{"id":"W4378532742","doi":"10.1142/s0219876222500517","title":"Solving Nonlinear Elliptic PDEs in 2D and 3D Using Polyharmonic Splines and Low-Degree of Polynomials","year":2023,"lang":"en","type":"article","venue":"International Journal of Computational Methods","topic":"Numerical methods in engineering","field":"Engineering","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Simons Foundation","keywords":"Mathematics; Discretization; Polynomial; Nonlinear system; Mathematical analysis; Basis function; Degree of a polynomial; Radial basis function; Polynomial basis; Boundary value problem; Polyharmonic spline; Collocation (remote sensing); Collocation method; Elliptic curve; Bernstein polynomial; Applied mathematics; Differential equation; Ordinary differential equation","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005568171,0.0005153327,0.0006509366,0.0005037889,0.0003292833,0.0005384404,0.0006551351,0.0009257871,0.0008005789],"category_scores_gemma":[0.001085678,0.000249697,0.0009744276,0.0005106698,0.000552387,0.0006310958,0.0008609617,0.000941498,0.0003154697],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002063331,"about_ca_system_score_gemma":0.0006680854,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001759449,"about_ca_topic_score_gemma":0.00178013,"domain_scores_codex":[0.999711,0.00009162801,0.00001716755,0.0000379821,0.0001199375,0.00002234529],"domain_scores_gemma":[0.9996296,0.000204905,0.00003479694,0.00004568412,0.00006549944,0.00001946754],"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":[0.00006343143,0.00006174927,0.001348486,0.0002957866,0.00005809726,0.000223581,0.0002774503,0.8218023,0.0257449,0.02531344,0.0006540538,0.1241567],"study_design_scores_gemma":[0.000003953844,0.00001870477,0.00008832952,0.000007202061,0.000004352058,0.0000500255,0.00001698741,0.9955983,0.001454519,0.001568973,0.001181799,0.000006775117],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.01276495,0.0003025139,0.9859583,0.00004658527,0.00003327306,0.00001362229,0.00001063199,0.00007024358,0.0007999139],"genre_scores_gemma":[0.2895787,0.001241657,0.7059967,0.00006109984,0.00007640409,0.0001157182,0.0001053036,0.00007247279,0.002752068],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.001759449,"threshold_uncertainty_score":0.003498435,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05604744595360355,"score_gpt":0.3880199952408656,"score_spread":0.3319725492872621,"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."}}