{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:07:55Z","timestamp":1758269275944,"version":"3.37.3"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"17","license":[{"start":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T00:00:00Z","timestamp":1655251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T00:00:00Z","timestamp":1655251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62006247"],"award-info":[{"award-number":["62006247"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"crossref","award":["2019YFC1510501"],"award-info":[{"award-number":["2019YFC1510501"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100010244","name":"Science Foundation of China University of Petroleum-Beijing","doi-asserted-by":"crossref","award":["2462020YXZZ025"],"award-info":[{"award-number":["2462020YXZZ025"]}],"id":[{"id":"10.13039\/501100010244","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s11227-022-04629-7","type":"journal-article","created":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T10:03:22Z","timestamp":1655287402000},"page":"19020-19045","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A novel neural network training framework with data assimilation"],"prefix":"10.1007","volume":"78","author":[{"given":"Chong","family":"Chen","sequence":"first","affiliation":[]},{"given":"Yixuan","family":"Dou","sequence":"additional","affiliation":[]},{"given":"Jie","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Yaru","family":"Xue","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,15]]},"reference":[{"key":"4629_CR1","first-page":"19","volume":"11","author":"X Huang","year":"2019","unstructured":"Huang X, Gao L, Crosbie RS, Zhang N, Fu GB, Doble R (2019) Groundwater recharge prediction using linear regression. Multi-Layer Perception Network, and Deep Learning, Water 11:19","journal-title":"Multi-Layer Perception Network, and Deep Learning, Water"},{"key":"4629_CR2","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1038\/nature14539","volume":"521","author":"Y LeCun","year":"2015","unstructured":"LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521:436\u2013444","journal-title":"Nature"},{"key":"4629_CR3","doi-asserted-by":"publisher","first-page":"4509","DOI":"10.1109\/TIP.2017.2713099","volume":"26","author":"KH Jin","year":"2017","unstructured":"Jin KH, McCann MT, Froustey E, Unser M (2017) Deep convolutional neural network for inverse problems in imaging. IEEE Trans Image Process 26:4509\u20134522","journal-title":"IEEE Trans Image Process"},{"key":"4629_CR4","doi-asserted-by":"crossref","unstructured":"Zhou H, Chen C, Liu H, Qin F, (2019) Liang H Proactive Knowledge-Goals Dialogue System Based on Pointer Network, CCF International Conference on Natural Language Processing and Chinese Computing, (Springer), pp. 724\u2013735.","DOI":"10.1007\/978-3-030-32236-6_66"},{"key":"4629_CR5","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/BF02478259","volume":"5","author":"WS McCulloch","year":"1943","unstructured":"McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5:115\u2013133","journal-title":"Bull Math Biophys"},{"key":"4629_CR6","unstructured":"Rosenblatt F, The perceptron, a perceiving and recognizing automaton Project Para (Cornell Aeronautical Laboratory, 1957)."},{"key":"4629_CR7","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","volume":"79","author":"JJ Hopfield","year":"1982","unstructured":"Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79:2554\u20132558","journal-title":"Proc Natl Acad Sci USA"},{"key":"4629_CR8","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1038\/323533a0","volume":"323","author":"DE Rumelhart","year":"1986","unstructured":"Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagating errors. Nature 323:533\u2013536","journal-title":"Nature"},{"key":"4629_CR9","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"G Cybenko","year":"1989","unstructured":"Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Systems 2:303\u2013314","journal-title":"Math Control Signals Systems"},{"key":"4629_CR10","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","volume":"4","author":"K Hornik","year":"1991","unstructured":"Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4:251\u2013257","journal-title":"Neural Netw"},{"key":"4629_CR11","unstructured":"Zhao H (2016) General vector machine, arXiv