{"id":"W2936334504","doi":"10.48550/arxiv.1904.07200","title":"A Discussion on Solving Partial Differential Equations using Neural Networks","year":2019,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Model Reduction and Neural Networks","field":"Physics and Astronomy","cited_by":42,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Artificial neural network; Partial differential equation; Initialization; Computer science; Applied mathematics; Function (biology); Mathematics; Mathematical optimization; Artificial intelligence; Mathematical analysis","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":[0.003227403,0.0008176059,0.000781731,0.0008065777,0.0009083352,0.001831147,0.002269436,0.004503176,0.00535224],"category_scores_gemma":[0.005485623,0.0004510543,0.001664285,0.001151019,0.003341284,0.005470281,0.001412494,0.005612665,0.001256866],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001157292,"about_ca_system_score_gemma":0.0005080097,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001701756,"about_ca_topic_score_gemma":0.001165764,"domain_scores_codex":[0.9987382,0.0005990383,0.00008069521,0.0001785119,0.000346987,0.00005661429],"domain_scores_gemma":[0.9982444,0.00137966,0.00008057674,0.0001049015,0.0001544892,0.00003599671],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002170185,0.00004572109,0.0002842906,0.0006753709,0.00004930417,0.0001120562,0.0001515961,0.05329138,0.0009999799,0.9091148,0.008308887,0.02694494],"study_design_scores_gemma":[0.00001549174,0.00007444479,0.0002954658,0.0003608083,0.00001930409,0.0001353119,0.00007394397,0.2146878,0.00104597,0.7206168,0.06264059,0.00003407629],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.009673175,0.08654584,0.7148754,0.09685338,0.004544613,0.000104222,0.0003634953,0.0002698137,0.08677011],"genre_scores_gemma":[0.3655542,0.1280175,0.3812186,0.03463573,0.01876486,0.0008851168,0.0004018509,0.0004507492,0.07007136],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.00535224,"threshold_uncertainty_score":0.017905,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06985187586401935,"score_gpt":0.2984781661036347,"score_spread":0.2286262902396153,"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."}}