@article{girolami2008bayesian,
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  year={2008},
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@inproceedings{turner2010state,
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  year={2010}
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@article{ko2009gp,
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  pages={75--90},
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@article{ko2011learning,
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  publisher={Springer}
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@inproceedings{deisenroth2009analytic,
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  year={2009},
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@article{frigola2013bayesian,
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  journal={NIPS},
  year={2013}
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@inproceedings{frigola2014variational,
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  author={Frigola, Roger and Chen, Yutian and Rasmussen, Carl},
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  year={2014}
}

@article{frigola2014identification,
  title={Identification of {G}aussian process state-space models with particle stochastic approximation EM},
  author={Frigola, Roger and Lindsten, Fredrik and Sch{\"o}n, Thomas B and Rasmussen, Carl E},
  journal={IFAC Proceedings Volumes},
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  number={3},
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  year={2014},
  publisher={Elsevier}
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@inproceedings{eleftheriadis2017identification,
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  year={2017}
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@article{stan,
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@inproceedings{alemi2018fixing,
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  pages={159--168},
  year={2018},
}
@article{blei2017variational,
  title={Variational inference: A review for statisticians},
  author={Blei, David and Kucukelbir, Alp and McAuliffe, Jon D},
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  number={518},
  pages={859--877},
  year={2017},
}
@article{stapor2018optimization,
  title={Optimization and profile calculation of {ODE} models using second order adjoint sensitivity analysis},
  author={Stapor, Paul and Fr{\"o}hlich, Fabian and Hasenauer, Jan},
  journal={Bioinformatics},
  volume={34},
  number={13},
  pages={i151--i159},
  year={2018},
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@article{rackauckas2017differentialequations,
  title={Differentialequations.jl -- a performant and feature-rich ecosystem for solving differential equations in {J}ulia},
  author={Rackauckas, Christopher and Nie, Qing},
  journal={Journal of Open Research Software},
  volume={5},
  number={1},
  year={2017},
  publisher={Ubiquity Press}
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@inproceedings{brault2016random,
  title={Random {F}ourier features for operator-valued kernels},
  author={Brault, Romain and Heinonen, Markus and Buc, Florence},
  booktitle={Asian Conference on Machine Learning},
  pages={110--125},
  year={2016},
}
@inproceedings{doerr2018probabilistic,
  title={Probabilistic recurrent state-space models},
  author={Doerr, Andreas and Daniel, Christian and Schiegg, Martin and Duy, Nguyen-Tuong and Schaal, Stefan and Toussaint, Marc and Sebastian, Trimpe},
  booktitle={International Conference on Machine Learning},
  pages={1280--1289},
  year={2018},
}
@inproceedings{ialongo2019overcoming,
  title={Overcoming mean-field approximations in recurrent Gaussian process models},
  author={Ialongo, Alessandro Davide and Van Der Wilk, Mark and Hensman, James and Rasmussen, Carl Edward},
  booktitle={International Conference on Machine Learning},
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  year={2019},
}


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 author = {Lindelöf, Ernst},
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@article{brunton2016discovering,
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  number={15},
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  year={2016},
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@article{bhouri2021,
    title = {Gaussian processes meet {N}eural{ODEs}: {A} {B}ayesian framework for learning the dynamics of partially observed systems from scarce and noisy data},
    author = {Bhouri, Mohamed and Perdikaris, Paris},
    year = {2021},
    journal = {arXiv},
}

@inproceedings{macdonald2015,
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    pages = {1539--1547},
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@inproceedings{calderhead2008,
    author = {Calderhead, Ben and Girolami, Mark and Lawrence, Neil},
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@inproceedings{heinonen2018learning,
  title={Learning unknown {ODE} models with {G}aussian processes},
  author={Heinonen, Markus and Yildiz, Cagatay and Mannerstr{\"o}m, Henrik and Intosalmi, Jukka and L{\"a}hdesm{\"a}ki, Harri},
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  year={2018},
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@inproceedings{course2019,
 author = {Course, Kevin and Evans, Trefor and Nair, Prasanth},
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@inproceedings{wenk2020odin,
  title={{ODIN}: {ODE}-informed regression for parameter and state inference in time-continuous dynamical systems},
  author={Wenk, Philippe and Abbati, Gabriele and Osborne, Michael and Sch{\"o}lkopf, Bernhard and Krause, Andreas and Bauer, Stefan},
  booktitle={AAAI Conference on Artificial Intelligence},
  volume={34},
  pages={6364--6371},
  year={2020}
}


