---
references:
- 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: AnilSorting2018
  accessed:
    - year: 2019
      month: 1
      day: 22
  author:
    - family: Anil
      given: Cem
    - family: Lucas
      given: James
    - family: Grosse
      given: Roger
  citation-key: AnilSorting2018
  issued:
    - year: 2018
      month: 11
      day: 13
  language: en
  title: Sorting out Lipschitz function approximation
  type: article-journal
  URL: https://arxiv.org/abs/1811.05381v1

- 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: BabtieTopological2014
  accessed:
    - year: 2019
      month: 1
      day: 30
  author:
    - family: Babtie
      given: Ann C.
    - family: Kirk
      given: Paul
    - family: Stumpf
      given: Michael P. H.
  citation-key: BabtieTopological2014
  container-title: Proceedings of the National Academy of Sciences
  container-title-short: PNAS
  DOI: 10.1073/pnas.1414026112
  ISSN: 0027-8424, 1091-6490
  issue: '52'
  issued:
    - year: 2014
      month: 12
      day: 30
  language: en
  page: 18507-18512
  PMID: '25512544'
  title: Topological sensitivity analysis for systems biology
  type: article-journal
  volume: '111'

- id: BachouchDeep2020
  accessed:
    - year: 2020
      month: 10
      day: 12
  author:
    - family: Bachouch
      given: Achref
    - family: Huré
      given: Côme
    - family: Langrené
      given: Nicolas
    - family: Pham
      given: Huyen
  citation-key: BachouchDeep2020
  container-title: arXiv:1812.05916 [math, q-fin, stat]
  issued:
    - year: 2020
      month: 1
      day: 27
  title: >-
    Deep neural networks algorithms for stochastic control problems on finite
    horizon: numerical applications
  type: article-journal
  URL: http://arxiv.org/abs/1812.05916

- id: BruntonKoopman2016
  accessed:
    - year: 2023
      month: 6
      day: 29
  author:
    - family: Brunton
      given: Steven L.
    - family: Brunton
      given: Bingni W.
    - family: Proctor
      given: Joshua L.
    - family: Kutz
      given: J. Nathan
  citation-key: BruntonKoopman2016
  container-title: PLOS ONE
  container-title-short: PLOS ONE
  DOI: 10.1371/journal.pone.0150171
  ISSN: 1932-6203
  issue: '2'
  issued:
    - year: 2016
      month: 2
      day: 26
  language: en
  page: e0150171
  publisher: Public Library of Science
  title: >-
    Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear
    Dynamical Systems for Control
  type: article-journal
  URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0150171
  volume: '11'

- 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: ChangAntisymmetricRNN2019
  accessed:
    - year: 2019
      month: 3
      day: 20
  author:
    - family: Chang
      given: Bo
    - family: Chen
      given: Minmin
    - family: Haber
      given: Eldad
    - family: Chi
      given: Ed H.
  citation-key: ChangAntisymmetricRNN2019
  container-title: Proceedings of ICLR
  event-title: Seventh International Conference on Learning Representations
  issued:
    - year: 2019
      month: 2
      day: 25
  title: 'AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks'
  type: paper-conference
  URL: http://arxiv.org/abs/1902.09689

- id: ChangMultilevel2018
  accessed:
    - year: 2018
      month: 4
      day: 23
  author:
    - family: Chang
      given: Bo
    - family: Meng
      given: Lili
    - family: Haber
      given: Eldad
    - family: Tung
      given: Frederick
    - family: Begert
      given: David
  citation-key: ChangMultilevel2018
  container-title: PRoceedings of ICLR
  event-title: ICLR
  issued:
    - year: 2018
  title: Multi-level Residual Networks from Dynamical Systems View
  type: paper-conference
  URL: http://arxiv.org/abs/1710.10348

- id: ChenAutomated2022
  accessed:
    - year: 2022
      month: 8
      day: 27
  author:
    - family: Chen
      given: Boyuan
    - family: Huang
      given: Kuang
    - family: Raghupathi
      given: Sunand
    - family: Chandratreya
      given: Ishaan
    - family: Du
      given: Qiang
    - family: Lipson
      given: Hod
  citation-key: ChenAutomated2022
  container-title: Nature Computational Science
  container-title-short: Nat Comput Sci
  DOI: 10.1038/s43588-022-00281-6
  ISSN: 2662-8457
  issue: '7'
  issued:
    - year: 2022
      month: 7
  language: en
  number: '7'
  page: 433-442
  publisher: Nature Publishing Group
  title: Automated discovery of fundamental variables hidden in experimental data
  type: article-journal
  URL: http://arxiv.org/abs/2112.10755
  volume: '2'

