{"id":"W4416702331","doi":"10.1016/j.jcp.2025.114530","title":"MscaleFNO: Multi-scale Fourier neural operator learning for oscillatory functions and wave scattering problems","year":2025,"lang":"en","type":"article","venue":"Journal of Computational Physics","topic":"Electromagnetic Simulation and Numerical Methods","field":"Engineering","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"National Key Research and Development Program of China; National Natural Science Foundation of China; Saint Mary’s University","keywords":"Helmholtz equation; Nonlinear system; Fourier series; Artificial neural network; Fourier transform; Operator (biology); Scattering; Helmholtz free energy","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001107579,0.0008032018,0.0006532696,0.000467777,0.0004050462,0.0006761224,0.001854375,0.001566761,0.006718122],"category_scores_gemma":[0.002945327,0.0003060913,0.0005401238,0.000395486,0.000506883,0.001158048,0.001774459,0.001782037,0.001263888],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005235418,"about_ca_system_score_gemma":0.0009305727,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004240299,"about_ca_topic_score_gemma":0.007510453,"domain_scores_codex":[0.9997501,0.00005207997,0.00001198741,0.00004513804,0.0001074089,0.00003333435],"domain_scores_gemma":[0.9992313,0.0003580325,0.00003885372,0.0001221678,0.0001880133,0.00006161558],"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":[0.0002700594,0.0002952224,0.0007804605,0.0002389428,0.0001116082,0.0001397585,0.00008118241,0.3302147,0.008270725,0.02656724,0.02566778,0.6073624],"study_design_scores_gemma":[0.000007689084,0.00001585062,0.00005332367,0.000004583006,0.000002704845,0.00001171225,0.000002888647,0.9953704,0.0008549462,0.0027253,0.0009470163,0.000003432486],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01230477,0.0003785245,0.9791517,0.000314979,0.0002952518,0.0000763424,0.0002354757,0.003370329,0.00387264],"genre_scores_gemma":[0.2316429,0.000322893,0.7508595,0.000555208,0.0002314577,0.0003802263,0.001142938,0.0008825397,0.01398235],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006718122,"threshold_uncertainty_score":0.02247441,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02023544272482577,"score_gpt":0.2757775587341588,"score_spread":0.2555421160093331,"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."}}