preprint"},{"key":"4629_CR12","doi-asserted-by":"publisher","first-page":"1279","DOI":"10.1177\/1461348418813015","volume":"38","author":"NA Khan","year":"2019","unstructured":"Khan NA, Hameed T, Razzaq OA, Ayaz M (2019) Tracking the chaotic behaviour of fractional-order Chua\u2019s system by Mexican hat wavelet-based artificial neural network. J Low Freq Noise Vib Act Control 38:1279\u20131296","journal-title":"J Low Freq Noise Vib Act Control"},{"key":"4629_CR13","doi-asserted-by":"publisher","first-page":"108210","DOI":"10.1016\/j.ymssp.2021.108210","volume":"165","author":"A Gray","year":"2022","unstructured":"Gray A, Wimbush A, de Angelis M, Hristov PO, Calleja D, Miralles-Dolz E, Rocchetta R (2022) From inference to design: A comprehensive framework for uncertainty quantification in engineering with limited information. Mech Syst Signal Process 165:108210","journal-title":"Mech Syst Signal Process"},{"key":"4629_CR14","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1007\/s11442-011-0881-2","volume":"21","author":"X Song","year":"2011","unstructured":"Song X, Zhan C, Kong F, Xia J (2011) Advances in the study of uncertainty quantification of large-scale hydrological modeling system. J Geog Sci 21:801","journal-title":"J Geog Sci"},{"key":"4629_CR15","doi-asserted-by":"crossref","unstructured":"Her Y, Yoo S-H, Cho J, Hwang S, Jeong J, Seong C (2019) Uncertainty in hydrological analysis of climate change: multi- parameter vs. multi-GCM ensemble predictions, Scientific Reports, p 9.","DOI":"10.1038\/s41598-019-41334-7"},{"key":"4629_CR16","doi-asserted-by":"publisher","first-page":"3141","DOI":"10.1002\/hyp.6396","volume":"20","author":"K Beven","year":"2006","unstructured":"Beven K (2006) On undermining the science? Hydrol Process 20:3141\u20133146","journal-title":"Hydrol Process"},{"key":"4629_CR17","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/j.jhydrol.2010.06.044","volume":"390","author":"L Li","year":"2010","unstructured":"Li L, Xia J, Xu C-Y, Singh VP (2010) Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models. J Hydrol 390:210\u2013221","journal-title":"J Hydrol"},{"key":"4629_CR18","doi-asserted-by":"crossref","unstructured":"Engeland K, Xu C-Y, Gottschalk L (2005) Assessing uncertainties in a conceptual water balance model using Bayesian methodology \/ Estimation bay\u00e9sienne des incertitudes au sein d\u2019une mod\u00e9lisation conceptuelle de bilan hydrologique, Hydrological Sciences Journal, 50 null-63.","DOI":"10.1623\/hysj.50.1.45.56334"},{"key":"4629_CR19","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/S0022-1694(01)00421-8","volume":"249","author":"K Beven","year":"2001","unstructured":"Beven K, Freer J (2001) Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology. J Hydrol 249:11\u201329","journal-title":"J Hydrol"},{"key":"4629_CR20","unstructured":"Daley R, Atmospheric Data Analysis (Cambridge University Press, 1993)"},{"key":"4629_CR21","doi-asserted-by":"publisher","first-page":"4489","DOI":"10.1175\/MWR-D-15-0440.1","volume":"144","author":"PL Houtekamer","year":"2016","unstructured":"Houtekamer PL, Zhang FQ (2016) Review of the ensemble kalman filter for atmospheric data assimilation. Mon Weather Rev 144:4489\u20134532","journal-title":"Mon Weather Rev"},{"key":"4629_CR22","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1175\/1520-0493(2004)132<0703:SIAAPA>2.0.CO;2","volume":"132","author":"J Tribbia","year":"2004","unstructured":"Tribbia J, Baumhefner D (2004) Scale interactions and atmospheric predictability: an updated perspective. Mon Weather Rev 132:703\u2013713","journal-title":"Mon Weather Rev"},{"key":"4629_CR23","doi-asserted-by":"publisher","first-page":"919","DOI":"10.1088\/0741-3335\/35\/8\/002","volume":"35","author":"C Leith","year":"1993","unstructured":"Leith C (1993) Numerical models of weather and climate. Plasma Phys Controlled Fusion 35:919","journal-title":"Plasma Phys Controlled Fusion"},{"key":"4629_CR24","doi-asserted-by":"crossref","unstructured":"Wunsch C, Discrete inverse and state estimation problems: with geophysical fluid applications (Cambridge University Press, 2006).","DOI":"10.1017\/CBO9780511535949"},{"key":"4629_CR25","unstructured":"Biegler LT, Coleman TF, Conn AR, Santosa FN, Large-Scale Optimization with Applications: Part I: Optimization in Inverse Problems and Design (Springer Science & Business Media, 2012)."