{"id":"W2949299135","doi":"10.48550/arxiv.1208.4870","title":"Numerical solution of the Optimal Transportation problem using the Monge-Ampere equation","year":2012,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Differential Equations and Boundary Problems","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Monge–Ampère equation; Stencil; Mathematics; Laplace's equation; Solver; Convergence (economics); Partial differential equation; Boundary value problem; Applied mathematics; Mathematical analysis; Elliptic partial differential equation; Biharmonic equation; Grid; Mathematical optimization; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006732454,0.0003749956,0.000748469,0.00041874,0.0006271447,0.0008734122,0.0007820454,0.001430357,0.003417971],"category_scores_gemma":[0.002101112,0.0002783737,0.0005357573,0.0004353207,0.0009198034,0.0008779224,0.001148763,0.001217682,0.0006056455],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005112477,"about_ca_system_score_gemma":0.001049189,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001718413,"about_ca_topic_score_gemma":0.001134514,"domain_scores_codex":[0.9997502,0.00008057524,0.0000152715,0.00003403386,0.0001002703,0.00001965061],"domain_scores_gemma":[0.9996132,0.0002108051,0.00003645936,0.00004921485,0.00006479723,0.00002552478],"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":[0.00004769713,0.0000583092,0.0006093994,0.0002353512,0.00002546228,0.0002023689,0.0001975114,0.672565,0.01831955,0.2609338,0.002581139,0.04422444],"study_design_scores_gemma":[0.00001651553,0.00002220866,0.00009713694,0.00001482808,0.000003338167,0.0001018301,0.00002333429,0.9585882,0.002066652,0.03444214,0.004611865,0.0000119405],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.008088874,0.0001771567,0.9860992,0.0002410993,0.00007109518,0.00003634214,0.0000462394,0.0001278765,0.005112142],"genre_scores_gemma":[0.247679,0.0004493562,0.7427915,0.0000911374,0.00007587139,0.0002413682,0.0001560844,0.0001424144,0.008373232],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003417971,"threshold_uncertainty_score":0.01143426,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1849789033617719,"score_gpt":0.3266942408165742,"score_spread":0.1417153374548023,"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."}}