- 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: 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: 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: DupontAugmented2019
  accessed:
    - year: 2019
      month: 10
      day: 2
  author:
    - family: Dupont
      given: Emilien
    - family: Doucet
      given: Arnaud
    - family: Teh
      given: Yee Whye
  citation-key: DupontAugmented2019
  container-title: arXiv:1904.01681 [cs, stat]
  issued:
    - year: 2019
      month: 4
      day: 2
  language: en
  title: Augmented Neural ODEs
  type: article-journal
  URL: http://arxiv.org/abs/1904.01681

- id: EDawning2021
  accessed:
    - year: 2023
      month: 1
      day: 9
  author:
    - family: E
      given: Weinan
  citation-key: EDawning2021
  container-title: Notices of the American Mathematical Society
  container-title-short: Notices Amer. Math. Soc.
  DOI: 10.1090/noti2259
  ISSN: 0002-9920, 1088-9477
  issue: '04'
  issued:
    - year: 2021
      month: 4
      day: 1
  language: en
  page: '1'
  title: The Dawning of a New Era in Applied Mathematics
  type: article-journal
  URL: https://www.ams.org/notices/202104/rnoti-p565.pdf
  volume: '68'

- id: EguchiSchwartztype
  accessed:
    - year: 2020
      month: 12
      day: 12
  author:
    - family: Eguchi
      given: Shoichi
    - family: Uehara
      given: Yuma
  citation-key: EguchiSchwartztype
  container-title: Scandinavian Journal of Statistics
  DOI: 10.1111/sjos.12474
  ISSN: 1467-9469
  issue: n/a
  language: en
  title: >-
    Schwartz-type model selection for ergodic stochastic differential equation
    models
  type: article-journal
  volume: n/a

- 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: EProposal2017
  accessed:
    - year: 2019
      month: 1
      day: 29
  author:
    - family: E
      given: Weinan
  citation-key: EProposal2017
  container-title: Communications in Mathematics and Statistics
  container-title-short: Commun. Math. Stat.
  DOI: 10.1007/s40304-017-0103-z
  ISSN: 2194-671X
  issue: '1'
  issued:
    - year: 2017
      month: 3
      day: 1
  language: en
  page: 1-11
  title: A Proposal on Machine Learning via Dynamical Systems
  type: article-journal
  volume: '5'

- 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: GarneloConditional2018
  accessed:
    - year: 2019
      month: 9
      day: 23
  author:
    - family: Garnelo
      given: Marta
    - family: Rosenbaum
      given: Dan
    - family: Maddison
      given: Chris J.
    - family: Ramalho
      given: Tiago
    - family: Saxton
      given: David
    - family: Shanahan
      given: Murray
    - family: Teh
      given: Yee Whye
    - family: Rezende
      given: Danilo J.
    - family: Eslami
      given: S. M. Ali
  citation-key: GarneloConditional2018
  container-title: arXiv:1807.01613 [cs, stat]
  issued:
    - year: 2018
      month: 7
      day: 4
  language: en
  page: '10'
  title: Conditional Neural Processes
  type: article-journal
  URL: https://arxiv.org/abs/1807.01613v1

- id: GarneloNeural2018
  accessed:
    - year: 2019
      month: 9
      day: 23
  author:
    - family: Garnelo
      given: Marta
    - family: Schwarz
      given: Jonathan
    - family: Rosenbaum
      given: Dan
    - family: Viola
      given: Fabio
    - family: Rezende
      given: Danilo J.
    - family: Eslami
      given: S. M. Ali
    - family: Teh
      given: Yee Whye
  citation-key: GarneloNeural2018
  issued:
    - year: 2018
      month: 7
      day: 4
  language: en
  title: Neural Processes
  type: article-journal
  URL: https://arxiv.org/abs/1807.01622v1

- 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: GierjatowiczRobust2020
  accessed:
    - year: 2020
      month: 10
      day: 5
  author:
    - family: Gierjatowicz
      given: Patryk
    - family: Sabate-Vidales
      given: Marc
    - family: Šiška
      given: David
    - family: Szpruch
      given: Lukasz
    - family: Žurič
      given: Žan
  citation-key: GierjatowiczRobust2020
  container-title: arXiv:2007.04154 [cs, q-fin, stat]
  issued:
    - year: 2020
      month: 7
      day: 8
  title: Robust pricing and hedging via neural SDEs
  type: article-journal
  URL: http://arxiv.org/abs/2007.04154

- id: GilpinModel2023
  accessed:
    - year: 2024
      month: 1
      day: 15
  author:
    - family: Gilpin
      given: William
  citation-key: GilpinModel2023
  container-title: Physical Review Research
  container-title-short: Phys. Rev. Res.
  DOI: 10.1103/PhysRevResearch.5.043252
  issue: '4'
  issued:
    - year: 2023
      month: 12
      day: 15
  page: '043252'
  publisher: American Physical Society
  title: >-
    Model scale versus domain knowledge in statistical forecasting of chaotic
    systems
  type: article-journal
  volume: '5'