@inproceedings{chen2018neural,
  title={Neural Ordinary Differential Equations},
  author={Chen, Tian Qi and Rubanova, Yulia and Bettencourt, Jesse and Duvenaud, David},
  booktitle={Advances in Neural Information Processing Systems},
  pages={6571--6583},
  year={2018}
}

@inproceedings{grathwohl2019ffjord,
  title={{FFJORD}: {F}ree-form Continuous Dynamics for Scalable Reversible Generative Models},
  author={Grathwohl, Will and Chen, Ricky T. Q. and Bettencourt, Jesse and Sutskever, Ilya and Duvenaud, David},
  booktitle={ICLR},
  year={2019}
}

@inproceedings{wang2005,
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@inproceedings{yildiz2019ode2vae,
  title={{ODE2VAE}: Deep generative second order {ODE}s with {B}ayesian neural networks},
  author={Yildiz, Cagatay and Heinonen, Markus and Lähdesmäki, Harri},
  booktitle={Advances in Neural Information Processing Systems},
  pages={13412--13421},
  year={2019}
}


@article{hoffman2013stochastic,
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@inproceedings{titsias2009variational,
  title={Variational learning of inducing variables in sparse {G}aussian processes},
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  pages={567--574},
  year={2009},
}

@inproceedings{hensman2013gaussian,
  title={Gaussian processes for Big data},
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  pages={282--290},
  year={2013}
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@InProceedings{pmlr-v130-rossi21a,
  title = 	 { Sparse {G}aussian Processes Revisited: {B}ayesian Approaches to Inducing-Variable Approximations},
  author =       {Rossi, Simone and Heinonen, Markus and Bonilla, Edwin and Shen, Zheyang and Filippone, Maurizio},
  booktitle = 	 {Artificial Intelligence and Statistics},
  pages = 	 {1837--1845},
  year = 	 {2021}}
}

@inproceedings{rahimi2007random,
  title={Random features for large-scale kernel machines},
  author={Rahimi, Ali and Recht, Benjamin},
  booktitle={Advances in Neural Information Processing Systems},
  pages={1177--1184},
  year={2007}
}

@article{gal2015improving,
  title={Improving the {G}aussian process sparse spectrum approximation by representing uncertainty in frequency inputs},
  author={Gal, Yarin and Turner, Richard},
  year={2015},
  publisher={Microtome Publishing}
}
@inproceedings{sutherland2015error,
  title={On the error of random fourier features},
  author={Sutherland, Dougal J and Schneider, Jeff},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={862--871},
  year={2015},
  organization={AUAI Press}
}

@InProceedings{pmlr-v108-ustyuzhaninov20a,
  title = 	 {Monotonic {G}aussian Process Flows},
  author =       {Ustyuzhaninov, Ivan and Kazlauskaite, Ieva and Ek, Carl Henrik and Campbell, Neill},
  booktitle = 	 {Artificial Intelligence and Statistics},
  pages = 	 {3057--3067},
  year = 	 {2020},
  volume = 	 {108},
}


@inproceedings{wilson2020efficiently,
  title={Efficiently sampling functions from {G}aussian process posteriors},
  author={Wilson, James and Borovitskiy, Viacheslav and Terenin, Alexander and Mostowsky, Peter and Deisenroth, Marc},
  booktitle={International Conference on Machine Learning},
  pages={10292--10302},
  year={2020},
}

@article{hicks1971,
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@inproceedings{bock1984,
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@article{osborne1969,
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@article{henderson2014network,
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  pages={e94003},
  year={2014},
}
@incollection{de2002inferring,
  title={Inferring gene regulatory networks from time-ordered gene expression data of Bacillus subtilis using differential equations},
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@article{aijo2009learning,
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  year={2008},
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@book{hirsch2012differential,
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@inproceedings{sargent1978,
 author = {Sargent, R.W. and Sullivan, G.R.},
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 pages = {158--168},
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@article{haber2017,
  title={Stable architectures for deep neural networks},
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  volume={34},
  pages={014004},
  year={2017},
  publisher={IOP Publishing}
}

@book{diehl2017,
 author = {Diehl, Moritz and Gros, Sebastian},
 title = {Numerical Optimal Control},
 year = {2017},
 publisher = {University of Freiburg},
}
@inproceedings{choromanski2020,
  title={An {O}de to an {ODE}},
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  booktitle={Advances in Neural Information Processing Systems},
  volume = {33},
  year={2020}
}
@article{ridderbusch2020learning,
  title={Learning {ODE} Models with Qualitative Structure Using {G}aussian Processes},
  author={Ridderbusch, Steffen and Offen, Christian and Ober-Bl{\"o}baum, Sina and Goulart, Paul},
  journal={arXiv:2011.05364},
  year={2020}
}
@book{rasmussen2006gaussian,
  title={Gaussian processes for machine learning},
  author={Rasmussen, Carl and Williams, Christopher},
  year={2006},
  publisher={The MIT Press}
}
@article{alvarez2012,
  author={Alvarez, Mauricio and Rosasco, Lorenzo and Lawrence, Neil},
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  pages = {195--266},
  year={2012}
}

