{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00009944995,0.0001047468,0.0002447396,0.000003553897,0.000353592,0.00006783621,0.000560826,0.00001532416,0.0002467374],"category_scores_gemma":[0.00003926421,0.00006310592,0.0003134231,0.0000470594,0.0008830039,0.00006456409,0.0002033967,0.0001568912,0.00001366951],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006963564,"about_ca_system_score_gemma":0.0000202778,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004005481,"about_ca_topic_score_gemma":3.85427e-7,"domain_scores_codex":[0.9993059,0.00002316998,0.000167828,0.0001337431,0.0002042472,0.0001651206],"domain_scores_gemma":[0.9987117,0.000147573,0.0004525343,0.0005920582,0.00004048278,0.00005562479],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0001572937,0.001651549,0.164783,0.0003777572,0.001338672,8.322289e-7,0.00491964,0.002978837,0.007118755,0.4504369,0.01099215,0.3552447],"study_design_scores_gemma":[0.002421637,0.0003413732,0.08351331,0.001004019,0.0006771718,0.000001835837,0.006709595,0.5977039,0.03218483,0.2653985,0.008278071,0.001765737],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9615208,0.000008576973,0.02344517,0.001508926,0.00009429512,0.0001176515,0.00001766606,0.00001621564,0.01327074],"genre_scores_gemma":[0.9943404,0.000002689702,0.004781553,0.0001136099,0.0001185395,0.000006312286,5.30619e-7,0.00000836706,0.0006279829],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5947251,"threshold_uncertainty_score":0.3253465,"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."}}