- 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: GuEfficiently2021
  accessed:
    - year: 2023
      month: 5
      day: 22
  author:
    - family: Gu
      given: Albert
    - family: Goel
      given: Karan
    - family: Ré
      given: Christopher
  citation-key: GuEfficiently2021
  issued:
    - year: 2021
      month: 10
      day: 31
  language: en
  title: Efficiently Modeling Long Sequences with Structured State Spaces
  type: article
  URL: https://arxiv.org/abs/2111.00396v3

- 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: HanSolving2018
  accessed:
    - year: 2019
      month: 8
      day: 27
  author:
    - family: Han
      given: Jiequn
    - family: Jentzen
      given: Arnulf
    - family: E
      given: Weinan
  citation-key: HanSolving2018
  container-title: Proceedings of the National Academy of Sciences
  container-title-short: PNAS
  DOI: 10.1073/pnas.1718942115
  ISSN: 0027-8424, 1091-6490
  issue: '34'
  issued:
    - year: 2018
      month: 8
      day: 21
  language: en
  page: 8505-8510
  PMCID: PMC6112690
  PMID: '30082389'
  publisher: National Academy of Sciences
  section: Physical Sciences
  title: Solving high-dimensional partial differential equations using deep learning
  type: article-journal
  volume: '115'

- id: HaroAutomatic2008
  author:
    - family: Haro
      given: A.
  citation-key: HaroAutomatic2008
  container-title: IMA Note
  issued:
    - year: 2008
  title: >-
    Automatic differentiation methods in computational dynamical systems:
    Invariant manifolds and normal forms of vector fields at fixed points
  type: article-journal
  URL: http://www.maia.ub.es/~alex/admcds/admcds.pdf

- id: HasaniClosedform2022
  accessed:
    - year: 2022
      month: 11
      day: 27
  author:
    - family: Hasani
      given: Ramin
    - family: Lechner
      given: Mathias
    - family: Amini
      given: Alexander
    - family: Liebenwein
      given: Lucas
    - family: Ray
      given: Aaron
    - family: Tschaikowski
      given: Max
    - family: Teschl
      given: Gerald
    - family: Rus
      given: Daniela
  citation-key: HasaniClosedform2022
  container-title: Nature Machine Intelligence
  container-title-short: Nat Mach Intell
  DOI: 10.1038/s42256-022-00556-7
  ISSN: 2522-5839
  issue: '11'
  issued:
    - year: 2022
      month: 11
  language: en
  number: '11'
  page: 992-1003
  publisher: Nature Publishing Group
  title: Closed-form continuous-time neural networks
  type: article-journal
  volume: '4'

- id: HasaniLiquid2020
  accessed:
    - year: 2022
      month: 1
      day: 28
  author:
    - family: Hasani
      given: Ramin
    - family: Lechner
      given: Mathias
    - family: Amini
      given: Alexander
    - family: Rus
      given: Daniela
    - family: Grosu
      given: Radu
  citation-key: HasaniLiquid2020
  container-title: arXiv:2006.04439 [cs, stat]
  issued:
    - year: 2020
      month: 12
      day: 14
  title: Liquid Time-constant Networks
  type: article-journal
  URL: http://arxiv.org/abs/2006.04439

- id: HeLagging2019
  accessed:
    - year: 2019
      month: 1
      day: 22
  author:
    - family: He
      given: Junxian
    - family: Spokoyny
      given: Daniel
    - family: Neubig
      given: Graham
    - family: Berg-Kirkpatrick
      given: Taylor
  citation-key: HeLagging2019
  container-title: PRoceedings of ICLR
  event-title: Internation Conference on Learning Representations
  issued:
    - year: 2019
      month: 1
      day: 16
  title: >-
    Lagging Inference Networks and Posterior Collapse in Variational
    Autoencoders
  type: paper-conference
  URL: http://arxiv.org/abs/1901.05534

- 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: HuhTimeReversal2020
  accessed:
    - year: 2020
      month: 12
      day: 14
  author:
    - family: Huh
      given: In
    - family: Yang
      given: Eunho
    - family: Hwang
      given: Sung Ju
    - family: Shin
      given: Jinwoo
  citation-key: HuhTimeReversal2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: Time-Reversal Symmetric ODE Network
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper_files/paper/2020/hash/db8419f41d890df802dca330e6284952-Abstract.html
  volume: '33'