@article{peifer2005parameter,
  title={Parameter estimation in ordinary differential equations using the method of multiple shooting},
  author={Peifer, Martin and Timmer, Jens},
  year={2007},
  volume = {1},
  issue = {2},
  pages = {78--88},
  journal = {IET Systems Biology}
}



@article{aydogmus2021modified,
  title={A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis},
  author={Aydogmus, Ozgur and Tor, Ali},
  journal={Applied Mathematics and Computation},
  volume={390},
  pages={125644},
  year={2021},
  publisher={Elsevier}
}
@inproceedings{zhuang2021mali,
  title={{MALI}: {A} memory efficient and reverse accurate integrator for Neural {ODE}s},
  author={Zhuang, Juntang and Dvornek, Nicha and Tatikonda, Sekhar and Duncan, James},
  booktitle={ICLR},
  year={2021}
}
@inproceedings{zhuang2020,
  title={Adaptive checkpoint adjoint method for gradient estimation in neural {ODE}},
  author={Zhuang, Juntang and Dvornek, Nicha and Li, Xiaoxiao and Tatikonda, Sekhar and Papademetris, Xenophon and Duncan, James},
  booktitle={International Conference on Machine Learning},
  pages={11639--11649},
  year={2020},
}
@article{kim2021stiff,
  title={Stiff Neural Ordinary Differential Equations},
  author={Kim, Suyong and Ji, Weiqi and Deng, Sili and Rackauckas, Christopher},
  journal={arXiv:2103.15341},
  year={2021}
}

% Gradient matching
@article{varah1982spline,
  title={A spline least squares method for numerical parameter estimation in differential equations},
  author={Varah, James},
  journal={SIAM Journal on Scientific and Statistical Computing},
  volume={3},
  number={1},
  pages={28--46},
  year={1982},
  publisher={SIAM}
}

@article{ellner2002fitting,
  title={Fitting population dynamic models to time-series data by gradient matching},
  author={Ellner, Stephen and Seifu, Yodit and Smith, Robert},
  journal={Ecology},
  volume={83},
  number={8},
  pages={2256--2270},
  year={2002},
  publisher={Wiley Online Library}
}

@article{ramsay2007parameter,
  title={Parameter estimation for differential equations: {A} generalized smoothing approach},
  author={Ramsay, Jim and Hooker, Giles and Campbell, David and Cao, Jiguo},
  journal={Journal of the Royal Statistical Society: Series B},
  volume={69},
  number={5},
  pages={741--796},
  year={2007},
  publisher={Wiley Online Library}
}



@inproceedings{dondelinger2013ode,
  title={{ODE} parameter inference using adaptive gradient matching with {G}aussian processes},
  author={Dondelinger, Frank and Husmeier, Dirk and Rogers, Simon and Filippone, Maurizio},
  booktitle={Artificial Intelligence and Statistics},
  pages={216--228},
  year={2013},
}

@inproceedings{rubanova2019,
 title = {Latent {ODE}s for Irregularly-Sampled Time Series},
 author = {Rubanova, Yulia and Chen, Ricky T. Q. and Duvenaud, David},
 booktitle = {Advances in Neural Information Processing Systems},
 year = {2019},
}

@article{aijo2013,
    author = {Äijö, Tarmo and Granberg, Kirsi and Lähdesmäki, Harri},
    title = {Sorad: {A} systems biology approach to predict and modulate dynamic signaling pathway response from phosphoproteome time-course measurements},
    journal = {Bioinformatics},
    year = {2013},
    volume = {29},
    pages = {1283--1291},
}

@techreport{heinonen2014learning,
  title={Learning nonparametric differential equations with operator-valued kernels and gradient matching},
  author={Heinonen, Markus and d'Alch{\'e}{-}Buc, Florence},
  year={2014},
  institution = {Universite d'Evry}
}


@article{4359316,  author={Wang, Jack and Fleet, David and Hertzmann, Aaron},  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},   title={Gaussian Process Dynamical Models for Human Motion},   
year={2008},  
volume={30},  
number={2},  
pages={283--298}
}

