---
references:
- id: AgarwalTime2018
  accessed:
    - year: 2018
      month: 3
      day: 21
  author:
    - family: Agarwal
      given: Anish
    - family: Amjad
      given: Muhammad Jehangir
    - family: Shah
      given: Devavrat
    - family: Shen
      given: Dennis
  citation-key: AgarwalTime2018
  container-title: arXiv:1802.09064 [cs, stat]
  issued:
    - year: 2018
      month: 2
      day: 25
  title: Time Series Analysis via Matrix Estimation
  type: article-journal
  URL: http://arxiv.org/abs/1802.09064

- id: AnderssonCasADi2019
  accessed:
    - year: 2020
      month: 4
      day: 16
  author:
    - family: Andersson
      given: Joel A. E.
    - family: Gillis
      given: Joris
    - family: Horn
      given: Greg
    - family: Rawlings
      given: James B.
    - family: Diehl
      given: Moritz
  citation-key: AnderssonCasADi2019
  container-title: Mathematical Programming Computation
  container-title-short: Math. Prog. Comp.
  DOI: 10.1007/s12532-018-0139-4
  ISSN: 1867-2949, 1867-2957
  issue: '1'
  issued:
    - year: 2019
      month: 3
  language: en
  page: 1-36
  title: 'CasADi: a software framework for nonlinear optimization and optimal control'
  type: article-journal
  URL: http://www.optimization-online.org/DB_FILE/2018/01/6420.pdf
  volume: '11'

- id: AndrewsEmpirical1994
  accessed:
    - year: 2015
      month: 5
      day: 12
  author:
    - family: Andrews
      given: Donald W. K.
  citation-key: AndrewsEmpirical1994
  container-title: Handbook of Econometrics
  editor:
    - family: McFadden
      given: Robert F. Engle and Daniel L.
  issued:
    - year: 1994
  page: 2247-2294
  publisher: Elsevier
  title: Empirical process methods in econometrics
  type: chapter
  URL: http://dido.econ.yale.edu/P/cp/p08b/p0887.pdf
  volume: '4'

- id: Antoniano-VillalobosNonparametric2016
  accessed:
    - year: 2016
      month: 1
      day: 19
  author:
    - family: Antoniano-Villalobos
      given: Isadora
    - family: Walker
      given: Stephen G.
  citation-key: Antoniano-VillalobosNonparametric2016
  container-title: Journal of Time Series Analysis
  container-title-short: J. Time Ser. Anal.
  DOI: 10.1111/jtsa.12146
  ISSN: 1467-9892
  issue: '1'
  issued:
    - year: 2016
      month: 1
      day: 1
  language: en
  page: 126-142
  title: A Nonparametric Model for Stationary Time Series
  type: article-journal
  volume: '37'

- id: ArridgeSolving2019
  accessed:
    - year: 2020
      month: 9
      day: 1
  author:
    - family: Arridge
      given: Simon
    - family: Maass
      given: Peter
    - family: Öktem
      given: Ozan
    - family: Schönlieb
      given: Carola-Bibiane
  citation-key: ArridgeSolving2019
  container-title: Acta Numerica
  DOI: 10.1017/S0962492919000059
  ISSN: 0962-4929, 1474-0508
  issued:
    - year: 2019
      month: 5
  language: en
  page: 1-174
  publisher: Cambridge University Press
  title: Solving inverse problems using data-driven models
  type: article-journal
  volume: '28'

- id: BengioScheduled2015
  accessed:
    - year: 2017
      month: 8
      day: 6
  author:
    - family: Bengio
      given: Samy
    - family: Vinyals
      given: Oriol
    - family: Jaitly
      given: Navdeep
    - family: Shazeer
      given: Noam
  citation-key: BengioScheduled2015
  collection-title: NIPS'15
  container-title: Advances in Neural Information Processing Systems 28
  event-place: Cambridge, MA, USA
  issued:
    - year: 2015
  page: 1171–1179
  publisher: Curran Associates, Inc.
  publisher-place: Cambridge, MA, USA
  title: Scheduled sampling for sequence prediction with recurrent neural networks
  type: paper-conference
  URL: >-
    http://papers.nips.cc/paper/5956-scheduled-sampling-for-sequence-prediction-with-recurrent-neural-networks

- id: BenTaiebBias2016
  author:
    - family: Ben Taieb
      given: Souhaib
    - family: Atiya
      given: Amir F.
  citation-key: BenTaiebBias2016
  container-title: IEEE transactions on neural networks and learning systems
  container-title-short: IEEE Trans Neural Netw Learn Syst
  DOI: 10.1109/TNNLS.2015.2411629
  ISSN: 2162-2388
  issue: '1'
  issued:
    - year: 2016
      month: 1
  language: eng
  page: 62-76
  PMID: '25807572'
  title: A Bias and Variance Analysis for Multistep-Ahead Time Series Forecasting
  type: article-journal
  volume: '27'

- id: BerryBridging2020
  accessed:
    - year: 2022
      month: 4
      day: 28
  author:
    - family: Berry
      given: Tyrus
    - family: Giannakis
      given: Dimitrios
    - family: Harlim
      given: John
  citation-key: BerryBridging2020
  container-title: arXiv:2002.07928 [physics, stat]
  issued:
    - year: 2020
      month: 6
      day: 29
  title: Bridging data science and dynamical systems theory
  type: article-journal
  URL: http://arxiv.org/abs/2002.07928

- id: BosqInference2007
  author:
    - family: Bosq
      given: Denis
    - family: Blanke
      given: Delphine
  call-number: QA276.8 .B6713 2007
  citation-key: BosqInference2007
  collection-title: Wiley series in probability and statistics
  contributor:
    - literal: Dunod (Firm)
  event-place: Chichester, England ; Hoboken, NJ
  ISBN: 978-0-470-01761-6
  issued:
    - year: 2007
  language: eng
  number-of-pages: '316'
  publisher: John Wiley/Dunod
  publisher-place: Chichester, England ; Hoboken, NJ
  title: Inference and prediction in large dimensions
  type: book

- id: BosqNonparametric1998
  author:
    - family: Bosq
      given: Denis
  call-number: QA278.8 .B67 1998
  citation-key: BosqNonparametric1998
  collection-number: '110'
  collection-title: Lecture notes in statistics
  edition: 2nd ed
  event-place: New York
  ISBN: 978-0-387-98590-9
  issued:
    - year: 1998
  number-of-pages: '210'
  publisher: Springer
  publisher-place: New York
  title: 'Nonparametric statistics for stochastic processes: estimation and prediction'
  type: book

- id: BretoTime2009
  accessed:
    - year: 2015
      month: 12
      day: 15
  author:
    - family: Bretó
      given: Carles
    - family: He
      given: Daihai
    - family: Ionides
      given: Edward L.
    - family: King
      given: Aaron A.
  citation-key: BretoTime2009
  container-title: The Annals of Applied Statistics
  container-title-short: Ann. Appl. Stat.
  DOI: 10.1214/08-AOAS201
  ISSN: 1932-6157, 1941-7330
  issue: '1'
  issued:
    - year: 2009
      month: 3
  language: EN
  page: 319-348
  title: Time series analysis via mechanistic models
  type: article-journal
  volume: '3'

- id: BruntonDiscovering2016
  accessed:
    - year: 2016
      month: 5
      day: 16
  author:
    - family: Brunton
      given: Steven L.
    - family: Proctor
      given: Joshua L.
    - family: Kutz
      given: J. Nathan
  citation-key: BruntonDiscovering2016
  container-title: Proceedings of the National Academy of Sciences
  container-title-short: PNAS
  DOI: 10.1073/pnas.1517384113
  ISSN: 0027-8424, 1091-6490
  issue: '15'
  issued:
    - year: 2016
      month: 12
      day: 4
  language: en
  page: 3932-3937
  PMID: '27035946'
  publisher: National Academy of Sciences
  section: Physical Sciences
  title: >-
    Discovering governing equations from data by sparse identification of
    nonlinear dynamical systems
  type: article-journal
  volume: '113'

- id: BuhlmannBlock1999
  accessed:
    - year: 2014
      month: 11
      day: 24
  author:
    - family: Bühlmann
      given: Peter
    - family: Künsch
      given: Hans R
  citation-key: BuhlmannBlock1999
  container-title: Computational Statistics & Data Analysis
  container-title-short: Computational Statistics & Data Analysis
  DOI: 10.1016/S0167-9473(99)00014-6
  ISSN: 0167-9473
  issue: '3'
  issued:
    - year: 1999
      month: 9
      day: 28
  page: 295-310
  title: Block length selection in the bootstrap for time series
  type: article-journal
  volume: '31'

- id: CampbellOnline2021
  accessed:
    - year: 2021
      month: 12
      day: 8
  author:
    - family: Campbell
      given: Andrew
    - family: Shi
      given: Yuyang
    - family: Rainforth
      given: Tom
    - family: Doucet
      given: Arnaud
  citation-key: CampbellOnline2021
  event-title: Thirty-Fifth Conference on Neural Information Processing Systems
  issued:
    - year: 2021
      month: 5
      day: 21
  language: en
  title: Online Variational Filtering and Parameter Learning
  type: paper-conference
  URL: http://arxiv.org/abs/2110.13549

- id: CarmiCompressive2014
  accessed:
    - year: 2016
      month: 1
      day: 5
  author:
    - family: Carmi
      given: Avishy Y.
  citation-key: CarmiCompressive2014
  collection-title: Signals and Communication Technology
  container-title: Compressed Sensing & Sparse Filtering
  DOI: 10.1007/978-3-642-38398-4_9
  editor:
    - family: Carmi
      given: Avishy Y.
    - family: Mihaylova
      given: Lyudmila
    - family: Godsill
      given: Simon J.
  ISBN: 978-3-642-38397-7 978-3-642-38398-4
  issued:
    - year: 2014
  language: en
  page: 281-324
  publisher: Springer Berlin Heidelberg
  title: Compressive System Identification
  type: chapter
  URL: http://link.springer.com/chapter/10.1007/978-3-642-38398-4_9

- id: CassidyBrain2015
  accessed:
    - year: 2016
      month: 7
      day: 28
  author:
    - family: Cassidy
      given: Ben
    - family: Rae
      given: Caroline
    - family: Solo
      given: Victor
  citation-key: CassidyBrain2015
  container-title: IEEE Transactions on Medical Imaging
  DOI: 10.1109/TMI.2014.2358681
  ISSN: 0278-0062, 1558-254X
  issue: '4'
  issued:
    - year: 2015
      month: 4
  page: 846-860
  title: 'Brain Activity: Connectivity, Sparsity, and Mutual Information'
  type: article-journal
  URL: >-
    https://www.researchgate.net/publication/266085582_Brain_Activity_Connectivity_Sparsity_and_Mutual_Information
  volume: '34'