},{"key":"4629_CR26","unstructured":"Emerick A, History Matching and Uncertainty Characterization: Using Ensemble-based Methods (LAP LAMBERT Academic Publishing, 2012)."},{"key":"4629_CR27","doi-asserted-by":"crossref","unstructured":"C.D. Rodgers, Inverse methods for atmospheric sounding: theory and practice (World scientific, 2000).","DOI":"10.1142\/3171"},{"key":"4629_CR28","doi-asserted-by":"crossref","unstructured":"A. Tarantola, Inverse problem theory and methods for model parameter estimation (siam, 2005).","DOI":"10.1137\/1.9780898717921"},{"key":"4629_CR29","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1029\/94JC00572","volume":"99","author":"G Evensen","year":"1994","unstructured":"Evensen G (1994) Sequential data assimilation with a nonlinear quasi-geostrophic model using monte carlo methods to forecast error statistics. J Geophys Res 99:10\u201310","journal-title":"J Geophys Res"},{"key":"4629_CR30","first-page":"35","volume":"82","author":"RE Kalman","year":"1960","unstructured":"Kalman RE (1960) A new approach to linear filtering and prediction problems. J Fluids Eng 82:35\u201345","journal-title":"J Fluids Eng"},{"key":"4629_CR31","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1115\/1.3658902","volume":"83","author":"RE Kalman","year":"1961","unstructured":"Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. J Basic Eng 83:95\u2013108","journal-title":"J Basic Eng"},{"key":"4629_CR32","doi-asserted-by":"publisher","first-page":"393","DOI":"10.2118\/117274-PA","volume":"14","author":"SI Aanonsen","year":"2009","unstructured":"Aanonsen SI, N\u00e6vdal G, Oliver DS, Reynolds AC, Vall\u00e9s B (2009) Review of ensemble Kalman filter in petroleum engineering. Spe J 14:393\u2013412","journal-title":"Spe J"},{"key":"4629_CR33","doi-asserted-by":"crossref","unstructured":"Hendricks Franssen HJ, Kinzelbach W (2008) Real\u2010time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem, Water Resour Res, p 44","DOI":"10.1029\/2007WR006505"},{"key":"4629_CR34","doi-asserted-by":"publisher","first-page":"1708","DOI":"10.1109\/TIE.2019.2905817","volume":"67","author":"DEG Erazo","year":"2020","unstructured":"Erazo DEG, Wallscheid O, Bocker J (2020) Improved fusion of permanent magnet temperature estimation techniques for synchronous motors using a kalman filter. IEEE Trans Ind Electron 67:1708\u20131717","journal-title":"IEEE Trans Ind Electron"},{"key":"4629_CR35","doi-asserted-by":"crossref","first-page":"55","DOI":"10.3390\/sci2030055","volume":"2","author":"M Bocquet","year":"2020","unstructured":"Bocquet M, Brajard J, Carrassi A, Bertino L (2020) Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization, Foundations of Data. Science 2:55\u201380","journal-title":"Science"},{"key":"4629_CR36","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.neucom.2019.01.070","volume":"337","author":"JP N\u00f3brega","year":"2019","unstructured":"N\u00f3brega JP, Oliveira ALI (2019) A sequential learning method with Kalman filter and extreme learning machine for regression and time series forecasting. Neurocomputing 337:235\u2013250","journal-title":"Neurocomputing"},{"key":"4629_CR37","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1111\/j.1468-0394.2009.00469.x","volume":"26","author":"T Mu","year":"2009","unstructured":"Mu T, Nandi AK (2009) Automatic tuning of L2-SVM parameters employing the extended Kalman filter. Expert Syst 26:160\u2013175","journal-title":"Expert Syst"},{"key":"4629_CR38","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1016\/S0893-6080(05)80139-X","volume":"5","author":"S Shah","year":"1992","unstructured":"Shah S, Palmieri F, Datum M (1992) Optimal filtering algorithms for fast learning in feedforward neural networks. Neural Netw 5:779\u2013787","journal-title":"Neural Netw"},{"key":"4629_CR39","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1109\/72.737502","volume":"10","author":"J Sum","year":"1999","unstructured":"Sum J, Chi-Sing L, Young GH, Wing-Kay K (1999) On the Kalman filtering method in neural network training and pruning. IEEE Trans Neural Networks 10:161\u2013166","journal-title":"IEEE Trans Neural Networks"},{"key":"4629_CR40","doi-asserted-by":"publisher","first-page":"930","DOI":"10.1109\/72.774266","volume":"10","author":"Z Youmin","year":"1999","unstructured":"Youmin Z, Li XR (1999) A fast U-D factorization-based learning algorithm with applications to nonlinear system