80 citations as recorded by crossref.

1. The back and forth nudging algorithm applied to a shallow water model, comparison and hybridization with the 4D‐VAR D. Auroux https://doi.org/10.1002/fld.1980
2. On the efficient low cost procedure for estimation of high-dimensional prediction error covariance matrices H. Hoang & R. Baraille https://doi.org/10.1016/j.automatica.2017.06.018
3. Evaluation and integration of reanalysis rainfall products under contrasting climatic conditions in India V. Kolluru et al. https://doi.org/10.1016/j.atmosres.2020.105121
4. Reconstructing Rayleigh–Bénard flows out of temperature-only measurements using nudging L. Agasthya et al. https://doi.org/10.1063/5.0079625
5. Stable explicit stepwise marching scheme in ill-posed time-reversed 2D Burgers' equation A. Carasso https://doi.org/10.1080/17415977.2018.1523905
6. Global Observations of Fine-Scale Ocean Surface Topography With the Surface Water and Ocean Topography (SWOT) Mission R. Morrow et al. https://doi.org/10.3389/fmars.2019.00232
7. Mathematical analysis of an observer for solving inverse source wave problem T. Delaunay et al. https://doi.org/10.3934/ipi.2025043
8. IMPROVING CONVERGENCE IN NUMERICAL ANALYSIS USING OBSERVERS — THE WAVE-LIKE EQUATION CASE D. CHAPELLE et al. https://doi.org/10.1142/S0218202512500406
9. Data assimilation with higher order finite element interpolants M. Jolly & A. Pakzad https://doi.org/10.1002/fld.5152
10. Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations G. Haine & K. Ramdani https://doi.org/10.1007/s00211-011-0408-x
11. New inversion methods for the single/multi-shape CLD-to-PSD problem with spheroid particles L. Brivadis & L. Sacchelli https://doi.org/10.1016/j.jprocont.2021.11.008
12. Regional mapping of energetic short mesoscale ocean dynamics from altimetry: performances from real observations F. Le Guillou et al. https://doi.org/10.5194/os-19-1517-2023
13. Data assimilation in 2D viscous Burgers equation using a stabilized explicit finite difference scheme run backward in time A. Carasso https://doi.org/10.1080/17415977.2021.2009476
14. Efficient nonlinear data assimilation using synchronization in a particle filter F. Pinheiro et al. https://doi.org/10.1002/qj.3576
15. Synchronization to Big Data: Nudging the Navier-Stokes Equations for Data Assimilation of Turbulent Flows P. Clark Di Leoni et al. https://doi.org/10.1103/PhysRevX.10.011023
16. Assimilation of low-level wind in a high-resolution mesoscale model using the back and forth nudging algorithm A. Boilley & J. Mahfouf https://doi.org/10.3402/tellusa.v64i0.18697
17. Back-and-forth nudging moving horizon estimation for discrete-time linear systems J. Xie & B. Huang https://doi.org/10.1016/j.automatica.2024.111691
18. A nudging data assimilation algorithm for the identification of groundwater pumping W. Cheng et al. https://doi.org/10.1029/2008WR007602
19. Analysis of an observer strategy for initial state reconstruction of wave-like systems in unbounded domains S. Imperiale et al. https://doi.org/10.1051/cocv/2019026
20. Optimal Feedback Force Locations in Measurement‐Integrated Simulation for Two‐Dimensional Flow Around a Circular Cylinder K. Hirose & S. Miyauchi https://doi.org/10.1002/fld.70045
21. A comparison of two nonlinear data assimilation methods V. Montiforte et al. https://doi.org/10.5194/npg-31-463-2024
22. A new back‐and‐forth iterative method for time‐reversed convection modeling: Implications for the Cenozoic evolution of 3‐D structure and dynamics of the mantle P. Glišović & A. Forte https://doi.org/10.1002/2016JB012841
23. State reconstruction of the wave equation with general viscosity and non-collocated observation and control F. Zheng & H. Zhou https://doi.org/10.1016/j.jmaa.2021.125257
24. Data assimilation for geophysical fluids D. Auroux https://doi.org/10.5802/afst.1552
25. Recovering the initial state of an infinite-dimensional system using observers K. Ramdani et al. https://doi.org/10.1016/j.automatica.2010.06.032
