@article{rue-inla,
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}

@article{le1986variational,
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@inproceedings{takahashi1973formation,
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@article{rue2007approximate,
  title={Approximate {B}ayesian inference for hierarchical {Gaussian Markov} random field models},
  author={Rue, H{\aa}vard and Martino, Sara},
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  year={2007},
  publisher={Elsevier},
  doi={10.1016/j.jspi.2006.07.016}
}

@article{lindgren2011explicit,
  title={{An explicit link between {G}aussian fields and {G}aussian {M}arkov random fields: the stochastic partial differential equation approach}},
  author={Lindgren, Finn and Rue, H{\aa}vard and Lindstr{\"o}m, Johan},
  journal={Journal of the Royal Statistical Society Series B: Statistical Methodology},
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 publisher = {Morgan Kaufmann}
}

@book{evensen2022data,
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@article{evensen2003ensemble,
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}

@book{rue2005gaussian,
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}


@book{nocedal1999numerical,
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@TechReport{mitchell80,
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@phdthesis{kearns89,
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@Book{MachineLearningI,
  editor = 	 "R. S. Michalski and J. G. Carbonell and T.
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@Book{DudaHart2nd,
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@misc{anonymous,
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@InCollection{Newell81,
  author =       "A. Newell and P. S. Rosenbloom",
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@Article{Samuel59,
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@incollection{bengtsson2008curse,
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@article{evensen1994sequential,
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@article{evensen2000ensemble,
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}

@misc{findiff,
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@misc{inlabru,
    title = {Iterative linearised {INLA} method},
    author = {Lindgren, Finn and Suen, Man Ho},
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    note = {From the inlabru 2.10.1 package documentation},
    year = {2023}
    }

@article{chen2008algorithm,
  title={Algorithm 887: {CHOLMOD}, supernodal sparse {C}holesky factorization and update/downdate},
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  journal={ACM Transactions on Mathematical Software (TOMS)},
  year={2008},
  publisher={ACM New York, NY, USA},
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}

@article{lindgren2015bayesian,
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  journal={Journal of statistical software},
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@book{lototsky2017stochastic,
  title={Stochastic partial differential equations},
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@article{morishita2024first,
  title={First application of data assimilation-based control to fusion plasma},
  author={Morishita, Yuya and Murakami, Sadayoshi and Kenmochi, Naoki and Funaba, Hisamichi and Yamada, Ichihiro and Mizuno, Yoshinori and Nagahara, Kazuki and Nuga, Hideo and Seki, Ryosuke and Yokoyama, Masayuki and others},
  journal={Scientific Reports},
  year={2024},
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}

@article{arridge2009optical,
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  author={Arridge, Simon R and Schotland, John C},
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  year={2009},
  publisher={IOP Publishing},
  doi={10.1088/0266-5611/15/2/022}
}

@inproceedings{alvarez2009latent,
  title={Latent force models},
  author={Alvarez, Mauricio and Luengo, David and Lawrence, Neil D},
  booktitle={Artificial Intelligence and Statistics},
  year={2009},
  organization={PMLR},
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}

@article{kassam2005fourth,
  title={Fourth-order time-stepping for stiff {PDE}s},
  author={Kassam, Aly-Khan and Trefethen, Lloyd N},
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  year={2005},
  publisher={SIAM},
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@misc{dapper,
    title = {{nansencenter/DAPPER}},
    author = {Raanes, Patrick and Grudzien, Colin and 14tondeu},
    url = {https://doi.org/10.5281/zenodo.2029296},
    key = {dapper},
    year = {2018}
}

@article{andrieu2010particle,
  title={{Particle Markov Chain Monte Carlo methods}},
  author={Andrieu, Christophe and Doucet, Arnaud and Holenstein, Roman},
  journal={Journal of the Royal Statistical Society Series B: Statistical Methodology},
  year={2010},
  publisher={Oxford University Press},
  doi={10.1111/j.1467-9868.2009.00736.x}
}