- id: ChanFactor2016
  accessed:
    - year: 2016
      month: 8
      day: 28
  author:
    - family: Chan
      given: Ngai Hang
    - family: Lu
      given: Ye
    - family: Yau
      given: Chun Yip
  citation-key: ChanFactor2016
  container-title: Journal of Time Series Analysis
  container-title-short: J. Time Ser. Anal.
  DOI: 10.1111/jtsa.12207
  ISSN: 1467-9892
  issued:
    - year: 2016
      month: 1
      day: 1
  language: en
  page: n/a-n/a
  title: >-
    Factor Modelling for High-Dimensional Time Series: Inference and Model
    Selection
  type: article-journal

- id: ChenNeural2018
  accessed:
    - year: 2019
      month: 1
      day: 29
  author:
    - family: Chen
      given: Tian Qi
    - family: Rubanova
      given: Yulia
    - family: Bettencourt
      given: Jesse
    - family: Duvenaud
      given: David K
  citation-key: ChenNeural2018
  container-title: Advances in Neural Information Processing Systems 31
  editor:
    - family: Bengio
      given: S.
    - family: Wallach
      given: H.
    - family: Larochelle
      given: H.
    - family: Grauman
      given: K.
    - family: Cesa-Bianchi
      given: N.
    - family: Garnett
      given: R.
  issued:
    - year: 2018
  page: 6572–6583
  publisher: Curran Associates, Inc.
  title: Neural Ordinary Differential Equations
  type: paper-conference
  URL: http://papers.nips.cc/paper/7892-neural-ordinary-differential-equations.pdf

- id: ChenNeural2019
  accessed:
    - year: 2023
      month: 8
      day: 8
  author:
    - family: Chen
      given: Ricky T. Q.
    - family: Duvenaud
      given: David K
  citation-key: ChenNeural2019
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2019
  publisher: Curran Associates, Inc.
  title: Neural Networks with Cheap Differential Operators
  type: paper-conference
  URL: http://arxiv.org/abs/1912.03579
  volume: '32'

- id: ChenNovel2022
  accessed:
    - year: 2022
      month: 9
      day: 20
  author:
    - family: Chen
      given: Chong
    - family: Dou
      given: Yixuan
    - family: Chen
      given: Jie
    - family: Xue
      given: Yaru
  citation-key: ChenNovel2022
  container-title: The Journal of Supercomputing
  container-title-short: J Supercomput
  DOI: 10.1007/s11227-022-04629-7
  ISSN: 0920-8542, 1573-0484
  issued:
    - year: 2022
      month: 6
      day: 15
  language: en
  title: A novel neural network training framework with data assimilation
  type: article-journal
  URL: http://arxiv.org/abs/2010.02626

- id: ChevillonDirect2007
  accessed:
    - year: 2018
      month: 1
      day: 13
  author:
    - family: Chevillon
      given: Guillaume
  citation-key: ChevillonDirect2007
  container-title: Journal of Economic Surveys
  DOI: 10.1111/j.1467-6419.2007.00518.x
  ISSN: 1467-6419
  issue: '4'
  issued:
    - year: 2007
      month: 9
      day: 1
  language: en
  page: 746-785
  title: Direct Multi-Step Estimation and Forecasting
  type: article-journal
  URL: http://www.vwl.tuwien.ac.at/hanappi/AgeSo/rp/Chevillon_2007.pdf
  volume: '21'

- id: ChoromanskiOde2020
  accessed:
    - year: 2020
      month: 12
      day: 13
  author:
    - family: Choromanski
      given: Krzysztof
    - family: Davis
      given: Jared Quincy
    - family: Likhosherstov
      given: Valerii
    - family: Song
      given: Xingyou
    - family: Slotine
      given: Jean-Jacques
    - family: Varley
      given: Jacob
    - family: Lee
      given: Honglak
    - family: Weller
      given: Adrian
    - family: Sindhwani
      given: Vikas
  citation-key: ChoromanskiOde2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
      month: 6
      day: 22
  title: An Ode to an ODE
  type: paper-conference
  URL: http://arxiv.org/abs/2006.11421
  volume: '33'

- id: ClarkPopulation2004
  accessed:
    - year: 2015
      month: 12
      day: 15
  author:
    - family: Clark
      given: James S.
    - family: Bjørnstad
      given: Ottar N.
  citation-key: ClarkPopulation2004
  container-title: Ecology
  container-title-short: Ecology
  DOI: 10.1890/03-0520
  ISSN: 0012-9658
  issue: '11'
  issued:
    - year: 2004
      month: 11
      day: 1
  page: 3140-3150
  title: >-
    Population time series: process variability, observation errors, missing
    values, lags, and hidden states
  type: article-journal
  volume: '85'

- id: CookEstimation2007
  accessed:
    - year: 2015
      month: 12
      day: 15
  author:
    - family: Cook
      given: Alex R.
    - family: Otten
      given: Wilfred
    - family: Marion
      given: Glenn
    - family: Gibson
      given: Gavin J.
    - family: Gilligan
      given: Christopher A.
  citation-key: CookEstimation2007
  container-title: Proceedings of the National Academy of Sciences
  container-title-short: PNAS
  DOI: 10.1073/pnas.0706461104
  ISSN: 0027-8424, 1091-6490
  issue: '51'
  issued:
    - year: 2007
      month: 12
      day: 18
  language: en
  page: 20392-20397
  PMID: '18077378'
  title: >-
    Estimation of multiple transmission rates for epidemics in heterogeneous
    populations
  type: article-journal
  volume: '104'

- id: CorenflosDifferentiable2021
  accessed:
    - year: 2021
      month: 7
      day: 30
  author:
    - family: Corenflos
      given: Adrien
    - family: Thornton
      given: James
    - family: Deligiannidis
      given: George
    - family: Doucet
      given: Arnaud
  citation-key: CorenflosDifferentiable2021
  container-title: arXiv:2102.07850 [cs, stat]
  issued:
    - year: 2021
      month: 6
      day: 30
  title: Differentiable Particle Filtering via Entropy-Regularized Optimal Transport
  type: article-journal
  URL: http://arxiv.org/abs/2102.07850

- id: CourseWeak2020
  accessed:
    - year: 2020
      month: 12
      day: 11
  author:
    - family: Course
      given: Kevin
    - family: Evans
      given: Trefor
    - family: Nair
      given: Prasanth
  citation-key: CourseWeak2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: Weak Form Generalized Hamiltonian Learning
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper_files/paper/2020/hash/d93c96e6a23fff65b91b900aaa541998-Abstract.html
  volume: '33'

- id: deBrouwerGRUODEBayes2019
  accessed:
    - year: 2023
      month: 3
      day: 1
  author:
    - family: Brouwer
      given: Edward
      non-dropping-particle: de
    - family: Simm
      given: Jaak
    - family: Arany
      given: Adam
    - family: Moreau
      given: Yves
  citation-key: deBrouwerGRUODEBayes2019
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2019
  publisher: Curran Associates, Inc.
  title: 'GRU-ODE-Bayes: Continuous Modeling of Sporadically-Observed Time Series'
  type: paper-conference
  URL: http://arxiv.org/abs/1905.12374
  volume: '32'

- id: DoucetDerivativeFree2013
  accessed:
    - year: 2014
      month: 2
      day: 20
  author:
    - family: Doucet
      given: Arnaud
    - family: Jacob
      given: Pierre E.
    - family: Rubenthaler
      given: Sylvain
  citation-key: DoucetDerivativeFree2013
  container-title: arXiv:1304.5768 [stat]
  issued:
    - year: 2013
      month: 4
      day: 21
  title: >-
    Derivative-Free Estimation of the Score Vector and Observed Information
    Matrix with Application to State-Space Models
  type: article-journal
  URL: http://arxiv.org/abs/1304.5768

- id: DurbinMonte1997
  accessed:
    - year: 2016
      month: 4
      day: 28
  author:
    - family: Durbin
      given: J.
    - family: Koopman
      given: S. J.
  citation-key: DurbinMonte1997
  container-title: Biometrika
  container-title-short: Biometrika
  DOI: 10.1093/biomet/84.3.669
  ISSN: 0006-3444, 1464-3510
  issue: '3'
  issued:
    - year: 1997
      month: 1
      day: 9
  language: en
  page: 669-684
  title: >-
    Monte Carlo maximum likelihood estimation for non-Gaussian state space
    models
  type: article-journal
  URL: >-
    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.127.4137&rep=rep1&type=pdf
  volume: '84'

- id: DurbinTime2012
  author:
    - family: Durbin
      given: J.
    - family: Koopman
      given: S. J.
  call-number: QA280 .D87 2012
  citation-key: DurbinTime2012
  collection-number: '38'
  collection-title: Oxford statistical science series
  edition: 2nd ed
  event-place: Oxford
  ISBN: 978-0-19-964117-8
  issued:
    - year: 2012
  number-of-pages: '346'
  publisher: Oxford University Press
  publisher-place: Oxford
  title: Time series analysis by state space methods
  type: book

- id: EMeanField2018
  accessed:
    - year: 2018
      month: 7
      day: 10
  author:
    - family: E
      given: Weinan
    - family: Han
      given: Jiequn
    - family: Li
      given: Qianxiao
  citation-key: EMeanField2018
  container-title: arXiv:1807.01083 [cs, math]
  issued:
    - year: 2018
      month: 7
      day: 3
  title: A Mean-Field Optimal Control Formulation of Deep Learning
  type: article-journal
  URL: http://arxiv.org/abs/1807.01083

- id: ErricoWhat1997
  accessed:
    - year: 2019
      month: 8
      day: 31
  author:
    - family: Errico
      given: Ronald M.
  citation-key: ErricoWhat1997
  container-title: Bulletin of the American Meteorological Society
  container-title-short: Bull. Amer. Meteor. Soc.
  DOI: 10.1175/1520-0477(1997)078<2577:WIAAM>2.0.CO;2
  ISSN: 0003-0007
  issue: '11'
  issued:
    - year: 1997
      month: 11
      day: 1
  page: 2577-2592
  publisher: American Meteorological Society
  section: Bulletin of the American Meteorological Society
  title: What Is an Adjoint Model?
  type: article-journal
  URL: http://bio.cgrer.uiowa.edu/people/tchai/HTM/Reference/adjoint_errico.pdf
  volume: '78'