- id: HureDeep2018
  accessed:
    - year: 2020
      month: 10
      day: 12
  author:
    - family: Huré
      given: Côme
    - family: Pham
      given: Huyên
    - family: Bachouch
      given: Achref
    - family: Langrené
      given: Nicolas
  citation-key: HureDeep2018
  container-title: arXiv:1812.04300 [math, stat]
  issued:
    - year: 2018
      month: 12
      day: 11
  title: >-
    Deep neural networks algorithms for stochastic control problems on finite
    horizon, part I: convergence analysis
  type: article-journal
  URL: http://arxiv.org/abs/1812.04300

- 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: KaulLinear2020
  accessed:
    - year: 2020
      month: 12
      day: 13
  author:
    - family: Kaul
      given: Shiva
  citation-key: KaulLinear2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: Linear Dynamical Systems as a Core Computational Primitive
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper_files/paper/2020/hash/c3581d2150ff68f3b33b22634b8adaea-Abstract.html
  volume: '33'

- 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: 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: KidgerNeural2021
  accessed:
    - year: 2023
      month: 4
      day: 13
  author:
    - family: Kidger
      given: Patrick
    - family: Foster
      given: James
    - family: Li
      given: Xuechen
    - family: Lyons
      given: Terry J.
  citation-key: KidgerNeural2021
  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: 5453-5463
  publisher: PMLR
  title: Neural SDEs as Infinite-Dimensional GANs
  type: paper-conference
  URL: causl

- id: KidgerNeural2022
  accessed:
    - year: 2022
      month: 12
      day: 5
  author:
    - family: Kidger
      given: Patrick
  citation-key: KidgerNeural2022
  issued:
    - year: 2022
      month: 2
      day: 4
  publisher: Oxford
  title: On Neural Differential Equations
  type: thesis
  URL: http://arxiv.org/abs/2202.02435

- id: KochkovLearning2020
  author:
    - family: Kochkov
      given: Dmitrii
    - family: Sanchez-Gonzalez
      given: Alvaro
    - family: Smith
      given: Jamie
    - family: Pfaff
      given: Tobias
    - family: Battaglia
      given: Peter
    - family: Brenner
      given: Michael P
  citation-key: KochkovLearning2020
  container-title: >-
    Machine Learning and the Physical Sciences  Workshop at the 33rd Conference
    on Neural Information Processing Systems (NeurIPS)
  issued:
    - year: 2020
  language: en
  page: '7'
  title: Learning latent ﬁeld dynamics of PDEs
  type: paper-conference

- id: KolterLearning2019
  author:
    - family: Kolter
      given: J Zico
    - family: Manek
      given: Gaurav
  citation-key: KolterLearning2019
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2019
  language: en
  page: '9'
  title: Learning Stable Deep Dynamics Models
  type: paper-conference
  URL: http://arxiv.org/abs/2001.06116

- 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: LaurentRecurrent2016
  author:
    - family: Laurent
      given: Thomas
    - family: Brecht
      given: James
      non-dropping-particle: von
  citation-key: LaurentRecurrent2016
  container-title: arXiv:1612.06212 [cs]
  issued:
    - year: 2016
      month: 12
      day: 19
  title: A recurrent neural network without chaos
  type: article-journal
  URL: http://arxiv.org/abs/1612.06212

- id: LawrenceAlmost2020
  accessed:
    - year: 2020
      month: 12
      day: 13
  author:
    - family: Lawrence
      given: Nathan
    - family: Loewen
      given: Philip
    - family: Forbes
      given: Michael
    - family: Backstrom
      given: Johan
    - family: Gopaluni
      given: Bhushan
  citation-key: LawrenceAlmost2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: Almost Surely Stable Deep Dynamics
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper_files/paper/2020/hash/daecf755df5b1d637033bb29b319c39a-Abstract.html
  volume: '33'

- 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: LiWhat2022
  accessed:
    - year: 2022
      month: 11
      day: 14
  author:
    - family: Li
      given: Yuhong
    - family: Cai
      given: Tianle
    - family: Zhang
      given: Yi
    - family: Chen
      given: Deming
    - family: Dey
      given: Debadeepta
  citation-key: LiWhat2022
  DOI: 10.48550/arXiv.2210.09298
  issued:
    - year: 2022
      month: 10
      day: 17
  number: arXiv:2210.09298
  publisher: arXiv
  title: What Makes Convolutional Models Great on Long Sequence Modeling?
  type: article
  URL: http://arxiv.org/abs/2210.09298

- id: LouizosFunctional2019
  accessed:
    - year: 2023
      month: 5
      day: 25
  author:
    - family: Louizos
      given: Christos
    - family: Shi
      given: Xiahan
    - family: Schutte
      given: Klamer
    - family: Welling
      given: Max
  citation-key: LouizosFunctional2019
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2019
  publisher: Curran Associates, Inc.
  title: The Functional Neural Process
  type: paper-conference
  URL: http://arxiv.org/abs/1906.08324
  volume: '32'

