{"id":"W292382557","doi":"10.1090/noti1617","title":"Nonstandard Finite Difference Schemes","year":2017,"lang":"en","type":"article","venue":"Notices of the American Mathematical Society","topic":"Model Reduction and Neural Networks","field":"Physics and Astronomy","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Air Force Institute of Technology; University of Colorado Denver; University of California, Santa Barbara; College of Engineering, Michigan State University; Uniwersytet Marii Curie-Skłodowskiej; Universidad de Murcia; Universität Wien; École Polytechnique Fédérale de Lausanne; George Fox University; University of South Alabama; Division of Mathematical Sciences; Kent State University; Saint Louis University; Youngstown State University; Pacific Northwest National Laboratory; Università degli Studi di Salerno; Idaho State University; Swarthmore College; College of Charleston; West Virginia University; Iowa State University; University of South Florida; University of Akron; Georgia State University; University of Louisiana at Lafayette; Coastal Carolina University; Wellesley College; University of Cincinnati; Pennsylvania State University; Clemson University; Grand Valley State University; University of Denver; University of Nebraska-Lincoln; University of Notre Dame; Sonoma State University; University of Wyoming; Louisiana State University; University of Southern California; University of Oklahoma; University of Pittsburgh; University of Central Florida; University of Washington; University of California, Irvine; University of Dayton; Michigan State University; Auburn University; South Dakota State University; Williams College; Baylor University; University of Rochester; Virginia Polytechnic Institute and State University; University of Canterbury; Case Western Reserve University; University of Minnesota; Wichita State University; City University of New York; Ohio State University; Wake Forest University; University of Pennsylvania; Rice University; Georgia Institute of Technology; San Diego State University; University of Toronto; Washington and Lee University; Technische Universität Kaiserslautern; Portland State University; Tulane University; Arizona State University; University of Oregon; Brown University; University of Wisconsin-Madison; Western Carolina University; Oregon State University; University of Miami; California State University, Fresno; Siemens Healthineers; Eastern Kentucky University; U.S. Naval Academy; University of North Carolina at Chapel Hill; Wayne State University; University of California, San Diego; University of Southern Mississippi; University of Waterloo; Brigham Young University; Rowan University; Temple University; Purdue University; Ohio Wesleyan University; Georgia Southern University; Pitzer College; Vanderbilt University; Central Washington University; Massachusetts Institute of Technology","keywords":"Mathematics; Finite difference; Applied mathematics; Calculus (dental); Mathematical analysis; Medicine","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":[0.001480152,0.0005958399,0.0007848166,0.0006071925,0.0007685957,0.002020997,0.001447578,0.001009605,0.01890495],"category_scores_gemma":[0.00547106,0.0003314072,0.0008448955,0.0008276047,0.001533177,0.002238045,0.002434525,0.002832241,0.005615945],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001021065,"about_ca_system_score_gemma":0.001046089,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001455953,"about_ca_topic_score_gemma":0.002075201,"domain_scores_codex":[0.9990036,0.000291011,0.00007418202,0.0001401082,0.0004198145,0.0000712871],"domain_scores_gemma":[0.99864,0.000448116,0.00008361616,0.0004620064,0.0002989741,0.00006738331],"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":[0.00003443293,0.00001716275,0.000158647,0.00007106415,0.00001586539,0.00003561843,0.0000813022,0.01559047,0.0009160001,0.9336184,0.008082753,0.04137836],"study_design_scores_gemma":[0.00005833485,0.00004255506,0.0001097237,0.00006608843,0.00001221993,0.00008701074,0.00003535233,0.4509265,0.001869891,0.4402062,0.1065593,0.00002679331],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.003078004,0.001844261,0.9547789,0.0009299595,0.00146985,0.00008871587,0.0003440964,0.0005327858,0.03693337],"genre_scores_gemma":[0.2044129,0.003295685,0.7090921,0.0009374222,0.0009868977,0.0005112195,0.0009957599,0.0007089419,0.07905912],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.01890495,"threshold_uncertainty_score":0.06324339,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0227590667712254,"score_gpt":0.2926728653022856,"score_spread":0.2699137985310602,"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."}}