@article{gretton2012kernel,
  title={A kernel two-sample test},
  author={Gretton, Arthur and Borgwardt, Karsten M and Rasch, Malte J and Sch{\"o}lkopf, Bernhard and Smola, Alexander},
  journal={The Journal of Machine Learning Research},
  year={2012},
  publisher={JMLR},
  url     = {http://jmlr.org/papers/v13/gretton12a.html}
}

@book{williams2006gaussian,
  title={Gaussian Processes for Machine Learning},
  author={Rasmussen, Carl Edward and Williams, Christopher KI},
  year={2006},
  publisher={MIT Press}
}

@book{chopin2020introduction,
  title={An introduction to sequential {M}onte {C}arlo},
  author={Chopin, Nicolas and Papaspiliopoulos, Omiros},
  year={2020},
  publisher={Springer}
}

@misc{metofficeDA,
  author = {UK Met Office},
  title = {Data assimilation methods},
  year = 2024,
  key = {UK Met Office},
  url = {https://www.metoffice.gov.uk/research/weather/satellite-and-surface-assimilation/data-assimilation-methods},
  urldate = {2024-01-28}
}

@article{bannister2017review,
  title={A review of operational methods of variational and ensemble-variational data assimilation},
  author={Bannister, Ross N},
  journal={Quarterly Journal of the Royal Meteorological Society},
  year={2017},
  publisher={Wiley Online Library},
  doi={10.1002/qj.2982}
}

@article{delsole2010state,
  title={State and parameter estimation in stochastic dynamical models},
  author={DelSole, Timothy and Yang, Xiaosong},
  journal={Physica D: Nonlinear Phenomena},
  year={2010},
  publisher={Elsevier},
  doi={10.1016/j.physd.2010.06.001}
}

@article{schneider2017earth,
  title={Earth system modeling 2.0: {A} blueprint for models that learn from observations and targeted high-resolution simulations},
  author={Schneider, Tapio and Lan, Shiwei and Stuart, Andrew and Teixeira, Jo{\~a}o},
  journal={Geophysical Research Letters},
  year={2017},
  publisher={Wiley Online Library},
  doi={10.1002/2017GL076101}
}

@article{evensen2009ensemble,
  title={The ensemble {K}alman filter for combined state and parameter estimation},
  author={Evensen, Geir},
  journal={IEEE Control Systems Magazine},
  year={2009},
  publisher={IEEE},
  doi={10.1109/MCS.2009.932223}
}

@article{bocquet2013joint,
  title={Joint state and parameter estimation with an iterative ensemble {K}alman smoother},
  author={Bocquet, Marc and Sakov, Pavel},
  journal={Nonlinear Processes in Geophysics},
  year={2013},
  publisher={Copernicus Publications G{\"o}ttingen, Germany},
  doi={10.5194/npg-20-803-2013}
}

@article{raissi2019physics,
  title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
  author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E},
  journal={Journal of Computational physics},
  year={2019},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2018.10.045}
}

@article{rue2013r,
  title={{R-INLA}: approximate Bayesian inference using integrated nested Laplace approximations},
  author={Rue, H and Martino, S and Lindgren, F and Simpson, D and Riebler, A},
  url={http://www.r-inla.org},
  year={2013}
}

@inproceedings{nikitin2022non,
  title={Non-separable spatio-temporal graph kernels via {SPDE}s},
  author={Nikitin, Alexander V and John, ST and Solin, Arno and Kaski, Samuel},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  year={2022},
  organization={PMLR},
  url={https://proceedings.mlr.press/v151/nikitin22a/nikitin22a.pdf}
}


@article{chen2021solving,
  title={Solving and learning nonlinear {PDE}s with {G}aussian processes},
  author={Chen, Yifan and Hosseini, Bamdad and Owhadi, Houman and Stuart, Andrew M},
  journal={Journal of Computational Physics},
  year={2021},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2021.110668}
}

@inproceedings{long2022autoip,
  title={{AutoIP: A united framework to integrate physics into Gaussian processes}},
  author={Long, Da and Wang, Zheng and Krishnapriyan, Aditi and Kirby, Robert and Zhe, Shandian and Mahoney, Michael},
  booktitle={International Conference on Machine Learning},
  year={2022},
  organization={PMLR},
  url={https://proceedings.mlr.press/v162/long22a/long22a.pdf}
}