26. Joint Estimation of Balanced Motions and Internal Tides From Future Wide‐Swath Altimetry F. Le Guillou et al. https://doi.org/10.1029/2021MS002613
27. Enhanced retrospective forecasting in dissipative dynamical systems using transformer and multi-scale ESRGAN models M. Zhang et al. https://doi.org/10.1016/j.rineng.2024.103597
28. 资料同化中的人工智能技术：新兴方法、关键挑战与未来展望 悟. 王 et al. https://doi.org/10.1360/N072025-0199
29. Effect of discrete time observations on synchronization in Chua model and applications to data assimilation M. Nurujjaman et al. https://doi.org/10.1063/1.4712591
30. Derivative‐free optimization for large‐scale nonlinear data assimilation problems S. Gratton et al. https://doi.org/10.1002/qj.2169
31. Improving Numerical Dispersion Modelling in Built Environments with Data Assimilation Using the Iterative Ensemble Kalman Smoother C. Defforge et al. https://doi.org/10.1007/s10546-020-00588-9
32. Data assimilation experiments using diffusive back-and-forth nudging for the NEMO ocean model G. Ruggiero et al. https://doi.org/10.5194/npg-22-233-2015
33. Iterative observer-based state and parameter estimation for linear systems A. Aalto https://doi.org/10.1051/cocv/2017005
34. Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows S. Pawar et al. https://doi.org/10.1063/5.0012853
35. Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data P. Moireau et al. https://doi.org/10.1007/s10237-012-0418-3
36. Downscaling data assimilation algorithm with applications to statistical solutions of the Navier–Stokes equations C. Mondaini et al. https://doi.org/10.1016/j.anihpc.2018.05.004
37. Data Assimilation in Large Prandtl Rayleigh--Bénard Convection from Thermal Measurements A. Farhat et al. https://doi.org/10.1137/19M1248327
38. Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator G. Haine https://doi.org/10.1007/s00498-014-0124-z
39. Continuous data assimilation for two-phase flow: Analysis and simulations Y. Chow et al. https://doi.org/10.1016/j.jcp.2022.111395
40. The Inverse Problem for Hamilton--Jacobi Equations and Semiconcave Envelopes C. Esteve & E. Zuazua https://doi.org/10.1137/20M1330130
41. NINNs: Nudging induced neural networks H. Antil et al. https://doi.org/10.1016/j.physd.2024.134364
42. Diffusive Back and Forth Nudging algorithm for data assimilation D. Auroux et al. https://doi.org/10.1016/j.crma.2011.07.004
43. Development of a High-Resolution Multiscale Modeling and Prediction System for Bay of Bengal, Part I: Climatology-Based Simulations A. Chakraborty & A. Gangopadhyay https://doi.org/10.4236/ojms.2016.61013
44. A Spatially Dependent Nudging Method and Its Application to a Global Tide Assimilation L. Liu & X. Chen https://doi.org/10.1007/s00376-024-4062-5
45. Mapping Altimetry in the Forthcoming SWOT Era by Back-and-Forth Nudging a One-Layer Quasigeostrophic Model F. Le Guillou et al. https://doi.org/10.1175/JTECH-D-20-0104.1
46. Data Assimilation for the Navier--Stokes Equations Using Local Observables A. Biswas et al. https://doi.org/10.1137/20M136058X
47. Reconstructing the initial state for the nonlinear system and analyzing its convergence W. Xie & Y. Chang https://doi.org/10.1186/1687-1847-2014-82
48. Back-and-forth nudging for the quasi-geostrophic ocean dynamics with altimetry: Theoretical convergence study and numerical experiments with the future SWOT observations S. Amraoui et al. https://doi.org/10.3934/dcdss.2022058
49. Full-field and anomaly initialization using a low-order climate model: a comparison and proposals for advanced formulations A. Carrassi et al. https://doi.org/10.5194/npg-21-521-2014
50. Reconstructing the Initial State of the Linear System and Estimating its Error in Discretization R. Wang & W. Xie https://doi.org/10.11650/tjm/221105
51. An easy-to-implement and efficient data assimilation method for the identification of the initial condition: the Back and Forth Nudging (BFN) algorithm D. Auroux et al. https://doi.org/10.1088/1742-6596/135/1/012011
52. Uniform exponential stabilization and the state reconstruction of the wave equation with viscosity Z. Fu et al. https://doi.org/10.1360/SSM-2020-0292
