{"id":"W4297923771","doi":"10.48550/arxiv.1110.5921","title":"Symmetry Preserving Numerical Schemes for Partial Differential Equations\\n and their Numerical Tests","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Differential Equations and Numerical Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Fonds Québécois de la Recherche sur la Nature et les Technologies","keywords":"Equivariant map; Mathematics; Partial differential equation; Invariant (physics); Mathematical analysis; Polygon mesh; Logarithm; Finite difference; Heat equation; Symmetry (geometry); Finite difference method; Symmetry group; Pure mathematics; Mathematical physics; 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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003026255,0.0005424829,0.0008398317,0.00022269,0.0002904101,0.0001184188,0.0006639843,0.0004722336,0.0003217224],"category_scores_gemma":[0.001372859,0.0005019958,0.0004279012,0.0003437675,0.0001721344,0.0001778383,0.001301932,0.0006186928,0.00001267909],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009649347,"about_ca_system_score_gemma":0.0001085508,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009287494,"about_ca_topic_score_gemma":0.000006098917,"domain_scores_codex":[0.9974605,0.0003598449,0.0004620752,0.001077323,0.0001124633,0.0005277981],"domain_scores_gemma":[0.9960694,0.002135809,0.0004181375,0.0008537594,0.0002083737,0.0003145545],"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":[0.0003952928,0.001155313,0.001324293,0.000693553,0.0006856354,0.00001519988,0.0005037457,0.0003318478,0.0002961648,0.9840826,0.0004681972,0.01004818],"study_design_scores_gemma":[0.0008260203,0.0001659223,0.0004575224,0.0001318203,0.0004628178,0.000001922227,0.0001179047,0.4206698,0.0007275938,0.5751525,0.0006037712,0.0006824272],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1472791,0.0000667115,0.8506776,0.00004516649,0.0004460735,0.0006867575,0.00008107912,0.0001857801,0.0005316957],"genre_scores_gemma":[0.9773259,0.00003813348,0.02147494,0.00002576098,0.0002659322,0.00002363198,0.00005514589,0.0000732126,0.0007173346],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8300468,"threshold_uncertainty_score":0.9997432,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2259457290280556,"score_gpt":0.2825772411793574,"score_spread":0.05663151215130183,"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."}}