- id: EvensenData2009
  accessed:
    - year: 2014
      month: 11
      day: 21
  author:
    - family: Evensen
      given: Geir
  citation-key: EvensenData2009
  DOI: 10.1007/978-3-642-03711-5
  event-place: Berlin; Heidelberg
  ISBN: 978-3-642-03711-5 3-642-03711-9
  issued:
    - year: 2009
  language: English
  number-of-pages: '314'
  publisher: Springer
  publisher-place: Berlin; Heidelberg
  title: Data Assimilation - The Ensemble Kalman Filter
  type: book

- id: EvensenEnsemble2000
  accessed:
    - year: 2022
      month: 7
      day: 22
  author:
    - family: Evensen
      given: Geir
    - family: Leeuwen
      given: Peter Jan
      non-dropping-particle: van
  citation-key: EvensenEnsemble2000
  container-title: Monthly Weather Review
  container-title-short: Mon. Wea. Rev.
  DOI: 10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2
  ISSN: 0027-0644, 1520-0493
  issue: '6'
  issued:
    - year: 2000
      month: 6
  language: en
  page: 1852-1867
  publisher: American Meteorological Society
  section: Monthly Weather Review
  title: An Ensemble Kalman Smoother for Nonlinear Dynamics
  type: article-journal
  URL: http://jrs390.georgetown.domains/papers/dynamic-image.pdf
  volume: '128'

- id: EvensenEnsemble2003
  accessed:
    - year: 2017
      month: 8
      day: 28
  author:
    - family: Evensen
      given: Geir
  citation-key: EvensenEnsemble2003
  container-title: Ocean Dynamics
  container-title-short: Ocean Dynamics
  DOI: 10.1007/s10236-003-0036-9
  ISSN: 1616-7341, 1616-7228
  issue: '4'
  issued:
    - year: 2003
      month: 11
      day: 1
  language: en
  page: 343-367
  title: >-
    The Ensemble Kalman Filter: theoretical formulation and practical
    implementation
  type: article-journal
  URL: https://idv.sinica.edu.tw/cytseng/current%20term/Evesen03a.pdf
  volume: '53'

- id: EvensenEnsemble2009
  author:
    - family: Evensen
      given: Geir
  citation-key: EvensenEnsemble2009
  container-title: IEEE Control Systems
  DOI: 10.1109/MCS.2009.932223
  ISSN: 1066-033X
  issue: '3'
  issued:
    - year: 2009
      month: 6
  page: 83-104
  title: The ensemble Kalman filter for combined state and parameter estimation
  type: article-journal
  URL: https://www.nersc.no/sites/www.nersc.no/files/Evensen.pdf
  volume: '29'

- id: FanNonlinear2003
  author:
    - family: Fan
      given: Jianqing
    - family: Yao
      given: Qiwei
  call-number: QA280 .F36 2003
  citation-key: FanNonlinear2003
  collection-title: Springer series in statistics
  event-place: New York
  ISBN: 978-0-387-95170-6
  issued:
    - year: 2003
  number-of-pages: '551'
  publisher: Springer
  publisher-place: New York
  title: 'Nonlinear time series: nonparametric and parametric methods'
  type: book

- id: FearnheadParticle2018
  accessed:
    - year: 2018
      month: 3
      day: 19
  author:
    - family: Fearnhead
      given: Paul
    - family: Künsch
      given: Hans R.
  citation-key: FearnheadParticle2018
  container-title: Annual Review of Statistics and Its Application
  DOI: 10.1146/annurev-statistics-031017-100232
  issue: '1'
  issued:
    - year: 2018
  page: 421-449
  title: Particle Filters and Data Assimilation
  type: article-journal
  URL: http://arxiv.org/abs/1709.04196
  volume: '5'

- id: FinkeApproximate2016
  accessed:
    - year: 2016
      month: 9
      day: 18
  author:
    - family: Finke
      given: Axel
    - family: Singh
      given: Sumeetpal S.
  citation-key: FinkeApproximate2016
  container-title: arXiv:1606.08650 [stat]
  issued:
    - year: 2016
      month: 6
      day: 28
  title: >-
    Approximate Smoothing and Parameter Estimation in High-Dimensional
    State-Space Models
  type: article-journal
  URL: http://arxiv.org/abs/1606.08650

- id: FinlayHow
  author:
    - family: Finlay
      given: Chris
    - family: Jacobsen
      given: Jörn-Henrik
    - family: Nurbekyan
      given: Levon
    - family: Oberman
      given: Adam M
  citation-key: FinlayHow
  container-title: ICML
  language: en
  page: '14'
  title: >-
    How to Train Your Neural ODE: the World of Jacobian and Kinetic
    Regularization
  type: paper-conference

- id: FinziSimplifying2020
  accessed:
    - year: 2020
      month: 12
      day: 10
  author:
    - family: Finzi
      given: Marc
    - family: Wang
      given: Ke Alexander
    - family: Wilson
      given: Andrew G.
  citation-key: FinziSimplifying2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: >-
    Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit
    Constraints
  type: paper-conference
  URL: >-
    https://papers.nips.cc/paper/2020/hash/9f655cc8884fda7ad6d8a6fb15cc001e-Abstract.html
  volume: '33'

- id: FlunkertDeepAR2017
  accessed:
    - year: 2018
      month: 1
      day: 13
  author:
    - family: Flunkert
      given: Valentin
    - family: Salinas
      given: David
    - family: Gasthaus
      given: Jan
  citation-key: FlunkertDeepAR2017
  container-title: arXiv:1704.04110 [cs, stat]
  issued:
    - year: 2017
      month: 4
      day: 13
  title: 'DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks'
  type: article-journal
  URL: http://arxiv.org/abs/1704.04110

- id: FraserHidden2008
  author:
    - family: Fraser
      given: Andrew M.
  call-number: QA274.7 .F726 2008
  citation-key: FraserHidden2008
  event-place: Philadelphia, PA
  ISBN: 978-0-89871-665-8
  issued:
    - year: 2008
  number-of-pages: '132'
  publisher: Society for Industrial and Applied Mathematics
  publisher-place: Philadelphia, PA
  title: Hidden Markov models and dynamical systems
  type: book

- id: GholamiANODE2019
  accessed:
    - year: 2019
      month: 3
      day: 21
  author:
    - family: Gholami
      given: Amir
    - family: Keutzer
      given: Kurt
    - family: Biros
      given: George
  citation-key: GholamiANODE2019
  container-title: arXiv:1902.10298 [cs]
  issued:
    - year: 2019
      month: 2
      day: 26
  title: 'ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs'
  type: article-journal
  URL: http://arxiv.org/abs/1902.10298

- id: GhoshSTEER2020
  accessed:
    - year: 2020
      month: 12
      day: 13
  author:
    - family: Ghosh
      given: Arnab
    - family: Behl
      given: Harkirat
    - family: Dupont
      given: Emilien
    - family: Torr
      given: Philip
    - family: Namboodiri
      given: Vinay
  citation-key: GhoshSTEER2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: 'STEER : Simple Temporal Regularization For Neural ODE'
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper_files/paper/2020/hash/a9e18cb5dd9d3ab420946fa19ebbbf52-Abstract.html
  volume: '33'

- id: GoradParameter2020
  author:
    - family: Gorad
      given: Ajinkya
    - family: Zhao
      given: Zheng
    - family: Särkkä
      given: Simo
  citation-key: GoradParameter2020
  event-title: MLSP
  issued:
    - year: 2020
  language: en
  page: '6'
  title: >-
    Parameter estimation in non-linear state-space models by automatic
    differentiation of non-linear kalman filters
  type: paper-conference

- id: GrathwohlFFJORD2018
  accessed:
    - year: 2019
      month: 9
      day: 23
  author:
    - family: Grathwohl
      given: Will
    - family: Chen
      given: Ricky T. Q.
    - family: Bettencourt
      given: Jesse
    - family: Sutskever
      given: Ilya
    - family: Duvenaud
      given: David
  citation-key: GrathwohlFFJORD2018
  container-title: arXiv:1810.01367 [cs, stat]
  issued:
    - year: 2018
      month: 10
      day: 2
  title: >-
    FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative
    Models
  type: article-journal
  URL: http://arxiv.org/abs/1810.01367

- id: GuCombining2021
  accessed:
    - year: 2022
      month: 8
      day: 6
  author:
    - family: Gu
      given: Albert
    - family: Johnson
      given: Isys
    - family: Goel
      given: Karan
    - family: Saab
      given: Khaled
    - family: Dao
      given: Tri
    - family: Rudra
      given: Atri
    - family: Ré
      given: Christopher
  citation-key: GuCombining2021
  container-title: Advances in Neural Information Processing Systems
  DOI: 10.48550/arXiv.2110.13985
  event-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2021
  page: 572–585
  publisher: Curran Associates, Inc.
  title: >-
    Combining Recurrent, Convolutional, and Continuous-time Models with Linear
    State Space Layers
  type: paper-conference
  URL: http://arxiv.org/abs/2110.13985
  volume: '34'

- id: HaberNever2018
  accessed:
    - year: 2018
      month: 7
      day: 10
  author:
    - family: Haber
      given: Eldad
    - family: Lucka
      given: Felix
    - family: Ruthotto
      given: Lars
  citation-key: HaberNever2018
  container-title: arXiv:1805.08034 [cs, math]
  issued:
    - year: 2018
      month: 5
      day: 21
  title: >-
    Never look back - A modified EnKF method and its application to the training
    of neural networks without back propagation
  type: article-journal
  URL: http://arxiv.org/abs/1805.08034

- id: HarveyStructural2005
  accessed:
    - year: 2016
      month: 4
      day: 28
  author:
    - family: Harvey
      given: A.
    - family: Koopman
      given: S. J.
  citation-key: HarveyStructural2005
  container-title: Encyclopedia of Biostatistics
  ISBN: 978-0-470-01181-2
  issued:
    - year: 2005
  language: en
  publisher: John Wiley & Sons, Ltd
  title: Structural Time Series Models
  type: chapter
  URL: http://onlinelibrary.wiley.com/doi/10.1002/0470011815.b2a12069/abstract

- id: HazanLearning2017
  author:
    - family: Hazan
      given: Elad
    - family: Singh
      given: Karan
    - family: Zhang
      given: Cyril
  citation-key: HazanLearning2017
  container-title: NIPS
  issued:
    - year: 2017
  title: Learning Linear Dynamical Systems via Spectral Filtering
  type: paper-conference
  URL: http://arxiv.org/abs/1711.00946