53. State reconstruction of a distributed parameter system with exact observability G. Xu https://doi.org/10.1016/j.jmaa.2013.06.014
54. An evolution of the back and forth nudging for geophysical data assimilation: application to Burgers equation and comparisons D. Auroux et al. https://doi.org/10.1080/17415977.2012.712528
55. Finite time synchronization of the continuous/discrete data assimilation algorithms for Lorenz 63 system based on the back and forth nudging techniques Y. Peng et al. https://doi.org/10.1016/j.rinam.2023.100407
56. Ocean‐depth measurement using shallow‐water wave models V. Vasan et al. https://doi.org/10.1111/sapm.12418
57. Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart D. Chapelle et al. https://doi.org/10.1007/s11517-012-0969-6
58. IMU-Enhanced Vessel Trajectory Prediction: Overcoming Kinematic Lag and Distribution Shift in Sparse Data Engineering Scenarios Z. Zhang et al. https://doi.org/10.3390/jmse14050461
59. First results of operational ionospheric dynamics prediction for the Brazilian Space Weather program A. Petry et al. https://doi.org/10.1016/j.asr.2014.03.017
60. Eccentricity Parameters Identification for a Motorized Spindle System Based on Improved Maximum Likelihood Method W. Mao et al. https://doi.org/10.1155/2020/5491957
61. On the physical nudging equations G. Conti et al. https://doi.org/10.1007/s00382-021-05972-w
62. Dynamic Initialization for Whole Atmospheric Global Modeling I. Song et al. https://doi.org/10.1029/2017MS001213
63. Data assimilation in the geosciences: An overview of methods, issues, and perspectives A. Carrassi et al. https://doi.org/10.1002/wcc.535
64. Continuous Data Assimilation for the Three-Dimensional Navier--Stokes Equations A. Biswas & R. Price https://doi.org/10.1137/20M1323229
65. Artificial Intelligence techniques in data assimilation: Emerging approaches, key challenges, and future prospects W. Wang et al. https://doi.org/10.1007/s11430-025-1807-8
66. A time reversal based algorithm for solving initial data inverse problems K. Ito et al. https://doi.org/10.3934/dcdss.2011.4.641
67. Continuous data assimilation for the 3D Ladyzhenskaya model: analysis and computations Y. Cao et al. https://doi.org/10.1016/j.nonrwa.2022.103659
68. On the Nudging Approach to Continuous Data Assimilation in the Limit of Infinite Error Feedback Gain E. Carlson et al. https://doi.org/10.1137/24M1689983
69. Data assimilation in 2D hyperbolic/parabolic systems using a stabilized explicit finite difference scheme run backward in time A. Carasso https://doi.org/10.1080/27690911.2023.2282641
70. Methods for Observation Data Assimilation in Problems of Physics of Atmosphere and Ocean V. Shutyaev https://doi.org/10.1134/S0001433819010080
71. Output error minimizing back and forth nudging method for initial state recovery A. Aalto https://doi.org/10.1016/j.sysconle.2016.06.002
72. Sources of skill in near-term climate prediction: generating initial conditions A. Carrassi et al. https://doi.org/10.1007/s00382-016-3036-4
73. Object-Based Analog Forecasts for Surface Wind Speed M. Frediani et al. https://doi.org/10.1175/MWR-D-17-0012.1
74. An efficient data assimilation algorithm using the Allen–Cahn equation B. Xia et al. https://doi.org/10.1016/j.enganabound.2023.06.029
75. Data assimilation with model errors A. Çıbık et al. https://doi.org/10.1016/j.camwa.2026.04.023
76. Data assimilation with regularized nonlinear instabilities H. Abarbanel et al. https://doi.org/10.1002/qj.600
77. A Switching Observer for a Class of Nonuniformly Observable Systems via Singular Time-Rescaling M. Aguado-Rojas et al. https://doi.org/10.1109/TAC.2021.3062340
78. Model and observation‐error covariance matrix information in the physical nudging equations G. Conti et al. https://doi.org/10.1002/qj.4979
79. Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process L. Brivadis et al. https://doi.org/10.1137/20M1329020
80. Symmetry-Based Observers for Some Water-Tank Problems D. Auroux & S. Bonnabel https://doi.org/10.1109/TAC.2010.2067291