{"id":"W4396615857","doi":"10.1007/s10915-024-02539-9","title":"Multilevel Monte Carlo Methods for Stochastic Convection–Diffusion Eigenvalue Problems","year":2024,"lang":"en","type":"article","venue":"Journal of Scientific Computing","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers; Natural Sciences and Engineering Research Council of Canada; Universität Wien; Erwin Schrödinger International Institute for Mathematics and Physics; Monash University","keywords":"Monte Carlo method; Mathematics; Applied mathematics; Eigenvalues and eigenvectors; Estimator; Discretization; Quasi-Monte Carlo method; Uncertainty quantification; Mathematical optimization; Hybrid Monte Carlo; Markov chain Monte Carlo; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.004862129,0.0001328559,0.0002908864,0.0003237011,0.00029602,0.0004811128,0.0001812906,0.00006274248,0.00008256846],"category_scores_gemma":[0.001931802,0.00009458111,0.0002375768,0.0003228784,0.00007647838,0.000227744,0.00004597446,0.0002406189,0.000009490878],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001019906,"about_ca_system_score_gemma":0.0001090794,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001613249,"about_ca_topic_score_gemma":0.000001351304,"domain_scores_codex":[0.9982398,0.0001064251,0.000890976,0.0002134031,0.0003528415,0.000196609],"domain_scores_gemma":[0.997219,0.001542219,0.0003834299,0.0001433115,0.0006165098,0.00009558736],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00004695404,0.0005593543,0.000005196752,0.003211316,0.0002297559,0.000005429069,0.02054065,0.004014219,0.0463276,0.2706858,0.01785666,0.636517],"study_design_scores_gemma":[0.0002191758,0.00006285127,0.000005152247,0.0007033416,0.00005361159,0.00006927846,0.0003086063,0.8419067,0.001289009,0.1525342,0.002758472,0.00008955131],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.07455812,0.0001788288,0.9217269,0.0002206802,0.002647278,0.0003967987,0.00000324366,0.000061004,0.0002071445],"genre_scores_gemma":[0.3461435,9.47442e-7,0.6515799,0.00001578891,0.0002701257,0.000005667207,0.000001192292,0.00002164069,0.001961257],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.8378925,"threshold_uncertainty_score":0.4639382,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1195366774912321,"score_gpt":0.4289420828425572,"score_spread":0.309405405351325,"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."}}