--- 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: ArjovskyUnitary2016 author: - family: Arjovsky given: Martin - family: Shah given: Amar - family: Bengio given: Yoshua citation-key: ArjovskyUnitary2016 collection-title: ICML'16 container-title: >- Proceedings of the 33rd International Conference on International Conference on Machine Learning - Volume 48 event-place: New York, NY, USA event-title: International Conference on Machine Learning issued: - year: 2016 month: 6 day: 11 language: en page: 1120-1128 publisher: JMLR.org publisher-place: New York, NY, USA title: Unitary Evolution Recurrent Neural Networks type: paper-conference URL: http://arxiv.org/abs/1511.06464 - 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: BrandstetterClifford2022 accessed: - year: 2023 month: 7 day: 31 author: - family: Brandstetter given: Johannes - family: Berg given: Rianne dropping-particle: van den - family: Welling given: Max - family: Gupta given: Jayesh K. citation-key: BrandstetterClifford2022 event-title: The Eleventh International Conference on Learning Representations issued: - year: 2022 month: 9 day: 29 language: en title: Clifford Neural Layers for PDE Modeling type: paper-conference URL: https://openreview.net/forum?id=okwxL_c4x84 - id: BrandstetterMessage2022 accessed: - year: 2023 month: 2 day: 20 author: - family: Brandstetter given: Johannes - family: Worrall given: Daniel - family: Welling given: Max citation-key: BrandstetterMessage2022 container-title: International Conference on Learning Representations DOI: 10.48550/arXiv.2202.03376 event-title: ICLR issued: - year: 2022 month: 3 day: 26 title: Message Passing Neural PDE Solvers type: paper-conference URL: http://arxiv.org/abs/2202.03376 - id: ChandramoorthyGeneralization2022 accessed: - year: 2022 month: 8 day: 23 author: - family: Chandramoorthy given: Nisha - family: Loukas given: Andreas - family: Gatmiry given: Khashayar - family: Jegelka given: Stefanie citation-key: ChandramoorthyGeneralization2022 DOI: 10.48550/arXiv.2208.07951 issued: - year: 2022 month: 8 day: 19 number: arXiv:2208.07951 publisher: arXiv title: On the generalization of learning algorithms that do not converge type: article URL: http://arxiv.org/abs/2208.07951 - id: ChangReversible2018 accessed: - year: 2018 month: 4 day: 23 author: - family: Chang given: Bo - family: Meng given: Lili - family: Haber given: Eldad - family: Ruthotto given: Lars - family: Begert given: David - family: Holtham given: Elliot citation-key: ChangReversible2018 container-title: arXiv:1709.03698 [cs, stat] event-title: AAAI issued: - year: 2018 title: Reversible Architectures for Arbitrarily Deep Residual Neural Networks type: paper-conference URL: http://arxiv.org/abs/1709.03698 - id: ChenNet2Net2015 accessed: - year: 2016 month: 7 day: 4 author: - family: Chen given: Tianqi - family: Goodfellow given: Ian - family: Shlens given: Jonathon citation-key: ChenNet2Net2015 container-title: arXiv:1511.05641 [cs] issued: - year: 2015 month: 11 day: 17 title: 'Net2Net: Accelerating Learning via Knowledge Transfer' type: article-journal URL: http://arxiv.org/abs/1511.05641 - 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: 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: 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: ChouRobust2023 accessed: - year: 2023 month: 6 day: 11 author: - family: Chou given: Hung-Hsu - family: Rauhut given: Holger - family: Ward given: Rachel citation-key: ChouRobust2023 DOI: 10.48550/arXiv.2305.05448 issued: - year: 2023 month: 5 day: 9 number: arXiv:2305.05448 publisher: arXiv title: Robust Implicit Regularization via Weight Normalization type: article URL: http://arxiv.org/abs/2305.05448 - 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: 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: EMachine2020 accessed: - year: 2023 month: 1 day: 9 author: - family: E given: Weinan - family: Ma given: Chao - family: Wu given: Lei citation-key: EMachine2020 container-title: Science China Mathematics container-title-short: Sci. China Math. DOI: 10.1007/s11425-020-1773-8 ISSN: 1869-1862 issue: '11' issued: - year: 2020 month: 11 day: 1 language: en page: 2233-2266 title: Machine learning from a continuous viewpoint, I type: article-journal volume: '63' - 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: GalimbertiNon2021 accessed: - year: 2021 month: 12 day: 15 author: - family: Galimberti given: Clara - family: Furieri given: Luca - family: Xu given: Liang - family: Ferrari-Trecate given: Giancarlo citation-key: GalimbertiNon2021 event-title: The Symbiosis of Deep Learning and Differential Equations issued: - year: 2021 month: 9 day: 27 language: en title: >- Non Vanishing Gradients for Arbitrarily Deep Neural Networks: a Hamiltonian System Approach type: paper-conference URL: https://openreview.net/forum?id=49WBX4hBY5X - id: GluchNoether2021 accessed: - year: 2021 month: 4 day: 15 author: - family: Głuch given: Grzegorz - family: Urbanke given: Rüdiger citation-key: GluchNoether2021 container-title: arXiv:2104.05508 [cs, stat] issued: - year: 2021 month: 4 day: 12 title: 'Noether: The More Things Change, the More Stay the Same' type: article-journal URL: http://arxiv.org/abs/2104.05508 - id: GrohsDeep2022 accessed: - year: 2023 month: 9 day: 6 author: - family: Grohs given: Philipp - family: Herrmann given: Lukas citation-key: GrohsDeep2022 