- id: HefnyNew2015
  accessed:
    - year: 2015
      month: 6
      day: 21
  author:
    - family: Hefny
      given: Ahmed
    - family: Downey
      given: Carlton
    - family: Gordon
      given: Geoffrey
  citation-key: HefnyNew2015
  container-title: arXiv:1505.05310 [cs, stat]
  issued:
    - year: 2015
      month: 5
      day: 20
  title: A New View of Predictive State Methods for Dynamical System Learning
  type: article-journal
  URL: http://arxiv.org/abs/1505.05310

- id: HePlugandplay2010
  accessed:
    - year: 2015
      month: 12
      day: 15
  author:
    - family: He
      given: Daihai
    - family: Ionides
      given: Edward L.
    - family: King
      given: Aaron A.
  citation-key: HePlugandplay2010
  container-title: Journal of The Royal Society Interface
  DOI: 10.1098/rsif.2009.0151
  ISSN: 1742-5689, 1742-5662
  issue: '43'
  issued:
    - year: 2010
      month: 2
      day: 6
  language: en
  page: 271-283
  PMID: '19535416'
  title: >-
    Plug-and-play inference for disease dynamics: measles in large and small
    populations as a case study
  type: article-journal
  volume: '7'

- id: HirshSparsifying2022
  accessed:
    - year: 2023
      month: 3
      day: 14
  author:
    - family: Hirsh
      given: Seth M.
    - family: Barajas-Solano
      given: David A.
    - family: Kutz
      given: J. Nathan
  citation-key: HirshSparsifying2022
  container-title: Royal Society Open Science
  DOI: 10.1098/rsos.211823
  issue: '2'
  issued:
    - year: 2022
      month: 2
      day: 23
  page: '211823'
  publisher: Royal Society
  title: >-
    Sparsifying priors for Bayesian uncertainty quantification in model
    discovery
  type: article-journal
  volume: '9'

- id: HolzschuhScore2022
  author:
    - family: Holzschuh
      given: Benjamin
    - family: Vegetti
      given: Simona
    - family: Thuerey
      given: Nils
  citation-key: HolzschuhScore2022
  issued:
    - year: 2022
  language: en
  page: '7'
  title: Score Matching via Differentiable Physics
  type: article-journal

- id: HongModel2008
  accessed:
    - year: 2015
      month: 5
      day: 12
  author:
    - family: Hong
      given: X.
    - family: Mitchell
      given: R. J.
    - family: Chen
      given: S.
    - family: Harris
      given: C. J.
    - family: Li
      given: K.
    - family: Irwin
      given: G. W.
  citation-key: HongModel2008
  container-title: International Journal of Systems Science
  DOI: 10.1080/00207720802083018
  ISSN: 0020-7721
  issue: '10'
  issued:
    - year: 2008
      month: 10
      day: 1
  page: 925-946
  title: 'Model selection approaches for non-linear system identification: a review'
  type: article-journal
  URL: http://eprints.soton.ac.uk/id/eprint/266152
  volume: '39'

- id: HongNonparametric2005
  accessed:
    - year: 2015
      month: 5
      day: 12
  author:
    - family: Hong
      given: Yongmiao
    - family: Li
      given: Haitao
  citation-key: HongNonparametric2005
  container-title: Review of Financial Studies
  container-title-short: Rev. Financ. Stud.
  DOI: 10.1093/rfs/hhh006
  ISSN: 0893-9454, 1465-7368
  issue: '1'
  issued:
    - year: 2005
      month: 3
      day: 20
  language: en
  page: 37-84
  title: >-
    Nonparametric Specification Testing for Continuous-Time Models with
    Applications to Term Structure of Interest Rates
  type: article-journal
  URL: >-
    http://hong.economics.cornell.edu/papers/Nonparametric%20specification%20testing%20for%20continuous-time%20models%20with%20applications%20to%20spot%20interest%20rates.pdf
  volume: '18'

- id: HoutekamerReview2016
  accessed:
    - year: 2023
      month: 1
      day: 23
  author:
    - family: Houtekamer
      given: P. L.
    - family: Zhang
      given: Fuqing
  citation-key: HoutekamerReview2016
  container-title: Monthly Weather Review
  DOI: 10.1175/MWR-D-15-0440.1
  ISSN: 1520-0493, 0027-0644
  issue: '12'
  issued:
    - year: 2016
      month: 12
      day: 1
  language: EN
  page: 4489-4532
  publisher: American Meteorological Society
  section: Monthly Weather Review
  title: Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation
  type: article-journal
  volume: '144'

- id: IonidesInference2006
  accessed:
    - year: 2014
      month: 2
      day: 20
  author:
    - family: Ionides
      given: E. L.
    - family: Bretó
      given: C.
    - family: King
      given: A. A.
  citation-key: IonidesInference2006
  container-title: Proceedings of the National Academy of Sciences
  container-title-short: PNAS
  DOI: 10.1073/pnas.0603181103
  ISSN: 0027-8424, 1091-6490
  issue: '49'
  issued:
    - year: 2006
      month: 5
      day: 12
  language: en
  page: 18438-18443
  PMID: '17121996'
  title: Inference for nonlinear dynamical systems
  type: article-journal
  volume: '103'

- id: IonidesIterated2011
  accessed:
    - year: 2015
      month: 12
      day: 15
  author:
    - family: Ionides
      given: Edward L.
    - family: Bhadra
      given: Anindya
    - family: Atchadé
      given: Yves
    - family: King
      given: Aaron
  citation-key: IonidesIterated2011
  container-title: The Annals of Statistics
  DOI: 10.1214/11-AOS886
  ISSN: 0090-5364
  issue: '3'
  issued:
    - year: 2011
      month: 6
  page: 1776-1802
  title: Iterated filtering
  type: article-journal
  URL: http://arxiv.org/abs/0902.0347
  volume: '39'

- id: JiaNeural2019
  accessed:
    - year: 2020
      month: 10
      day: 29
  author:
    - family: Jia
      given: Junteng
    - family: Benson
      given: Austin R
  citation-key: JiaNeural2019
  container-title: Advances in Neural Information Processing Systems 32
  editor:
    - family: Wallach
      given: H.
    - family: Larochelle
      given: H.
    - family: Beygelzimer
      given: A.
    - family: Alché-Buc
      given: F.
      dropping-particle: d\textquotesingle
    - family: Fox
      given: E.
    - family: Garnett
      given: R.
  issued:
    - year: 2019
  page: 9847–9858
  publisher: Curran Associates, Inc.
  title: Neural Jump Stochastic Differential Equations
  type: paper-conference
  URL: >-
    http://papers.nips.cc/paper/9177-neural-jump-stochastic-differential-equations.pdf

- id: JonschkowskiDifferentiable2018
  accessed:
    - year: 2021
      month: 7
      day: 30
  author:
    - family: Jonschkowski
      given: Rico
    - family: Rastogi
      given: Divyam
    - family: Brock
      given: Oliver
  citation-key: JonschkowskiDifferentiable2018
  container-title: arXiv:1805.11122 [cs, stat]
  issued:
    - year: 2018
      month: 5
      day: 29
  title: 'Differentiable Particle Filters: End-to-End Learning with Algorithmic Priors'
  type: article-journal
  URL: http://arxiv.org/abs/1805.11122

- id: KalliBayesian2018
  accessed:
    - year: 2021
      month: 12
      day: 3
  author:
    - family: Kalli
      given: Maria
    - family: Griffin
      given: Jim E.
  citation-key: KalliBayesian2018
  container-title: Journal of Econometrics
  container-title-short: Journal of Econometrics
  DOI: 10.1016/j.jeconom.2017.11.009
  ISSN: 0304-4076
  issue: '2'
  issued:
    - year: 2018
      month: 4
      day: 1
  language: en
  page: 267-282
  title: Bayesian nonparametric vector autoregressive models
  type: article-journal
  volume: '203'

- id: KantasParticle2015
  author:
    - family: Kantas
      given: Nikolas
    - family: Doucet
      given: Arnaud
    - family: Singh
      given: Sumeetpal S.
    - family: Maciejowski
      given: Jan
    - family: Chopin
      given: Nicolas
  citation-key: KantasParticle2015
  container-title: Statistical Science
  DOI: 10.1214/14-STS511
  ISSN: 0883-4237
  issue: '3'
  issued:
    - year: 2015
  page: 328–351
  publisher: Institute of Mathematical Statistics
  title: On Particle Methods for Parameter Estimation in State-Space Models
  type: article-journal
  URL: https://spiral.imperial.ac.uk/bitstream/10044/1/26663/2/1412.8695v2.pdf
  volume: '30'

- id: KantzNonlinear2004
  author:
    - family: Kantz
      given: Holger
    - family: Schreiber
      given: Thomas
  call-number: QA280 .K355 2004
  citation-key: KantzNonlinear2004
  edition: 2nd ed
  event-place: Cambridge, UK ; New York
  ISBN: 978-0-521-82150-6 978-0-521-52902-0
  issued:
    - year: 2004
  number-of-pages: '369'
  publisher: Cambridge University Press
  publisher-place: Cambridge, UK ; New York
  title: Nonlinear time series analysis
  type: book

- id: KassComputational2018
  accessed:
    - year: 2018
      month: 3
      day: 19
  author:
    - family: Kass
      given: Robert E.
    - family: Amari
      given: Shun-Ichi
    - family: Arai
      given: Kensuke
    - family: Brown
      given: Emery N.
    - family: Diekman
      given: Casey O.
    - family: Diesmann
      given: Markus
    - family: Doiron
      given: Brent
    - family: Eden
      given: Uri T.
    - family: Fairhall
      given: Adrienne L.
    - family: Fiddyment
      given: Grant M.
    - family: Fukai
      given: Tomoki
    - family: Grün
      given: Sonja
    - family: Harrison
      given: Matthew T.
    - family: Helias
      given: Moritz
    - family: Nakahara
      given: Hiroyuki
    - family: Teramae
      given: Jun-nosuke
    - family: Thomas
      given: Peter J.
    - family: Reimers
      given: Mark
    - family: Rodu
      given: Jordan
    - family: Rotstein
      given: Horacio G.
    - family: Shea-Brown
      given: Eric
    - family: Shimazaki
      given: Hideaki
    - family: Shinomoto
      given: Shigeru
    - family: Yu
      given: Byron M.
    - family: Kramer
      given: Mark A.
  citation-key: KassComputational2018
  container-title: Annual Review of Statistics and Its Application
  DOI: 10.1146/annurev-statistics-041715-033733
  issue: '1'
  issued:
    - year: 2018
  page: 183-214
  title: 'Computational Neuroscience: Mathematical and Statistical Perspectives'
  type: article-journal
  volume: '5'