@inproceedings{kingma2014adam,
  title={Adam: A method for stochastic optimization},
  author={Kingma, Diederik P and Ba, Jimmy Lei},
  booktitle={Proceedings of 3rd International Conference on Learning Representations},
  year={2014}
}


@article{kuss2005assessing,
  title={Assessing Approximate Inference for Binary Gaussian Process Classification.},
  author={Kuss, Malte and Rasmussen, Carl Edward and Herbrich, Ralf},
  journal={Journal of machine learning research},
  volume={6},
  number={10},
  year={2005}
}

@article{hensman2015mcmc,
  title={MCMC for Variationally Sparse Gaussian Processes},
  author={Hensman, James and Matthews, Alexander G and Filippone, Maurizio and Ghahramani, Zoubin},
  journal={Advances in Neural Information Processing Systems},
  volume={28},
  pages={1648--1656},
  year={2015}
}


@article{vandomselaar1975nonlinear,
  title={Nonlinear parameter estimation in initial value problems},
  author={vanDomselaar, B and Hemker, Piet W},
  journal={Stichting Mathematisch Centrum. Numerieke Wiskunde},
  number={NW 18/75},
  year={1975},
  publisher={Stichting Mathematisch Centrum}
}

@article{bock1983recent,
  title={Recent advances in parameter identification techniques for ode},
  author={Bock, Hans Georg},
  journal={Numerical treatment of inverse problems in differential and integral equations},
  pages={95--121},
  year={1983},
  publisher={Springer}
}


@article{dandekar2020bayesian,
  title={Bayesian neural ordinary differential equations},
  author={Dandekar, Raj and Chung, Karen and Dixit, Vaibhav and Tarek, Mohamed and Garcia-Valadez, Aslan and Vemula, Krishna Vishal and Rackauckas, Chris},
  journal={arXiv preprint arXiv:2012.07244},
  year={2020}
}

@article{ensinger2021symplectic,
  title={Symplectic Gaussian Process Dynamics},
  author={Ensinger, Katharina and Solowjow, Friedrich and Tiemann, Michael and Trimpe, Sebastian},
  journal={arXiv preprint arXiv:2102.01606},
  year={2021}
}

@article{mikheeva2021aligned,
  title={Aligned Multi-Task Gaussian Process},
  author={Mikheeva, Olga and Kazlauskaite, Ieva and Hartshorne, Adam and Kjellstr{\"o}m, Hedvig and Ek, Carl Henrik and Campbell, Neill DF},
  journal={arXiv preprint arXiv:2110.15761},
  year={2021}
}

@inproceedings{archambeau2007gaussian,
  title={Gaussian process approximations of stochastic differential equations},
  author={Archambeau, Cedric and Cornford, Dan and Opper, Manfred and Shawe-Taylor, John},
  booktitle={Gaussian Processes in Practice},
  pages={1--16},
  year={2007},
  organization={PMLR}
}

@inproceedings{duncker2019learning,
  title={Learning interpretable continuous-time models of latent stochastic dynamical systems},
  author={Duncker, Lea and Bohner, Gergo and Boussard, Julien and Sahani, Maneesh},
  booktitle={International Conference on Machine Learning},
  pages={1726--1734},
  year={2019},
  organization={PMLR}
}

@inproceedings{jorgensen2020stochastic,
  title={Stochastic differential equations with variational wishart diffusions},
  author={J{\o}rgensen, Martin and Deisenroth, Marc and Salimbeni, Hugh},
  booktitle={International Conference on Machine Learning},
  pages={4974--4983},
  year={2020},
  organization={PMLR}
}

@inproceedings{li2020scalable,
  title={Scalable gradients for stochastic differential equations},
  author={Li, Xuechen and Wong, Ting-Kam Leonard and Chen, Ricky TQ and Duvenaud, David},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={3870--3882},
  year={2020},
  organization={PMLR}
}

@article{tzen2019neural,
  title={Neural stochastic differential equations: Deep latent gaussian models in the diffusion limit},
  author={Tzen, Belinda and Raginsky, Maxim},
  journal={arXiv preprint arXiv:1905.09883},
  year={2019}
}

@article{turan2021multiple,
  title={Multiple shooting with neural differential equations},
  author={Turan, Evren Mert and J{\"a}schke, Johannes},
  journal={arXiv preprint arXiv:2109.06786},
  year={2021}
}

@article{massaroli2021differentiable,
  title={Differentiable Multiple Shooting Layers},
  author={Massaroli, Stefano and Poli, Michael and Sonoda, Sho and Suzuki, Taiji and Park, Jinkyoo and Yamashita, Atsushi and Asama, Hajime},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  year={2021}
}

