Neural networks singular evolutive interpolated Kalman filter and its application to data assimilation for 2D water pollution model
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Thu Ha Tran
,
Hong Son Hoang
Abstract
The present study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers. To date, the widely used variational method suffers from the large computational burden, which limits its application in practice. Moreover, this method, considering the initial state as a control variable, is very sensitive in specifying initial error, especially for unstable dynamical systems. The Neural Network Filter (NNF), proposed in the present paper, is aimed at overcoming these two drawbacks in the variational method: by its nature, the NNF is sequential (no batch large assimilation window used) and stable even for unstable dynamics, with the gain parameters as control variables.
The NNF, developed in the present paper, is a Neural Network Filter (NNF) version of the Singular Evolutive Interpolated Kalman Filter (SEIKF). One of the new versions of this NNF is that it uses structure of the gain of SEIKF0 taken by the SEIKF at the first time moment of correction process. To deal with the uncertainty of the system parameters and of the noise covariance, the proposed Neural Network SEIKF0 named by NNSEIKF0 makes use of the covariance of a reduced rank iterated during assimilation process and of some pertinent gain parameters tuned adaptively to yield the minimum prediction error for the system output. The computational burden in implementation of the NNSEIKF0 is reduced drastically due to applying the optimization tool known as a simultaneous perturbation stochastic approximation (SPSA) algorithm, which requires only two integrations of the numerical model. No iterative loop is required at each assimilation instant as usually happens with the standard gradient descent optimization algorithms. Data assimilation experiment, carried out by the SEIKF0 and NNSEIKF0, is implemented for the Thanh Nhan Lake in Hanoi and the performance comparison between the NNSEIKF0 and SEIKF0 is given to show the high efficiency of the proposed NNSEIKF0.
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Funding: The work of V. Shutyaev was supported by the Russian Science Foundation (project 20-11-20057, in the part of research of Sections 1–3) and the Moscow Center for Fundamental and Applied Mathematics (agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2022-286). The other authors gratefully acknowledge the financial support from the CSCL03.01/22-23 funds.
References
[1] O. Bozorg-Haddad, S. Soleimani, and H. A. Loáiciga, Modeling water-quality parameters using genetic algorithm–least squares support vector regression and genetic programming. J. Environmental Engrg. 143 (2017), No. 7, 04017021.10.1061/(ASCE)EE.1943-7870.0001217Search in Google Scholar
[2] R. G. Brown and P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering. With MATLAB exercises, 4th ed., John Wiley and Sons, 2012.Search in Google Scholar
[3] G. Evensen, The ensemble Kalman filter: Theoretical formulation and practical implementation. J. Ocean Dynamics 53, (2003), 343–367.10.1007/s10236-003-0036-9Search in Google Scholar
[4] S. Haykin, Neural Networks and Learning Machines. Pearson Prentice Hall, 2009.Search in Google Scholar
[5] C. Licht, T. H. Tran, and Q. P. Vu, On some linears problems on shallow water flows. J. Differ. Integral Equ. 22 (2009), No. 3-4, 275–283.10.57262/die/1356019774Search in Google Scholar
[6] D. Pham, J. Verron, and M. Roubaud, Singular evolutive Kalman filter with eof initialization for data assimilation in oceanography. J. Marine Systems 16 (1997), 323–340.Search in Google Scholar
[7] D. T. Pham, J. Verron, and M. C. Roubaud, A singular evolutive extended Kalman filter for data assimilation in oceanography. J. Marine Systems 16 (1998), No. 3-4, 323–340.10.1016/S0924-7963(97)00109-7Search in Google Scholar
[8] D. T. Pham, J. Verron, and L. Gourdeau, Filtres de Kalman singuliers évolutif pour l'assimilation de données en océnographie. Comptes Rendus Aca. Sci. Science de la terre et des planètres 326 (1998), 255–260.10.1016/S1251-8050(97)86815-2Search in Google Scholar
[9] D. T. Pham, Stochastic methods for sequential data assimilation in strongly nonlinear systems. Monthly Weather Review 129 (2001), No. 5, 1194–1207.10.1175/1520-0493(2001)129<1194:SMFSDA>2.0.CO;2Search in Google Scholar
[10] P. Shanahan, M. Henze, L. Koncsos, W. Rauch, P. Reichert, L. Somlyody, and P. Vanrolleghem, River water quality modelling: II. Problems of the art. Water Science and Technology 38 (1998), No. 11, 245–252.10.2166/wst.1998.0474Search in Google Scholar
[11] V. Shutyaev, T. H. Tran, F.-X. Le Dimet, H. S. Hoang, and H. P. Nguyen, On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems. Russ. J. Numer. Anal. Math. Modelling 37 (2022), No. 1, 41–61.10.1515/rnam-2022-0004Search in Google Scholar
[12] D. Simon, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches. John Wiley and Sons, 2006.10.1002/0470045345Search in Google Scholar
[13] P. A. Sleigh, P. H. Gaskell, M. Berzins, and N. G. Wright, An unstructured finite volume algorithm for predicting flow in rivers and estuaries. Computers & Fluids 27 (1998), 479–508.10.1016/S0045-7930(97)00071-6Search in Google Scholar
[14] J. C. Spall, Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control. Wiley, 2003, Chapter 7.10.1002/0471722138Search in Google Scholar
[15] T. H. Tran, D. T. Pham, V. L. Hoang, and H. P. Nguyen, Pollution estimation based on the 2D water transport model and the singular evolutive interpolated filter. C. R. Mechanique 342 (2014), 106–124.10.1016/j.crme.2013.10.007Search in Google Scholar
[16] G. Welch and G. Bishop, An introduction to the Kalman Filter. 2001. https://courses.cs.washington.edu/courses/cse571/03wi/notes/welch-bishop-tutorial.pdfSearch in Google Scholar
[17] L. Zhang, D. Sidoti, A. Bienkowski, K. R. Pattipati, Y. Bar-Shalom, and D. L. Kleinman, On the identification of noise covariances and adaptive Kalman filtering: A new look at a 50 year-old problem. IEEE Access. 8 (2020), 59362–59388.10.1109/ACCESS.2020.2982407Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Particle tracking for face-based flux data on general polyhedral grids with applications to groundwater flow modelling
- CarNum: parallel numerical framework for computational cardiac electromechanics
- SIMUG – finite element model of sea ice dynamics on triangular grid in local Cartesian basis
- Validation of boundary conditions for coronary circulation model based on a lumped parameter approach
- Ensemble-based statistical verification of INM RAS Earth system model
- Neural networks singular evolutive interpolated Kalman filter and its application to data assimilation for 2D water pollution model