- id: KellyLearning2020
  accessed:
    - year: 2020
      month: 12
      day: 8
  author:
    - family: Kelly
      given: Jacob
    - family: Bettencourt
      given: Jesse
    - family: Johnson
      given: Matthew James
    - family: Duvenaud
      given: David
  citation-key: KellyLearning2020
  issued:
    - year: 2020
      month: 7
      day: 9
  language: en
  title: Learning Differential Equations that are Easy to Solve
  type: paper-conference
  URL: https://arxiv.org/abs/2007.04504v2

- id: KemeraitSignal1972
  author:
    - family: Kemerait
      given: R.
    - family: Childers
      given: D.
  citation-key: KemeraitSignal1972
  container-title: IEEE Transactions on Information Theory
  DOI: 10.1109/TIT.1972.1054926
  ISSN: 0018-9448
  issue: '6'
  issued:
    - year: 1972
      month: 11
  page: 745-759
  title: Signal detection and extraction by cepstrum techniques
  type: article-journal
  volume: '18'

- id: KendallPopulation2005
  accessed:
    - year: 2014
      month: 12
      day: 23
  author:
    - family: Kendall
      given: Bruce E.
    - family: Ellner
      given: Stephen P.
    - family: McCauley
      given: Edward
    - family: Wood
      given: Simon N.
    - family: Briggs
      given: Cheryl J.
    - family: Murdoch
      given: William W.
    - family: Turchin
      given: Peter
  citation-key: KendallPopulation2005
  container-title: Ecological Monographs
  ISSN: 0012-9615
  issue: '2'
  issued:
    - year: 2005
      month: 5
      day: 1
  page: 259–276
  title: >-
    Population cycles in the pine looper moth: Dynamical tests of mechanistic
    hypotheses
  type: article-journal
  URL: http://www.sysecol2.ethz.ch/Refs/EntClim/K/Ke169.pdf
  volume: '75'

- id: KidgerHey2021
  accessed:
    - year: 2023
      month: 4
      day: 16
  author:
    - family: Kidger
      given: Patrick
    - family: Chen
      given: Ricky T. Q.
    - family: Lyons
      given: Terry J.
  citation-key: KidgerHey2021
  container-title: Proceedings of the 38th International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
  issued:
    - year: 2021
      month: 7
      day: 1
  language: en
  page: 5443-5452
  publisher: PMLR
  title: '"Hey, that’s not an ODE": Faster ODE Adjoints via Seminorms'
  type: paper-conference
  URL: http://arxiv.org/abs/2009.09457

- id: KidgerNeural2020
  accessed:
    - year: 2021
      month: 9
      day: 28
  author:
    - family: Kidger
      given: Patrick
    - family: Morrill
      given: James
    - family: Foster
      given: James
    - family: Lyons
      given: Terry
  citation-key: KidgerNeural2020
  container-title: arXiv:2005.08926 [cs, stat]
  issued:
    - year: 2020
      month: 11
      day: 5
  title: Neural Controlled Differential Equations for Irregular Time Series
  type: article-journal
  URL: http://arxiv.org/abs/2005.08926

- id: KitagawaMonte1996
  accessed:
    - year: 2016
      month: 4
      day: 28
  author:
    - family: Kitagawa
      given: Genshiro
  citation-key: KitagawaMonte1996
  container-title: Journal of Computational and Graphical Statistics
  DOI: 10.1080/10618600.1996.10474692
  ISSN: 1061-8600
  issue: '1'
  issued:
    - year: 1996
      month: 3
      day: 1
  page: 1-25
  title: >-
    Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space
    Models
  type: article-journal
  volume: '5'

- id: KitagawaNonGaussian1987
  accessed:
    - year: 2016
      month: 4
      day: 28
  author:
    - family: Kitagawa
      given: Genshiro
  citation-key: KitagawaNonGaussian1987
  container-title: Journal of the American Statistical Association
  container-title-short: Journal of the American Statistical Association
  DOI: 10.1080/01621459.1987.10478534
  ISSN: 0162-1459
  issue: '400'
  issued:
    - year: 1987
      month: 12
      day: 1
  page: 1032-1041
  title: Non-Gaussian State—Space Modeling of Nonstationary Time Series
  type: article-journal
  volume: '82'

- id: KitagawaSmoothness1996
  accessed:
    - year: 2016
      month: 4
      day: 28
  author:
    - family: Kitagawa
      given: Genshiro
    - family: Gersch
      given: Will
  call-number: QA280 .K58 1996
  citation-key: KitagawaSmoothness1996
  collection-number: '116'
  collection-title: Lecture notes in statistics
  event-place: New York, NY
  ISBN: 978-1-4612-0761-0
  issued:
    - year: 1996
  language: English
  publisher: 'Springer New York : Imprint : Springer'
  publisher-place: New York, NY
  title: Smoothness Priors Analysis of Time Series
  type: book
  URL: http://dx.doi.org/10.1007/978-1-4612-0761-0

- id: KovachkiEnsemble2019
  accessed:
    - year: 2022
      month: 8
      day: 23
  author:
    - family: Kovachki
      given: Nikola B.
    - family: Stuart
      given: Andrew M.
  citation-key: KovachkiEnsemble2019
  container-title: Inverse Problems
  container-title-short: Inverse Problems
  DOI: 10.1088/1361-6420/ab1c3a
  ISSN: 0266-5611
  issue: '9'
  issued:
    - year: 2019
      month: 8
  language: en
  page: '095005'
  publisher: IOP Publishing
  title: >-
    Ensemble Kalman inversion: a derivative-free technique for machine learning
    tasks
  type: article-journal
  URL: https://arxiv.org/abs/1808.03620v1
  volume: '35'

- id: KrishnamurthyTheory2022
  author:
    - family: Krishnamurthy
      given: Kamesh
    - family: Can
      given: Tankut
    - family: Schwab
      given: David J.
  citation-key: KrishnamurthyTheory2022
  container-title: Physical Review. X
  container-title-short: Phys Rev X
  DOI: 10.1103/physrevx.12.011011
  ISSN: 2160-3308
  issue: '1'
  issued:
    - year: 2022
  language: eng
  page: '011011'
  PMCID: PMC9762509
  PMID: '36545030'
  title: Theory of Gating in Recurrent Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/2007.14823
  volume: '12'

- id: LambProfessor2016
  accessed:
    - year: 2018
      month: 1
      day: 13
  author:
    - family: Lamb
      given: Alex
    - family: Goyal
      given: Anirudh
    - family: Zhang
      given: Ying
    - family: Zhang
      given: Saizheng
    - family: Courville
      given: Aaron
    - family: Bengio
      given: Yoshua
  citation-key: LambProfessor2016
  container-title: Advances In Neural Information Processing Systems
  event-title: NIPS
  issued:
    - year: 2016
      month: 10
      day: 27
  title: 'Professor Forcing: A New Algorithm for Training Recurrent Networks'
  type: paper-conference
  URL: http://arxiv.org/abs/1610.09038

- id: LevinInner2017
  author:
    - family: Levin
      given: David N.
  citation-key: LevinInner2017
  container-title: arXiv:1703.08596 [cs, math, stat]
  issued:
    - year: 2017
      month: 3
      day: 24
  title: The Inner Structure of Time-Dependent Signals
  type: article-journal
  URL: http://arxiv.org/abs/1703.08596

- id: LiDataDriven2021
  accessed:
    - year: 2021
      month: 7
      day: 27
  author:
    - family: Li
      given: Yang
    - family: Duan
      given: Jinqiao
  citation-key: LiDataDriven2021
  container-title: 'Physica D: Nonlinear Phenomena'
  container-title-short: 'Physica D: Nonlinear Phenomena'
  DOI: 10.1016/j.physd.2020.132830
  ISSN: '01672789'
  issued:
    - year: 2021
      month: 3
  page: '132830'
  title: >-
    A Data-Driven Approach for Discovering Stochastic Dynamical Systems with
    Non-Gaussian Levy Noise
  type: article-journal
  URL: http://arxiv.org/abs/2005.03769
  volume: '417'

- id: LiExtracting2021
  accessed:
    - year: 2021
      month: 7
      day: 27
  author:
    - family: Li
      given: Yang
    - family: Duan
      given: Jinqiao
  citation-key: LiExtracting2021
  container-title: arXiv:2107.10127 [math, stat]
  issued:
    - year: 2021
      month: 7
      day: 21
  title: >-
    Extracting Governing Laws from Sample Path Data of Non-Gaussian Stochastic
    Dynamical Systems
  type: article-journal
  URL: http://arxiv.org/abs/2107.10127

- id: LiScalable2020
  accessed:
    - year: 2020
      month: 8
      day: 23
  author:
    - family: Li
      given: Xuechen
    - family: Wong
      given: Ting-Kam Leonard
    - family: Chen
      given: Ricky T. Q.
    - family: Duvenaud
      given: David
  citation-key: LiScalable2020
  container-title: International Conference on Artificial Intelligence and Statistics
  event-title: International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
    - year: 2020
      month: 6
      day: 3
  language: en
  page: 3870-3882
  publisher: PMLR
  title: Scalable Gradients for Stochastic Differential Equations
  type: paper-conference
  URL: http://proceedings.mlr.press/v108/li20i.html

- id: LjungPerspectives2010
  accessed:
    - year: 2018
      month: 4
      day: 13
  author:
    - family: Ljung
      given: Lennart
  citation-key: LjungPerspectives2010
  container-title: Annual Reviews in Control
  container-title-short: Annual Reviews in Control
  DOI: 10.1016/j.arcontrol.2009.12.001
  ISSN: 1367-5788
  issue: '1'
  issued:
    - year: 2010
      month: 4
      day: 1
  page: 1-12
  title: Perspectives on system identification
  type: article-journal
  URL: http://users.isy.liu.se/en/rt/ljung/seoul2dvinew/plenary2.pdf
  volume: '34'

