{"id":"W4386228403","doi":"10.1016/j.cma.2023.116666","title":"Multi-level neural networks for accurate solutions of boundary-value problems","year":2023,"lang":"en","type":"article","venue":"Computer Methods in Applied Mechanics and Engineering","topic":"Model Reduction and Neural Networks","field":"Physics and Astronomy","cited_by":22,"is_retracted":false,"has_abstract":false,"ca_institutions":"Polytechnique Montréal","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Residual; Discretization; Artificial neural network; Partial differential equation; Computer science; Boundary value problem; Reduction (mathematics); Deep learning; Mathematical optimization; Applied mathematics; Algorithm; Finite element method; Artificial intelligence; Mathematics; 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":[0.0004936632,0.0001494321,0.0002385361,0.0001104882,0.00007393298,0.00003234809,0.0001018733,0.00005651182,0.000003542474],"category_scores_gemma":[0.000002613298,0.0001526223,0.00006477795,0.0002886218,0.000008143606,0.00003696022,0.0001221396,0.000180799,3.165649e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009251555,"about_ca_system_score_gemma":0.000008832973,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004563108,"about_ca_topic_score_gemma":3.419952e-7,"domain_scores_codex":[0.9991134,0.00002184144,0.0002664815,0.0002324845,0.00004883412,0.0003169964],"domain_scores_gemma":[0.9995897,0.000136104,0.00006043736,0.0001308945,0.00001932494,0.00006354031],"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":[0.000004049783,0.00001553892,0.000002192726,0.00003493431,0.00001920417,1.189498e-7,0.0000699845,0.7784065,0.003491056,0.1004423,0.00004820789,0.1174659],"study_design_scores_gemma":[0.0004518979,0.00001674002,0.0000412452,0.00002505263,0.000009818063,6.18979e-7,0.00001975815,0.9929331,0.0002824878,0.005438792,0.000633347,0.0001471342],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.001197519,0.00007443266,0.9975749,0.00002595361,0.0006896787,0.000341916,0.00001296817,0.00006566024,0.00001700551],"genre_scores_gemma":[0.2905321,0.00002046509,0.7090032,0.000014581,0.0002392823,0.0001228472,0.00002612115,0.00002721006,0.0000142552],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.2893345,"threshold_uncertainty_score":0.6223756,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08371317002252855,"score_gpt":0.3255139822104681,"score_spread":0.2418008121879395,"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."}}