{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001269007,0.0001417966,0.0003406128,0.0007056301,0.00001788527,0.00003699493,0.0001909392,0.00005972871,0.000009703536],"category_scores_gemma":[0.000662002,0.0001427642,0.00005670484,0.0003397938,0.00006463952,0.0002178318,0.0000801624,0.0002269417,8.489032e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007803292,"about_ca_system_score_gemma":0.00004698353,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006966776,"about_ca_topic_score_gemma":4.602674e-7,"domain_scores_codex":[0.998556,0.0001282758,0.0007218172,0.0001119006,0.0003275746,0.0001544813],"domain_scores_gemma":[0.9977289,0.001705642,0.0001884274,0.00005296684,0.0002505492,0.0000735104],"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":[0.00002441158,0.00001501729,0.001258058,0.00006590364,0.0001248074,0.0000280629,0.0001904364,0.8695218,0.03729379,0.0001800876,0.000006191056,0.09129144],"study_design_scores_gemma":[0.0004786013,0.00002881023,0.01775558,0.0002706645,0.0000192955,0.000172998,0.00005832843,0.9705821,0.005193852,0.005236078,0.00007279098,0.0001308522],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.5294506,0.0008723155,0.468784,0.0000669583,0.0007295719,0.00003832037,0.000006681803,0.00002294672,0.0000286634],"genre_scores_gemma":[0.3546513,0.0001695343,0.6449367,0.00001293815,0.0002035032,8.174724e-7,0.00000140388,0.0000209043,0.000002845552],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.1761528,"threshold_uncertainty_score":0.5821755,"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."}}