{"id":"W4408461761","doi":"10.1016/j.cma.2025.117897","title":"Gradient flow based phase-field modeling using separable neural networks","year":2025,"lang":"en","type":"article","venue":"Computer Methods in Applied Mechanics and Engineering","topic":"Model Reduction and Neural Networks","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Artificial Intelligence in Medicine (Canada)","funders":"Office of Science; National Energy Research Scientific Computing Center; Michigan Technological University; U.S. Department of Energy","keywords":"Artificial neural network; Separable space; Balanced flow; Flow (mathematics); Field (mathematics); Computer science; Phase (matter); Two-phase flow; Mechanics; Applied mathematics; Mathematics; Physics; Artificial intelligence; Mathematical analysis; Pure mathematics","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":[0.0003795137,0.0007166089,0.0005516573,0.0004012283,0.0003336348,0.0006909288,0.001116526,0.0009021801,0.001879892],"category_scores_gemma":[0.0009414657,0.0003875118,0.0006076174,0.000392184,0.0006081,0.001202959,0.0008053753,0.001059594,0.0003890675],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009023835,"about_ca_system_score_gemma":0.001044052,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.008469175,"about_ca_topic_score_gemma":0.007303349,"domain_scores_codex":[0.9998944,0.00002863122,0.000004814216,0.0000214264,0.00003720331,0.00001353669],"domain_scores_gemma":[0.9997709,0.00009969906,0.00003731505,0.00002072675,0.00005314382,0.0000181825],"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":[0.00002554976,0.00001532945,0.000233749,0.00003742482,0.00001253339,0.00003993456,0.00002983192,0.9675181,0.00260862,0.01612965,0.0004445405,0.01290479],"study_design_scores_gemma":[7.397756e-7,0.000001230831,0.000007341632,7.215947e-7,4.660828e-7,0.000001466829,5.565909e-7,0.9989226,0.0001079102,0.0008609192,0.00009519566,8.751938e-7],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01225189,0.0002065745,0.9843026,0.0001497891,0.00003180076,0.00002999046,0.00005872103,0.0002439462,0.0027247],"genre_scores_gemma":[0.6182575,0.0008589452,0.3661531,0.0001928041,0.00007770484,0.0002840093,0.0003363312,0.0002406502,0.01359898],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008469175,"threshold_uncertainty_score":0.01683974,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02623521517432949,"score_gpt":0.3180730851856339,"score_spread":0.2918378700113045,"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."}}