- id: LouNeural2020
  accessed:
    - year: 2020
      month: 12
      day: 10
  author:
    - family: Lou
      given: Aaron
    - family: Lim
      given: Derek
    - family: Katsman
      given: Isay
    - family: Huang
      given: Leo
    - family: Jiang
      given: Qingxuan
    - family: Lim
      given: Ser Nam
    - family: De Sa
      given: Christopher M.
  citation-key: LouNeural2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: Neural Manifold Ordinary Differential Equations
  type: paper-conference
  URL: >-
    https://papers.nips.cc/paper/2020/hash/cbf8710b43df3f2c1553e649403426df-Abstract.html
  volume: '33'

- id: LuDiscovering2021
  accessed:
    - year: 2021
      month: 7
      day: 27
  author:
    - family: Lu
      given: Peter Y.
    - family: Ariño
      given: Joan
    - family: Soljačić
      given: Marin
  citation-key: LuDiscovering2021
  container-title: arXiv:2107.10879 [physics]
  issued:
    - year: 2021
      month: 7
      day: 22
  title: Discovering Sparse Interpretable Dynamics from Partial Observations
  type: article-journal
  URL: http://arxiv.org/abs/2107.10879

- id: LuoIterative2015
  accessed:
    - year: 2022
      month: 5
      day: 10
  author:
    - family: Luo
      given: Xiaodong
    - family: Stordal
      given: Andreas S.
    - family: Lorentzen
      given: Rolf J.
    - family: Nævdal
      given: Geir
  citation-key: LuoIterative2015
  container-title: SPE Journal
  container-title-short: SPE Journal
  DOI: 10.2118/176023-PA
  ISSN: 1086-055X
  issue: '05'
  issued:
    - year: 2015
      month: 10
      day: 20
  page: 962-982
  title: >-
    Iterative Ensemble Smoother as an Approximate Solution to a Regularized
    Minimum-Average-Cost Problem: Theory and Applications
  type: article-journal
  volume: '20'

- id: MalarticState2021
  accessed:
    - year: 2021
      month: 7
      day: 27
  author:
    - family: Malartic
      given: Quentin
    - family: Farchi
      given: Alban
    - family: Bocquet
      given: Marc
  citation-key: MalarticState2021
  container-title: arXiv:2107.11253 [nlin, physics:physics, stat]
  issued:
    - year: 2021
      month: 7
      day: 26
  title: >-
    State, global and local parameter estimation using local ensemble Kalman
    filters: applications to online machine learning of chaotic dynamics
  type: article-journal
  URL: http://arxiv.org/abs/2107.11253

- id: MassaroliDissecting2020
  accessed:
    - year: 2020
      month: 12
      day: 8
  author:
    - family: Massaroli
      given: Stefano
    - family: Poli
      given: Michael
    - family: Park
      given: Jinkyoo
    - family: Yamashita
      given: Atsushi
    - family: Asama
      given: Hajime
  citation-key: MassaroliDissecting2020
  container-title: arXiv:2002.08071 [cs, stat]
  issued:
    - year: 2020
      month: 6
      day: 20
  title: Dissecting Neural ODEs
  type: paper-conference
  URL: http://arxiv.org/abs/2002.08071

- id: MitchellAdaptive2000
  accessed:
    - year: 2023
      month: 1
      day: 24
  author:
    - family: Mitchell
      given: Herschel L.
    - family: Houtekamer
      given: P. L.
  citation-key: MitchellAdaptive2000
  container-title: Monthly Weather Review
  container-title-short: Monthly Weather Rev
  DOI: 10.1175/1520-0493(2000)128<0416:AAEKF>2.0.CO;2
  ISSN: 0027-0644, 1520-0493
  issue: '2'
  issued:
    - year: 2000
  language: en
  page: '416'
  title: An Adaptive Ensemble Kalman Filter
  type: article-journal
  volume: '128'

- id: MorrillNeural2020
  author:
    - family: Morrill
      given: James
    - family: Kidger
      given: Patrick
    - family: Salvi
      given: Cristopher
    - family: Foster
      given: James
    - family: Lyons
      given: Terry
  citation-key: MorrillNeural2020
  issued:
    - year: 2020
  language: en
  page: '5'
  title: Neural CDEs for Long Time Series via the Log-ODE Method
  type: paper-conference

- id: NerrandNeural1993
  author:
    - family: Nerrand
      given: O.
    - family: Roussel-Ragot
      given: P.
    - family: Personnaz
      given: L.
    - family: Dreyfus
      given: G.
    - family: Marcos
      given: S.
  citation-key: NerrandNeural1993
  container-title: Neural Computation
  DOI: 10.1162/neco.1993.5.2.165
  ISSN: 0899-7667
  issue: '2'
  issued:
    - year: 1993
      month: 3
  page: 165-199
  title: >-
    Neural Networks and Nonlinear Adaptive Filtering: Unifying Concepts and New
    Algorithms
  type: article-journal
  URL: https://www.neurones.espci.fr/Articles_PS/NeuralComp_Filtrage.pdf
  volume: '5'

- id: NguyenExploration2020
  author:
    - family: Nguyen
      given: Long
    - family: Malinsky
      given: Andy
  citation-key: NguyenExploration2020
  issued:
    - year: 2020
  language: en
  page: '34'
  title: Exploration and Implementation of Neural Ordinary Diﬀerential Equations
  type: article-journal

- id: PereyraSurvey2016
  author:
    - family: Pereyra
      given: M.
    - family: Schniter
      given: P.
    - family: Chouzenoux
      given: É
    - family: Pesquet
      given: J. C.
    - family: Tourneret
      given: J. Y.
    - family: Hero
      given: A. O.
    - family: McLaughlin
      given: S.
  citation-key: PereyraSurvey2016
  container-title: IEEE Journal of Selected Topics in Signal Processing
  DOI: 10.1109/JSTSP.2015.2496908
  ISSN: 1932-4553
  issue: '2'
  issued:
    - year: 2016
      month: 3
  page: 224-241
  title: >-
    A Survey of Stochastic Simulation and Optimization Methods in Signal
    Processing
  type: article-journal
  URL: http://arxiv.org/abs/1505.00273
  volume: '10'

- id: PhamMethodology2016
  author:
    - family: Pham
      given: Tung
    - family: Panaretos
      given: Victor
  citation-key: PhamMethodology2016
  container-title: arXiv:1612.07197 [math, stat]
  issued:
    - year: 2016
      month: 12
      day: 21
  title: Methodology and Convergence Rates for Functional Time Series Regression
  type: article-journal
  URL: http://arxiv.org/abs/1612.07197

- id: PillonettoInterplay2016
  author:
    - family: Pillonetto
      given: Gianluigi
  citation-key: PillonettoInterplay2016
  container-title: arXiv:1612.09158 [cs, stat]
  issued:
    - year: 2016
      month: 12
      day: 29
  title: The interplay between system identification and machine learning
  type: article-journal
  URL: http://arxiv.org/abs/1612.09158

- id: PlisMesochronal2015
  accessed:
    - year: 2016
      month: 11
      day: 2
  author:
    - family: Plis
      given: Sergey
    - family: Danks
      given: David
    - family: Yang
      given: Jianyu
  citation-key: PlisMesochronal2015
  container-title: >-
    Uncertainty in artificial intelligence : proceedings of the ... conference.
    Conference on Uncertainty in Artificial Intelligence
  container-title-short: Uncertain Artif Intell
  ISSN: 1525-3384
  issued:
    - year: 2015
      month: 7
      day: 12
  PMCID: PMC4827356
  PMID: '27076793'
  title: Mesochronal Structure Learning
  type: article-journal
  URL: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4827356/
  volume: '31'

- id: PoliTorchDyn2020
  accessed:
    - year: 2020
      month: 12
      day: 8
  author:
    - family: Poli
      given: Michael
    - family: Massaroli
      given: Stefano
    - family: Yamashita
      given: Atsushi
    - family: Asama
      given: Hajime
    - family: Park
      given: Jinkyoo
  citation-key: PoliTorchDyn2020
  container-title: arXiv:2009.09346 [cs]
  issued:
    - year: 2020
      month: 9
      day: 19
  title: 'TorchDyn: A Neural Differential Equations Library'
  type: article-journal
  URL: http://arxiv.org/abs/2009.09346

- id: PugachevStochastic2001
  author:
    - family: Pugachev
      given: V. S.
    - family: Sinit︠s︡yn
      given: I. N.
  call-number: QA274.23 .P8513 2001
  citation-key: PugachevStochastic2001
  event-place: River Edge, NJ
  ISBN: 978-981-02-4742-3
  issued:
    - year: 2001
  language: eng
  number-of-pages: '908'
  publisher: World Scientific
  publisher-place: River Edge, NJ
  title: 'Stochastic systems: theory and applications'
  type: book

- id: RackauckasComparison2018
  accessed:
    - year: 2019
      month: 1
      day: 29
  author:
    - family: Rackauckas
      given: Christopher
    - family: Ma
      given: Yingbo
    - family: Dixit
      given: Vaibhav
    - family: Guo
      given: Xingjian
    - family: Innes
      given: Mike
    - family: Revels
      given: Jarrett
    - family: Nyberg
      given: Joakim
    - family: Ivaturi
      given: Vijay
  citation-key: RackauckasComparison2018
  container-title: arXiv:1812.01892 [cs]
  issued:
    - year: 2018
      month: 12
      day: 5
  title: >-
    A Comparison of Automatic Differentiation and Continuous Sensitivity
    Analysis for Derivatives of Differential Equation Solutions
  type: article-journal
  URL: http://arxiv.org/abs/1812.01892

- id: RackauckasEssential2019
  accessed:
    - year: 2019
      month: 8
      day: 27
  author:
    - family: Rackauckas
      given: Christopher
  citation-key: RackauckasEssential2019
  DOI: 10.15200/winn.156631.13064
  issued:
    - year: 2019
      month: 8
      day: 20
  language: en
  title: The Essential Tools of Scientific Machine Learning (Scientific ML)
  type: article
  URL: https://authorea.com/doi/full/10.15200/winn.156631.13064

- id: RackauckasUniversal2020a
  accessed:
    - year: 2023
      month: 11
      day: 15
  author:
    - family: Rackauckas
      given: Christopher
    - family: Ma
      given: Yingbo
    - family: Martensen
      given: Julius
    - family: Warner
      given: Collin
    - family: Zubov
      given: Kirill
    - family: Supekar
      given: Rohit
    - family: Skinner
      given: Dominic
    - family: Ramadhan
      given: Ali
    - family: Edelman
      given: Alan
  citation-key: RackauckasUniversal2020a
  container-title: arXiv.org
  issued:
    - year: 2020
      month: 1
      day: 13
  language: en
  title: Universal Differential Equations for Scientific Machine Learning
  type: article-journal
  URL: https://arxiv.org/abs/2001.04385v4

