026430674657,"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."}}