- 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: LuDeepONet2020
  accessed:
    - year: 2020
      month: 9
      day: 15
  author:
    - family: Lu
      given: Lu
    - family: Jin
      given: Pengzhan
    - family: Karniadakis
      given: George Em
  citation-key: LuDeepONet2020
  container-title: arXiv:1910.03193 [cs, stat]
  issued:
    - year: 2020
      month: 4
      day: 14
  title: >-
    DeepONet: Learning nonlinear operators for identifying differential
    equations based on the universal approximation theorem of operators
  type: article-journal
  URL: http://arxiv.org/abs/1910.03193

- id: LuschDeep2018
  accessed:
    - year: 2021
      month: 4
      day: 9
  author:
    - family: Lusch
      given: Bethany
    - family: Kutz
      given: J. Nathan
    - family: Brunton
      given: Steven L.
  citation-key: LuschDeep2018
  container-title: Nature Communications
  DOI: 10.1038/s41467-018-07210-0
  ISSN: 2041-1723
  issue: '1'
  issued:
    - year: 2018
      month: 11
      day: 23
  language: en
  number: '1'
  page: '4950'
  publisher: Nature Publishing Group
  title: Deep learning for universal linear embeddings of nonlinear dynamics
  type: article-journal
  volume: '9'

- id: LuUniversal2020
  accessed:
    - year: 2020
      month: 12
      day: 10
  author:
    - family: Lu
      given: Yulong
    - family: Lu
      given: Jianfeng
  citation-key: LuUniversal2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: >-
    A Universal Approximation Theorem of Deep Neural Networks for Expressing
    Probability Distributions
  type: paper-conference
  URL: >-
    https://papers.nips.cc/paper/2020/hash/2000f6325dfc4fc3201fc45ed01c7a5d-Abstract.html
  volume: '33'

- 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: MassaroliStable2020
  accessed:
    - year: 2020
      month: 12
      day: 8
  author:
    - family: Massaroli
      given: Stefano
    - family: Poli
      given: Michael
    - family: Bin
      given: Michelangelo
    - family: Park
      given: Jinkyoo
    - family: Yamashita
      given: Atsushi
    - family: Asama
      given: Hajime
  citation-key: MassaroliStable2020
  container-title: arXiv:2003.08063 [cs, math, stat]
  issued:
    - year: 2020
      month: 3
      day: 18
  title: Stable Neural Flows
  type: article-journal
  URL: http://arxiv.org/abs/2003.08063

- id: MhammediEfficient2017
  author:
    - family: Mhammedi
      given: Zakaria
    - family: Hellicar
      given: Andrew
    - family: Rahman
      given: Ashfaqur
    - family: Bailey
      given: James
  citation-key: MhammediEfficient2017
  container-title: PMLR
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  language: en
  page: 2401-2409
  title: >-
    Efficient Orthogonal Parametrisation of Recurrent Neural Networks Using
    Householder Reflections
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/mhammedi17a.html

- id: MishlerFADE2021
  accessed:
    - year: 2021
      month: 10
      day: 26
  author:
    - family: Mishler
      given: Alan
    - family: Kennedy
      given: Edward
  citation-key: MishlerFADE2021
  container-title: arXiv:2109.00173 [cs, stat]
  issued:
    - year: 2021
      month: 8
      day: 31
  title: >-
    FADE: FAir Double Ensemble Learning for Observable and Counterfactual
    Outcomes
  type: article-journal
  URL: http://arxiv.org/abs/2109.00173

- 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: 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: NiuRecurrent2019
  accessed:
    - year: 2019
      month: 6
      day: 3
  author:
    - family: Niu
      given: Murphy Yuezhen
    - family: Horesh
      given: Lior
    - family: Chuang
      given: Isaac
  citation-key: NiuRecurrent2019
  container-title: arXiv:1904.12933 [quant-ph, stat]
  issued:
    - year: 2019
      month: 4
      day: 29
  title: Recurrent Neural Networks in the Eye of Differential Equations
  type: article-journal
  URL: http://arxiv.org/abs/1904.12933

- id: NorcliffeNeural2020
  accessed:
    - year: 2020
      month: 12
      day: 13
  author:
    - family: Norcliffe
      given: Alexander
    - family: Bodnar
      given: Cristian
    - family: Day
      given: Ben
    - family: Moss
      given: Jacob
    - family: Liò
      given: Pietro
  citation-key: NorcliffeNeural2020
  issued:
    - year: 2020
  title: Neural ODE Processes
  type: paper-conference
  URL: https://ml4physicalsciences.github.io/2020/files/NeurIPS_ML4PS_2020_66.pdf