- id: RobinsonNonparametric1983
  accessed:
    - year: 2015
      month: 5
      day: 12
  author:
    - family: Robinson
      given: P. M.
  citation-key: RobinsonNonparametric1983
  container-title: Journal of Time Series Analysis
  DOI: 10.1111/j.1467-9892.1983.tb00368.x
  ISSN: 1467-9892
  issue: '3'
  issued:
    - year: 1983
      month: 5
      day: 1
  language: en
  page: 185-207
  title: Nonparametric Estimators for Time Series
  type: article-journal
  volume: '4'

- id: RoederEfficient2019
  accessed:
    - year: 2019
      month: 10
      day: 17
  author:
    - family: Roeder
      given: Geoffrey
    - family: Grant
      given: Paul K.
    - family: Phillips
      given: Andrew
    - family: Dalchau
      given: Neil
    - family: Meeds
      given: Edward
  citation-key: RoederEfficient2019
  container-title: arXiv:1905.12090 [cs, stat]
  issued:
    - year: 2019
      month: 5
      day: 28
  title: >-
    Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear
    Dynamical Systems
  type: article-journal
  URL: http://arxiv.org/abs/1905.12090

- id: RouttenbergBlind2010
  accessed:
    - year: 2016
      month: 4
      day: 14
  author:
    - family: Routtenberg
      given: Tirza
    - family: Tabrikian
      given: Joseph
  citation-key: RouttenbergBlind2010
  container-title: IEEE Transactions on Signal Processing
  DOI: 10.1109/TSP.2009.2036043
  ISSN: 1053-587X
  issue: '3'
  issued:
    - year: 2010
      month: 3
  page: 990–1000
  title: >-
    Blind MIMO-AR System Identification and Source Separation with
    Finite-alphabet
  type: article-journal
  volume: '58'

- id: RungeOptimal2015
  accessed:
    - year: 2015
      month: 7
      day: 18
  author:
    - family: Runge
      given: Jakob
    - family: Donner
      given: Reik V.
    - family: Kurths
      given: Jürgen
  citation-key: RungeOptimal2015
  container-title: Physical Review E
  DOI: 10.1103/PhysRevE.91.052909
  ISSN: 1539-3755, 1550-2376
  issue: '5'
  issued:
    - year: 2015
      month: 5
      day: 13
  title: Optimal model-free prediction from multivariate time series
  type: article-journal
  URL: http://arxiv.org/abs/1506.05822
  volume: '91'

- id: RuthottoDeep2020
  accessed:
    - year: 2023
      month: 5
      day: 22
  author:
    - family: Ruthotto
      given: Lars
    - family: Haber
      given: Eldad
  citation-key: RuthottoDeep2020
  container-title: Journal of Mathematical Imaging and Vision
  container-title-short: J Math Imaging Vis
  DOI: 10.1007/s10851-019-00903-1
  ISSN: 1573-7683
  issue: '3'
  issued:
    - year: 2020
      month: 4
      day: 1
  language: en
  page: 352-364
  title: Deep Neural Networks Motivated by Partial Differential Equations
  type: article-journal
  URL: http://arxiv.org/abs/1804.04272
  volume: '62'

- id: SattarNonasymptotic2022
  accessed:
    - year: 2022
      month: 8
      day: 10
  author:
    - family: Sattar
      given: Yahya
    - family: Oymak
      given: Samet
  citation-key: SattarNonasymptotic2022
  container-title: Journal of Machine Learning Research
  ISSN: 1533-7928
  issue: '140'
  issued:
    - year: 2022
  page: 1-49
  title: Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems
  type: article-journal
  URL: http://jmlr.org/papers/v23/20-617.html
  volume: '23'

- id: SchillingsAnalysis2017
  accessed:
    - year: 2022
      month: 8
      day: 23
  author:
    - family: Schillings
      given: Claudia
    - family: Stuart
      given: Andrew M.
  citation-key: SchillingsAnalysis2017
  container-title: SIAM Journal on Numerical Analysis
  container-title-short: SIAM J. Numer. Anal.
  DOI: 10.1137/16M105959X
  ISSN: 0036-1429
  issue: '3'
  issued:
    - year: 2017
      month: 1
      day: 1
  page: 1264–1290
  publisher: Society for Industrial and Applied Mathematics
  title: Analysis of the Ensemble Kalman Filter for Inverse Problems
  type: article-journal
  URL: http://arxiv.org/abs/1602.02020
  volume: '55'

- id: SchirmerModeling2022
  accessed:
    - year: 2023
      month: 3
      day: 1
  author:
    - family: Schirmer
      given: Mona
    - family: Eltayeb
      given: Mazin
    - family: Lessmann
      given: Stefan
    - family: Rudolph
      given: Maja
  citation-key: SchirmerModeling2022
  DOI: 10.48550/arXiv.2111.11344
  issued:
    - year: 2022
      month: 7
      day: 26
  number: arXiv:2111.11344
  publisher: arXiv
  title: Modeling Irregular Time Series with Continuous Recurrent Units
  type: article
  URL: http://arxiv.org/abs/2111.11344

- id: SchmidtProbabilistic2021
  accessed:
    - year: 2022
      month: 2
      day: 14
  author:
    - family: Schmidt
      given: Jonathan
    - family: Krämer
      given: Nicholas
    - family: Hennig
      given: Philipp
  citation-key: SchmidtProbabilistic2021
  container-title: arXiv:2103.10153 [cs, stat]
  issued:
    - year: 2021
      month: 6
      day: 21
  language: en
  title: >-
    A Probabilistic State Space Model for Joint Inference from Differential
    Equations and Data
  type: article-journal
  URL: http://arxiv.org/abs/2103.10153

- id: SchneiderEnsemble2022
  accessed:
    - year: 2022
      month: 10
      day: 12
  author:
    - family: Schneider
      given: Tapio
    - family: Stuart
      given: Andrew M.
    - family: Wu
      given: Jin-Long
  citation-key: SchneiderEnsemble2022
  container-title: Journal of Computational Physics
  container-title-short: Journal of Computational Physics
  DOI: 10.1016/j.jcp.2022.111559
  ISSN: 0021-9991
  issued:
    - year: 2022
      month: 12
      day: 1
  language: en
  page: '111559'
  title: >-
    Ensemble Kalman inversion for sparse learning of dynamical systems from
    time-averaged data
  type: article-journal
  volume: '470'

- id: SjobergNonlinear1995
  accessed:
    - year: 2017
      month: 9
      day: 19
  author:
    - family: Sjöberg
      given: Jonas
    - family: Zhang
      given: Qinghua
    - family: Ljung
      given: Lennart
    - family: Benveniste
      given: Albert
    - family: Delyon
      given: Bernard
    - family: Glorennec
      given: Pierre-Yves
    - family: Hjalmarsson
      given: Håkan
    - family: Juditsky
      given: Anatoli
  citation-key: SjobergNonlinear1995
  collection-title: Trends in System Identification
  container-title: Automatica
  container-title-short: Automatica
  DOI: 10.1016/0005-1098(95)00120-8
  ISSN: 0005-1098
  issue: '12'
  issued:
    - year: 1995
      month: 12
      day: 1
  page: 1691-1724
  title: 'Nonlinear black-box modeling in system identification: a unified overview'
  type: article-journal
  URL: http://www.diva-portal.org/smash/get/diva2:315882/FULLTEXT02.pdf
  volume: '31'

- id: StadlerPenalized2013
  accessed:
    - year: 2014
      month: 10
      day: 16
  author:
    - family: Städler
      given: Nicolas
    - family: Mukherjee
      given: Sach
  citation-key: StadlerPenalized2013
  container-title: The Annals of Applied Statistics
  container-title-short: Ann. Appl. Stat.
  DOI: 10.1214/13-AOAS662
  ISSN: 1932-6157, 1941-7330
  issue: '4'
  issued:
    - year: 2013
      month: 12
  language: EN
  page: 2157-2179
  title: >-
    Penalized estimation in high-dimensional hidden Markov models with
    state-specific graphical models
  type: article-journal
  volume: '7'

- id: StaporOptimization2018
  accessed:
    - year: 2021
      month: 8
      day: 2
  author:
    - family: Stapor
      given: Paul
    - family: Fröhlich
      given: Fabian
    - family: Hasenauer
      given: Jan
  citation-key: StaporOptimization2018
  container-title: bioRxiv
  DOI: 10.1101/272005
  issued:
    - year: 2018
      month: 2
      day: 28
  language: en
  page: '272005'
  publisher: Cold Spring Harbor Laboratory
  section: New Results
  title: >-
    Optimization and uncertainty analysis of ODE models using 2nd order adjoint
    sensitivity analysis
  type: article-journal
  URL: https://www.biorxiv.org/content/10.1101/272005v2

- id: StroudBayesian2018
  accessed:
    - year: 2022
      month: 5
      day: 10
  author:
    - family: Stroud
      given: Jonathan R.
    - family: Katzfuss
      given: Matthias
    - family: Wikle
      given: Christopher K.
  citation-key: StroudBayesian2018
  container-title: Monthly Weather Review
  DOI: 10.1175/MWR-D-16-0427.1
  ISSN: 1520-0493, 0027-0644
  issue: '1'
  issued:
    - year: 2018
      month: 1
      day: 1
  language: EN
  page: 373-386
  publisher: American Meteorological Society
  section: Monthly Weather Review
  title: >-
    A Bayesian Adaptive Ensemble Kalman Filter for Sequential State and
    Parameter Estimation
  type: article-journal
  volume: '146'

- id: StroudEnsemble2010
  accessed:
    - year: 2022
      month: 7
      day: 22
  author:
    - family: Stroud
      given: Jonathan R.
    - family: Stein
      given: Michael L.
    - family: Lesht
      given: Barry M.
    - family: Schwab
      given: David J.
    - family: Beletsky
      given: Dmitry
  citation-key: StroudEnsemble2010
  container-title: Journal of the American Statistical Association
  DOI: 10.1198/jasa.2010.ap07636
  ISSN: 0162-1459
  issue: '491'
  issued:
    - year: 2010
      month: 9
      day: 1
  page: 978-990
  publisher: Taylor & Francis
  title: An Ensemble Kalman Filter and Smoother for Satellite Data Assimilation
  type: article-journal
  URL: http://jrs390.georgetown.domains/papers/dynamic-image.pdf
  volume: '105'