modeling and identification. IEEE Trans Neural Networks 10:930\u2013938","journal-title":"IEEE Trans Neural Networks"},{"key":"4629_CR41","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/S0925-2312(01)00611-7","volume":"48","author":"D Simon","year":"2002","unstructured":"Simon D (2002) Training radial basis neural networks with the extended Kalman filter. Neurocomputing 48:455\u2013475","journal-title":"Neurocomputing"},{"key":"4629_CR42","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1109\/72.478408","volume":"7","author":"D Obradovic","year":"1996","unstructured":"Obradovic D (1996) On-line training of recurrent neural networks with continuous topology adaptation. IEEE Trans Neural Networks 7:222\u2013228","journal-title":"IEEE Trans Neural Networks"},{"key":"4629_CR43","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1109\/72.279191","volume":"5","author":"GV Puskorius","year":"1994","unstructured":"Puskorius GV, Feldkamp LA (1994) Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks. IEEE Trans Neural Networks 5:279\u2013297","journal-title":"IEEE Trans Neural Networks"},{"key":"4629_CR44","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.neunet.2018.11.009","volume":"110","author":"Y Chen","year":"2019","unstructured":"Chen Y, Chang H, Meng J, Zhang D (2019) Ensemble Neural Networks (ENN): a gradient-free stochastic method. Neural Netw 110:170\u2013185","journal-title":"Neural Netw"},{"key":"4629_CR45","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.cageo.2012.03.011","volume":"55","author":"AA Emerick","year":"2013","unstructured":"Emerick AA, Reynolds AC (2013) Ensemble smoother with multiple data assimilation. Comput Geosci 55:3\u201315","journal-title":"Comput Geosci"},{"key":"4629_CR46","doi-asserted-by":"publisher","first-page":"2898","DOI":"10.1175\/1520-0493(1996)124<2898:DAAIMI>2.0.CO;2","volume":"124","author":"PJv Leeuwen","year":"1996","unstructured":"Leeuwen PJv, Evensen G (1996) Data assimilation and inverse methods in terms of a probabilistic formulation. Mon Weather Rev 124:2898\u20132913","journal-title":"Mon Weather Rev"},{"key":"4629_CR47","doi-asserted-by":"publisher","first-page":"125443","DOI":"10.1016\/j.jhydrol.2020.125443","volume":"590","author":"J Bao","year":"2020","unstructured":"Bao J, Li L, Redoloza F (2020) Coupling ensemble smoother and deep learning with generative adversarial networks to deal with non-Gaussianity in flow and transport data assimilation. J Hydrol 590:125443","journal-title":"J Hydrol"},{"key":"4629_CR48","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1504\/IJES.2016.073743","volume":"8","author":"Y Li","year":"2016","unstructured":"Li Y, Chen C, Zhou J, Zhang G, Chen X (2016) Dual state-parameter simultaneous estimation using localised Ensemble Kalman Filter and application in environmental model. Int J Embedded Syst 8:93\u2013103","journal-title":"Int J Embedded Syst"},{"key":"4629_CR49","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1007\/s10596-012-9275-5","volume":"16","author":"AA Emerick","year":"2012","unstructured":"Emerick AA, Reynolds AC (2012) History matching time-lapse seismic data using the ensemble Kalman filter with multiple data assimilations. Computat Geosci 16:639\u2013659","journal-title":"Computat Geosci"},{"key":"4629_CR50","doi-asserted-by":"publisher","first-page":"885","DOI":"10.13031\/2013.23153","volume":"50","author":"DN Moriasi","year":"2007","unstructured":"Moriasi DN (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50:885\u2013880","journal-title":"Trans ASABE"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-04629-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-022-04629-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-04629-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T23:31:48Z","timestamp":1727393508000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-022-04629-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,15]]},"references-count":50,"journal-issue":{"issue":"17","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["4629"],"URL":"https:\/\/doi.org\/10.1007\/s11227-022-04629-7","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"type":"print","value":"0920-8542"},{"type":"electronic","value":"1573-0484"}],"subject":[],"published":{"date-parts":[[2022,6,15]]},"assertion":[{"value":"23 May 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}