- id: OreshkinNBEATS2020
  accessed:
    - year: 2021
      month: 6
      day: 18
  author:
    - family: Oreshkin
      given: Boris N.
    - family: Carpov
      given: Dmitri
    - family: Chapados
      given: Nicolas
    - family: Bengio
      given: Yoshua
  citation-key: OreshkinNBEATS2020
  container-title: arXiv:1905.10437 [cs, stat]
  issued:
    - year: 2020
      month: 2
      day: 20
  title: >-
    N-BEATS: Neural basis expansion analysis for interpretable time series
    forecasting
  type: article-journal
  URL: http://arxiv.org/abs/1905.10437

- id: OttResNet2020
  accessed:
    - year: 2023
      month: 10
      day: 11
  author:
    - family: Ott
      given: Katharina
    - family: Katiyar
      given: Prateek
    - family: Hennig
      given: Philipp
    - family: Tiemann
      given: Michael
  citation-key: OttResNet2020
  event-title: International Conference on Learning Representations
  issued:
    - year: 2020
      month: 10
      day: 2
  language: en
  title: 'ResNet After All: Neural ODEs and Their Numerical Solution'
  type: paper-conference
  URL: https://openreview.net/forum?id=HxzSxSxLOJZ

- id: PalisVector1974
  accessed:
    - year: 2020
      month: 12
      day: 7
  author:
    - family: Palis
      given: J.
  citation-key: PalisVector1974
  container-title: Bulletin of the American Mathematical Society
  container-title-short: Bull. Amer. Math. Soc.
  ISSN: 0002-9904, 1936-881X
  issue: '3'
  issued:
    - year: 1974
      month: 5
  language: EN
  page: 503-505
  publisher: American Mathematical Society
  title: Vector fields generate few diffeomorphisms
  type: article-journal
  URL: https://projecteuclid.org/euclid.bams/1183535529
  volume: '80'

- id: PeluchettiInfinitely2020
  accessed:
    - year: 2020
      month: 8
      day: 23
  author:
    - family: Peluchetti
      given: Stefano
    - family: Favaro
      given: Stefano
  citation-key: PeluchettiInfinitely2020
  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: 1126-1136
  publisher: PMLR
  title: Infinitely deep neural networks as diffusion processes
  type: paper-conference
  URL: http://proceedings.mlr.press/v108/peluchetti20a.html

- id: PeluchettiNeural2019
  author:
    - family: Peluchetti
      given: Stefano
    - family: Favaro
      given: Stefano
  citation-key: PeluchettiNeural2019
  container-title: Workshop on Bayesian Deep LEarning
  event-title: NeurIPS 2019
  issued:
    - year: 2019
  language: en
  page: '7'
  title: Neural SDE - Information propagation through the lens of diffusion processes
  type: paper-conference

- id: PfauIntegrable2020
  author:
    - family: Pfau
      given: David
    - family: Rezende
      given: Danilo
  citation-key: PfauIntegrable2020
  issued:
    - year: 2020
  language: en
  page: '7'
  title: Integrable Nonparametric Flows
  type: paper-conference

- id: PoliHypersolvers2020
  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: PoliHypersolvers2020
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2020
  language: en
  title: 'Hypersolvers: Toward Fast Continuous-Depth Models'
  type: paper-conference
  URL: >-
    https://proceedings.neurips.cc//paper/2020/hash/f1686b4badcf28d33ed632036c7ab0b8-Abstract.html
  volume: '33'

- 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: 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: RayDeep2023
  accessed:
    - year: 2023
      month: 1
      day: 9
  author:
    - family: Ray
      given: Deep
    - family: Pinti
      given: Orazio
    - family: Oberai
      given: Assad A.
  citation-key: RayDeep2023
  DOI: 10.48550/ARXIV.2301.00942
  issued:
    - year: 2023
  publisher: arXiv
  title: Deep Learning and Computational Physics (Lecture Notes)
  type: article-journal
  URL: https://arxiv.org/abs/2301.00942
  version: '1'

- id: RevachKalmannet2021
  author:
    - family: Revach
      given: Guy
    - family: Shlezinger
      given: Nir
    - family: Sloun
      given: Ruud J. G.
      non-dropping-particle: van
    - family: Eldar
      given: Yonina C.
  citation-key: RevachKalmannet2021
  container-title: >-
    ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and
    Signal Processing (ICASSP)
  DOI: 10.1109/ICASSP39728.2021.9413750
  event-title: >-
    ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and
    Signal Processing (ICASSP)
  ISSN: 2379-190X
  issued:
    - year: 2021
      month: 6
  page: 3905-3909
  title: 'Kalmannet: Data-Driven Kalman Filtering'
  type: paper-conference

- 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: 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: SaemundssonVariational2020
  accessed:
    - year: 2020
      month: 3
      day: 19
  author:
    - family: Saemundsson
      given: Steindor
    - family: Terenin
      given: Alexander
    - family: Hofmann
      given: Katja
    - family: Deisenroth
      given: Marc Peter
  citation-key: SaemundssonVariational2020
  container-title: arXiv:1910.09349 [cs, stat]
  issued:
    - year: 2020
      month: 3
      day: 2
  language: en
  title: Variational Integrator Networks for Physically Structured Embeddings
  type: article-journal
  URL: http://arxiv.org/abs/1910.09349

