Articles | Volume 22, issue 2
https://doi.org/10.5194/npg-22-205-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-22-205-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
07 Apr 2015
Research article |
| 07 Apr 2015
Improved variational methods in statistical data assimilation
J. Ye
Department of Physics, University of California, San Diego, La Jolla, CA 92093-0374, USA
N. Kadakia
Department of Physics, University of California, San Diego, La Jolla, CA 92093-0374, USA
P. J. Rozdeba
Department of Physics, University of California, San Diego, La Jolla, CA 92093-0374, USA
H. D. I. Abarbanel
CORRESPONDING AUTHOR
Department of Physics, University of California, San Diego, La Jolla, CA 92093-0374, USA
Marine Physical Laboratory (Scripps Institution of Oceanography), University of California, San Diego, La Jolla, CA 92093-0374, USA
J. C. Quinn
Intellisis Corporation, 10350 Science Center Drive, Suite 140, San Diego, CA 92121, USA
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Cited
15 citations as recorded by crossref.
- Model selection of chaotic systems from data with hidden variables using sparse data assimilation H. Ribera et al. https://doi.org/10.1063/5.0066066
- Statistical data assimilation for estimating electrophysiology simultaneously with connectivity within a biological neuronal network E. Armstrong https://doi.org/10.1103/PhysRevE.101.012415
- Assimilation of Biophysical Neuronal Dynamics in Neuromorphic VLSI J. Wang et al. https://doi.org/10.1109/TBCAS.2017.2776198
- Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation E. Armstrong et al. https://doi.org/10.1016/j.idm.2020.10.010
- Precision annealing Monte Carlo methods for statistical data assimilation and machine learning Z. Fang et al. https://doi.org/10.1103/PhysRevResearch.2.013050
- Data assimilation in the geosciences: An overview of methods, issues, and perspectives A. Carrassi et al. https://doi.org/10.1002/wcc.535
- Machine Learning of Time Series Using Time-Delay Embedding and Precision Annealing A. Ty et al. https://doi.org/10.1162/neco_a_01224
- Machine Learning: Deepest Learning as Statistical Data Assimilation Problems H. Abarbanel et al. https://doi.org/10.1162/neco_a_01094
- Basin structure of optimization based state and parameter estimation J. Schumann-Bischoff et al. https://doi.org/10.1063/1.4920942
- Simultaneous Model Discovery and State Estimation under High Data Corruption T. Meissner & K. Glasner https://doi.org/10.1137/24M1681008
- Optimal control methods for nonlinear parameter estimation in biophysical neuron models N. Kadakia & A. Nogaret https://doi.org/10.1371/journal.pcbi.1010479
- Statistical Data Assimilation: Formulation and Examples From Neurobiology A. Miller et al. https://doi.org/10.3389/fams.2018.00053
- Consecutive shooting during adjoint optimization enables highly accurate estimation of unobserved state variables of high-dimensional chaotic systems K. Shiozawa et al. https://doi.org/10.1103/8c7w-dpdt
- Nonlinear statistical data assimilation for HVC $$_{\mathrm{RA}}$$ RA neurons in the avian song system N. Kadakia et al. https://doi.org/10.1007/s00422-016-0697-3
- Symplectic structure of statistical variational data assimilation N. Kadakia et al. https://doi.org/10.1002/qj.2962
15 citations as recorded by crossref.
- Model selection of chaotic systems from data with hidden variables using sparse data assimilation H. Ribera et al. https://doi.org/10.1063/5.0066066
- Statistical data assimilation for estimating electrophysiology simultaneously with connectivity within a biological neuronal network E. Armstrong https://doi.org/10.1103/PhysRevE.101.012415
- Assimilation of Biophysical Neuronal Dynamics in Neuromorphic VLSI J. Wang et al. https://doi.org/10.1109/TBCAS.2017.2776198
- Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation E. Armstrong et al. https://doi.org/10.1016/j.idm.2020.10.010
- Precision annealing Monte Carlo methods for statistical data assimilation and machine learning Z. Fang et al. https://doi.org/10.1103/PhysRevResearch.2.013050
- Data assimilation in the geosciences: An overview of methods, issues, and perspectives A. Carrassi et al. https://doi.org/10.1002/wcc.535
- Machine Learning of Time Series Using Time-Delay Embedding and Precision Annealing A. Ty et al. https://doi.org/10.1162/neco_a_01224
- Machine Learning: Deepest Learning as Statistical Data Assimilation Problems H. Abarbanel et al. https://doi.org/10.1162/neco_a_01094
- Basin structure of optimization based state and parameter estimation J. Schumann-Bischoff et al. https://doi.org/10.1063/1.4920942
- Simultaneous Model Discovery and State Estimation under High Data Corruption T. Meissner & K. Glasner https://doi.org/10.1137/24M1681008
- Optimal control methods for nonlinear parameter estimation in biophysical neuron models N. Kadakia & A. Nogaret https://doi.org/10.1371/journal.pcbi.1010479
- Statistical Data Assimilation: Formulation and Examples From Neurobiology A. Miller et al. https://doi.org/10.3389/fams.2018.00053
- Consecutive shooting during adjoint optimization enables highly accurate estimation of unobserved state variables of high-dimensional chaotic systems K. Shiozawa et al. https://doi.org/10.1103/8c7w-dpdt
- Nonlinear statistical data assimilation for HVC $$_{\mathrm{RA}}$$ RA neurons in the avian song system N. Kadakia et al. https://doi.org/10.1007/s00422-016-0697-3
- Symplectic structure of statistical variational data assimilation N. Kadakia et al. https://doi.org/10.1002/qj.2962
Saved (final revised paper)
Latest update: 10 Aug 2026
Short summary
We propose an improved method of data assimilation, in which measured data are incorporated into a physically based model. In data assimilation, one typically seeks to minimize some cost function; here, we discuss a variational approximation in which model and measurement errors are Gaussian, combined with an annealing method, to consistently identify a global minimum of this cost function. We illustrate this procedure with archetypal chaotic systems, and discuss higher-order corrections.
We propose an improved method of data assimilation, in which measured data are incorporated into...