- id: TakamotoPDEBench2022
  accessed:
    - year: 2022
      month: 8
      day: 4
  author:
    - family: Takamoto
      given: Makoto
    - family: Praditia
      given: Timothy
    - family: Leiteritz
      given: Raphael
    - family: MacKinlay
      given: Dan
    - family: Alesiani
      given: Francesco
    - family: Pflüger
      given: Dirk
    - family: Niepert
      given: Mathias
  citation-key: TakamotoPDEBench2022
  issued:
    - year: 2022
      month: 6
      day: 16
  language: en
  title: 'PDEBench: An Extensive Benchmark for Scientific Machine Learning'
  type: paper-conference
  URL: https://openreview.net/forum?id=dh_MkX0QfrK

- id: TallecUnbiasing2017
  accessed:
    - year: 2023
      month: 4
      day: 16
  author:
    - family: Tallec
      given: Corentin
    - family: Ollivier
      given: Yann
  citation-key: TallecUnbiasing2017
  DOI: 10.48550/arXiv.1705.08209
  issued:
    - year: 2017
      month: 5
      day: 23
  number: arXiv:1705.08209
  publisher: arXiv
  title: Unbiasing Truncated Backpropagation Through Time
  type: article
  URL: http://arxiv.org/abs/1705.08209

- id: TaniguchiAsymptotic2000
  author:
    - family: Taniguchi
      given: Masanobu
    - family: Kakizawa
      given: Yoshihide
  call-number: QA280 .T355 2000
  citation-key: TaniguchiAsymptotic2000
  collection-title: Springer series in statistics
  event-place: New York
  ISBN: 978-0-387-95039-6
  issued:
    - year: 2000
  number-of-pages: '661'
  publisher: Springer
  publisher-place: New York
  title: Asymptotic theory of statistical inference for time series
  type: book

- id: TanizakiEstimation2001
  accessed:
    - year: 2016
      month: 3
      day: 29
  author:
    - family: Tanizaki
      given: Hisashi
  citation-key: TanizakiEstimation2001
  container-title: Journal of Statistical Planning and Inference
  container-title-short: Journal of Statistical Planning and Inference
  DOI: 10.1016/S0378-3758(00)00218-4
  ISSN: 0378-3758
  issue: '2'
  issued:
    - year: 2001
      month: 7
      day: 1
  page: 301-323
  title: >-
    Estimation of unknown parameters in nonlinear and non-Gaussian state-space
    models
  type: article-journal
  URL: http://stat.econ.osaka-u.ac.jp/cv/papers/mle.pdf
  volume: '96'

- id: TzenNeural2019
  accessed:
    - year: 2024
      month: 3
      day: 15
  author:
    - family: Tzen
      given: Belinda
    - family: Raginsky
      given: Maxim
  citation-key: TzenNeural2019
  DOI: 10.48550/arXiv.1905.09883
  issued:
    - year: 2019
      month: 10
      day: 27
  number: arXiv:1905.09883
  publisher: arXiv
  title: >-
    Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the
    Diffusion Limit
  type: article
  URL: http://arxiv.org/abs/1905.09883

- id: UnserIntroduction2014
  author:
    - family: Unser
      given: Michael A.
    - family: Tafti
      given: Pouya
  call-number: QA274.23 .U57 2014
  citation-key: UnserIntroduction2014
  event-place: New York
  ISBN: 978-1-107-05854-5
  issued:
    - year: 2014
  number-of-pages: '387'
  publisher: Cambridge University Press
  publisher-place: New York
  title: An introduction to sparse stochastic processes
  type: book
  URL: http://www.sparseprocesses.org/sparseprocesses-123456.pdf

- id: UzielNonparametric2020
  accessed:
    - year: 2020
      month: 8
      day: 23
  author:
    - family: Uziel
      given: Guy
  citation-key: UzielNonparametric2020
  container-title: International Conference on Artificial Intelligence and Statistics
  event-title: International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
    - year: 2020
      month: 6
      day: 3
  language: en
  page: 111-121
  publisher: PMLR
  title: Nonparametric Sequential Prediction While Deep Learning the Kernel
  type: paper-conference
  URL: http://proceedings.mlr.press/v108/uziel20b.html

- id: VardasbiState2023
  accessed:
    - year: 2023
      month: 5
      day: 22
  author:
    - family: Vardasbi
      given: Ali
    - family: Pires
      given: Telmo Pessoa
    - family: Schmidt
      given: Robin M.
    - family: Peitz
      given: Stephan
  citation-key: VardasbiState2023
  DOI: 10.48550/arXiv.2304.12776
  issued:
    - year: 2023
      month: 4
      day: 25
  number: arXiv:2304.12776
  publisher: arXiv
  title: 'State Spaces Aren''t Enough: Machine Translation Needs Attention'
  type: article
  URL: http://arxiv.org/abs/2304.12776

- id: WedigCritical1984
  accessed:
    - year: 2021
      month: 5
      day: 10
  author:
    - family: Wedig
      given: W.
  citation-key: WedigCritical1984
  container-title: Nuclear Engineering and Design
  container-title-short: Nuclear Engineering and Design
  DOI: 10.1016/0029-5493(84)90043-8
  ISSN: 0029-5493
  issue: '3'
  issued:
    - year: 1984
      month: 6
      day: 1
  language: en
  page: 281-287
  title: A critical review of methods in stochastic structural dynamics
  type: article-journal
  volume: '79'

- id: WenMultiHorizon2017
  accessed:
    - year: 2018
      month: 1
      day: 13
  author:
    - family: Wen
      given: Ruofeng
    - family: Torkkola
      given: Kari
    - family: Narayanaswamy
      given: Balakrishnan
  citation-key: WenMultiHorizon2017
  container-title: arXiv:1711.11053 [stat]
  issued:
    - year: 2017
      month: 11
      day: 29
  title: A Multi-Horizon Quantile Recurrent Forecaster
  type: article-journal
  URL: http://arxiv.org/abs/1711.11053

- id: WerbosGeneralization1988
  accessed:
    - year: 2017
      month: 9
      day: 19
  author:
    - family: Werbos
      given: Paul J.
  citation-key: WerbosGeneralization1988
  container-title: Neural Networks
  container-title-short: Neural Networks
  DOI: 10.1016/0893-6080(88)90007-X
  ISSN: 0893-6080
  issue: '4'
  issued:
    - year: 1988
      month: 1
      day: 1
  page: 339-356
  title: >-
    Generalization of backpropagation with application to a recurrent gas market
    model
  type: article-journal
  volume: '1'

- id: WilliamsLearning1989
  accessed:
    - year: 2018
      month: 1
      day: 13
  author:
    - family: Williams
      given: Ronald J.
    - family: Zipser
      given: David
  citation-key: WilliamsLearning1989
  container-title: Neural Computation
  container-title-short: Neural Computation
  DOI: 10.1162/neco.1989.1.2.270
  ISSN: 0899-7667
  issue: '2'
  issued:
    - year: 1989
      month: 6
      day: 1
  page: 270-280
  title: A Learning Algorithm for Continually Running Fully Recurrent Neural Networks
  type: article-journal
  URL: >-
    https://pdfs.semanticscholar.org/8adb/8257a423f55b1f20ba62c8b20118d76a25c7.pdf
  volume: '1'

- id: YangSequential2018
  accessed:
    - year: 2022
      month: 7
      day: 22
  author:
    - family: Yang
      given: Biao
    - family: Stroud
      given: Jonathan R.
    - family: Huerta
      given: Gabriel
  citation-key: YangSequential2018
  container-title: Bayesian Analysis
  DOI: 10.1214/17-BA1088
  ISSN: 1936-0975, 1931-6690
  issue: '4'
  issued:
    - year: 2018
      month: 12
  page: 1137-1161
  publisher: International Society for Bayesian Analysis
  title: Sequential Monte Carlo Smoothing with Parameter Estimation
  type: article-journal
  volume: '13'

- id: ZammitMangionDeep2020
  accessed:
    - year: 2020
      month: 8
      day: 13
  author:
    - family: Zammit-Mangion
      given: Andrew
    - family: Wikle
      given: Christopher K.
  citation-key: ZammitMangionDeep2020
  container-title: Spatial Statistics
  container-title-short: Spatial Statistics
  DOI: 10.1016/j.spasta.2020.100408
  ISSN: '22116753'
  issued:
    - year: 2020
      month: 6
  page: '100408'
  title: Deep Integro-Difference Equation Models for Spatio-Temporal Forecasting
  type: article-journal
  URL: http://arxiv.org/abs/1910.13524
  volume: '37'

- id: ZhangApproximation2020
  accessed:
    - year: 2020
      month: 12
      day: 7
  author:
    - family: Zhang
      given: Han
    - family: Gao
      given: Xi
    - family: Unterman
      given: Jacob
    - family: Arodz
      given: Tom
  citation-key: ZhangApproximation2020
  container-title: arXiv:1907.12998 [cs, stat]
  issued:
    - year: 2020
      month: 2
      day: 29
  title: Approximation Capabilities of Neural ODEs and Invertible Residual Networks
  type: article-journal
  URL: http://arxiv.org/abs/1907.12998

- id: ZhangIterative2018
  accessed:
    - year: 2022
      month: 5
      day: 10
  author:
    - family: Zhang
      given: Jiangjiang
    - family: Lin
      given: Guang
    - family: Li
      given: Weixuan
    - family: Wu
      given: Laosheng
    - family: Zeng
      given: Lingzao
  citation-key: ZhangIterative2018
  container-title: Water Resources Research
  container-title-short: Water Resour. Res.
  DOI: 10.1002/2017WR020906
  ISSN: 0043-1397, 1944-7973
  issue: '3'
  issued:
    - year: 2018
      month: 3
  language: en
  page: 1716-1733
  title: >-
    An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty
    Assessment of Hydrologic Model Parameters With Multimodal Distributions
  type: article-journal
  URL: http://arxiv.org/abs/1611.04702
  volume: '54'

- id: ZhaoTensorbased2023
  accessed:
    - year: 2023
      month: 2
      day: 21
  author:
    - family: Zhao
      given: Yiran
    - family: Cui
      given: Tiangang
  citation-key: ZhaoTensorbased2023
  DOI: 10.48550/arXiv.2301.09891
  issued:
    - year: 2023
      month: 1
      day: 24
  number: arXiv:2301.09891
  publisher: arXiv
  title: >-
    Tensor-based Methods for Sequential State and Parameter Estimation in State
    Space Models
  type: article
  URL: http://arxiv.org/abs/2301.09891
...