- id: SanchezGonzalezLearning2020
  accessed:
    - year: 2023
      month: 4
      day: 16
  author:
    - family: Sanchez-Gonzalez
      given: Alvaro
    - family: Godwin
      given: Jonathan
    - family: Pfaff
      given: Tobias
    - family: Ying
      given: Rex
    - family: Leskovec
      given: Jure
    - family: Battaglia
      given: Peter
  citation-key: SanchezGonzalezLearning2020
  container-title: Proceedings of the 37th International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
  issued:
    - year: 2020
      month: 11
      day: 21
  language: en
  page: 8459-8468
  publisher: PMLR
  title: Learning to Simulate Complex Physics with Graph Networks
  type: paper-conference
  URL: http://arxiv.org/abs/2002.09405

- 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: ShlezingerModelBased2020
  accessed:
    - year: 2021
      month: 6
      day: 10
  author:
    - family: Shlezinger
      given: Nir
    - family: Whang
      given: Jay
    - family: Eldar
      given: Yonina C.
    - family: Dimakis
      given: Alexandros G.
  citation-key: ShlezingerModelBased2020
  container-title: arXiv:2012.08405 [cs, eess]
  issued:
    - year: 2020
      month: 12
      day: 15
  title: Model-Based Deep Learning
  type: article-journal
  URL: http://arxiv.org/abs/2012.08405

- id: SimchoniIntegrating2023
  accessed:
    - year: 2023
      month: 8
      day: 29
  author:
    - family: Simchoni
      given: Giora
    - family: Rosset
      given: Saharon
  citation-key: SimchoniIntegrating2023
  DOI: 10.48550/arXiv.2206.03314
  issued:
    - year: 2023
      month: 1
      day: 27
  number: arXiv:2206.03314
  publisher: arXiv
  title: Integrating Random Effects in Deep Neural Networks
  type: article
  URL: http://arxiv.org/abs/2206.03314

- id: SimsekliHausdorff2020
  accessed:
    - year: 2020
      month: 6
      day: 19
  author:
    - family: Şimşekli
      given: Umut
    - family: Sener
      given: Ozan
    - family: Deligiannidis
      given: George
    - family: Erdogdu
      given: Murat A.
  citation-key: SimsekliHausdorff2020
  container-title: CoRR
  issued:
    - year: 2020
  title: >-
    Hausdorff Dimension, Stochastic Differential Equations, and Generalization
    in Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/2006.09313
  volume: abs/2006.09313

- id: SinghSequential2019
  accessed:
    - year: 2019
      month: 9
      day: 25
  author:
    - family: Singh
      given: Gautam
    - family: Yoon
      given: Jaesik
    - family: Son
      given: Youngsung
    - family: Ahn
      given: Sungjin
  citation-key: SinghSequential2019
  container-title: arXiv:1906.10264 [cs, stat]
  issued:
    - year: 2019
      month: 6
      day: 24
  title: Sequential Neural Processes
  type: article-journal
  URL: http://arxiv.org/abs/1906.10264

- 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: ThuereyPhysicsbased2021
  author:
    - family: Thuerey
      given: Nils
    - family: Holl
      given: Philipp
    - family: Mueller
      given: Maximilian
    - family: Schnell
      given: Patrick
    - family: Trost
      given: Felix
    - family: Um
      given: Kiwon
  citation-key: ThuereyPhysicsbased2021
  issued:
    - year: 2021
  publisher: WWW
  title: Physics-based deep learning
  type: book
  URL: https://physicsbaseddeeplearning.org

- id: TranRadflow2021
  accessed:
    - year: 2021
      month: 6
      day: 18
  author:
    - family: Tran
      given: Alasdair
    - family: Mathews
      given: Alexander
    - family: Ong
      given: Cheng Soon
    - family: Xie
      given: Lexing
  citation-key: TranRadflow2021
  container-title: Proceedings of the Web Conference 2021
  DOI: 10.1145/3442381.3449945
  event-place: Ljubljana Slovenia
  event-title: 'WWW ''21: The Web Conference 2021'
  ISBN: 978-1-4503-8312-7
  issued:
    - year: 2021
      month: 4
      day: 19
  language: en
  page: 730-742
  publisher: ACM
  publisher-place: Ljubljana Slovenia
  title: >-
    Radflow: A Recurrent, Aggregated, and Decomposable Model for Networks of
    Time Series
  type: paper-conference
  URL: http://arxiv.org/abs/2102.07289

- 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: TzenTheoretical2019
  accessed:
    - year: 2024
      month: 3
      day: 15
  author:
    - family: Tzen
      given: Belinda
    - family: Raginsky
      given: Maxim
  citation-key: TzenTheoretical2019
  container-title: Proceedings of the Thirty-Second Conference on Learning Theory
  event-title: Conference on Learning Theory
  ISSN: 2640-3498
  issued:
    - year: 2019
      month: 6
      day: 25
  language: en
  page: 3084-3114
  publisher: PMLR
  title: >-
    Theoretical guarantees for sampling and inference in generative models with
    latent diffusions
  type: paper-conference
  URL: https://proceedings.mlr.press/v99/tzen19a.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: VorontsovOrthogonality2017
  author:
    - family: Vorontsov
      given: Eugene
    - family: Trabelsi
      given: Chiheb
    - family: Kadoury
      given: Samuel
    - family: Pal
      given: Chris
  citation-key: VorontsovOrthogonality2017
  container-title: PMLR
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  language: en
  page: 3570-3578
  title: On orthogonality and learning recurrent networks with long term dependencies
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/vorontsov17a.html

- id: WangData2022
  accessed:
    - year: 2022
      month: 7
      day: 20
  author:
    - family: Wang
      given: Rui
    - family: Walters
      given: Robin
    - family: Yu
      given: Rose
  citation-key: WangData2022
  DOI: 10.48550/arXiv.2206.09450
  issued:
    - year: 2022
      month: 6
      day: 19
  number: arXiv:2206.09450
  publisher: arXiv
  title: >-
    Data Augmentation vs. Equivariant Networks: A Theory of Generalization on
    Dynamics Forecasting
  type: article
  URL: http://arxiv.org/abs/2206.09450

- id: WangSolvable2019
  accessed:
    - year: 2019
      month: 11
      day: 26
  author:
    - family: Wang
      given: Chuang
    - family: Hu
      given: Hong
    - family: Lu
      given: Yue M.
  citation-key: WangSolvable2019
  container-title: arXiv:1805.08349 [cond-mat, stat]
  issued:
    - year: 2019
      month: 10
      day: 28
  title: A Solvable High-Dimensional Model of GAN
  type: article-journal
  URL: http://arxiv.org/abs/1805.08349

- id: WangWhen2020
  accessed:
    - year: 2021
      month: 3
      day: 3
  author:
    - family: Wang
      given: Sifan
    - family: Yu
      given: Xinling
    - family: Perdikaris
      given: Paris
  citation-key: WangWhen2020
  issued:
    - year: 2020
      month: 7
      day: 28
  language: en
  title: 'When and why PINNs fail to train: A neural tangent kernel perspective'
  type: article-journal
  URL: https://arxiv.org/abs/2007.14527v1

- id: YangPhysicsInformed2020
  accessed:
    - year: 2020
      month: 9
      day: 16
  author:
    - family: Yang
      given: Liu
    - family: Zhang
      given: Dongkun
    - family: Karniadakis
      given: George Em
  citation-key: YangPhysicsInformed2020
  container-title: SIAM Journal on Scientific Computing
  container-title-short: SIAM J. Sci. Comput.
  DOI: 10.1137/18M1225409
  ISSN: 1064-8275
  issue: '1'
  issued:
    - year: 2020
      month: 1
      day: 1
  page: A292-A317
  publisher: Society for Industrial and Applied Mathematics
  title: >-
    Physics-Informed Generative Adversarial Networks for Stochastic Differential
    Equations
  type: article-journal
  URL: https://arxiv.org/abs/1811.02033v1
  volume: '42'

- id: YildizODE2019
  accessed:
    - year: 2019
      month: 11
      day: 11
  author:
    - family: Yıldız
      given: Çağatay
    - family: Heinonen
      given: Markus
    - family: Lähdesmäki
      given: Harri
  citation-key: YildizODE2019
  container-title: arXiv:1905.10994 [cs, stat]
  issued:
    - year: 2019
      month: 10
      day: 24
  title: 'ODE$^2$VAE: Deep generative second order ODEs with Bayesian neural networks'
  type: article-journal
  URL: http://arxiv.org/abs/1905.10994

- 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: ZhiLearning2022
  author:
    - family: Zhi
      given: Weiming
    - family: Lai
      given: Tin
    - family: Ott
      given: Lionel
    - family: Bonilla
      given: Edwin V.
    - family: Ramos
      given: Fabio
  citation-key: ZhiLearning2022
  container-title: International Conference on Machine Learning
  issued:
    - year: 2022
  page: 27060–27074
  publisher: PMLR
  title: >-
    Learning Efficient and Robust Ordinary Differential Equations via Invertible
    Neural Networks
  type: paper-conference
  URL: https://openreview.net/forum?id=4DNcpO77XH8
...