container-title: IMA Journal of Numerical Analysis container-title-short: IMA Journal of Numerical Analysis DOI: 10.1093/imanum/drab031 ISSN: 0272-4979 issue: '3' issued: - year: 2022 month: 7 day: 22 page: 2055-2082 title: >- Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions type: article-journal URL: http://arxiv.org/abs/2007.05384 volume: '42' - 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: HaberIMEXnet2019 accessed: - year: 2020 month: 9 day: 1 author: - family: Haber given: Eldad - family: Lensink given: Keegan - family: Treister given: Eran - family: Ruthotto given: Lars citation-key: HaberIMEXnet2019 container-title: International Conference on Machine Learning event-title: International Conference on Machine Learning ISSN: 2640-3498 issued: - year: 2019 month: 5 day: 24 language: en page: 2525-2534 publisher: PMLR title: IMEXnet A Forward Stable Deep Neural Network type: paper-conference URL: http://proceedings.mlr.press/v97/haber19a.html - id: HaberLearning2017 accessed: - year: 2018 month: 4 day: 23 author: - family: Haber given: Eldad - family: Ruthotto given: Lars - family: Holtham given: Elliot - family: Jun given: Seong-Hwan citation-key: HaberLearning2017 container-title: arXiv:1703.02009 [cs] issued: - year: 2017 month: 3 day: 6 title: Learning across scales - A multiscale method for Convolution Neural Networks type: article-journal URL: http://arxiv.org/abs/1703.02009 - 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: HaberStable2018 author: - family: Haber given: Eldad - family: Ruthotto given: Lars citation-key: HaberStable2018 container-title: Inverse Problems container-title-short: Inverse Problems DOI: 10.1088/1361-6420/aa9a90 ISSN: 0266-5611 issue: '1' issued: - year: 2018 language: en page: '014004' title: Stable architectures for deep neural networks type: article-journal URL: http://arxiv.org/abs/1705.03341 volume: '34' - 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: HardtTrain2015 accessed: - year: 2015 month: 9 day: 5 author: - family: Hardt given: Moritz - family: Recht given: Benjamin - family: Singer given: Yoram citation-key: HardtTrain2015 container-title: arXiv:1509.01240 [cs, math, stat] issued: - year: 2015 month: 9 day: 3 title: 'Train faster, generalize better: Stability of stochastic gradient descent' type: article-journal URL: http://arxiv.org/abs/1509.01240 - 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: HayouImpact2019 accessed: - year: 2022 month: 10 day: 30 author: - family: Hayou given: Soufiane - family: Doucet given: Arnaud - family: Rousseau given: Judith citation-key: HayouImpact2019 container-title: Proceedings of the 36th International Conference on Machine Learning DOI: 10.48550/arXiv.1902.06853 event-title: International Conference on Machine Learning ISSN: 2640-3498 issued: - year: 2019 month: 5 day: 24 language: en page: 2672-2680 publisher: PMLR title: On the Impact of the Activation function on Deep Neural Networks Training type: paper-conference URL: http://arxiv.org/abs/1902.06853 - id: HayouPruning2020 accessed: - year: 2021 month: 3 day: 14 author: - family: Hayou given: Soufiane - family: Ton given: Jean-Francois - family: Doucet given: Arnaud - family: Teh given: Yee Whye citation-key: HayouPruning2020 container-title: arXiv:2002.08797 [cs, stat] issued: - year: 2020 month: 6 day: 24 title: 'Pruning untrained neural networks: Principles and Analysis' type: article-journal URL: http://arxiv.org/abs/2002.08797 - 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: 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: JingTunable2017 author: - family: Jing given: Li - family: Shen given: Yichen - family: Dubcek given: Tena - family: Peurifoy given: John - family: Skirlo given: Scott - family: LeCun given: Yann - family: Tegmark given: Max - family: Soljačić given: Marin citation-key: JingTunable2017 container-title: PMLR event-title: International Conference on Machine Learning issued: - year: 2017 month: 7 day: 17 language: en page: 1733-1741 title: >- Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs type: paper-conference URL: http://proceedings.mlr.press/v70/jing17a.html - 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: 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: 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: 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: LongPDENet2018 accessed: - year: 2022 month: 3 day: 4 author: - family: Long given: Zichao - family: Lu given: Yiping - family: Ma given: Xianzhong - family: Dong given: Bin citation-key: LongPDENet2018 container-title: Proceedings of the 35th International Conference on Machine Learning event-title: International Conference on Machine Learning ISSN: 2640-3498 issued: - year: 2018 month: 7 day: 3 language: en page: 3208-3216 publisher: PMLR title: 'PDE-Net: Learning PDEs from Data' type: paper-conference URL: http://arxiv.org/abs/1710.09668 - 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: MengGeneralization2016 accessed: - year: 2016 month: 9 day: 28 author: - family: Meng given: Qi - family: Wang given: Yue - family: Chen given: Wei - family: Wang given: Taifeng - family: Ma given: Zhi-Ming - family: Liu given: Tie-Yan citation-key: MengGeneralization2016 container-title: arXiv:1609.08397 [stat] issued: - year: 2016 month: 9 day: 27 page: 441–474 title: Generalization Error Bounds for Optimization Algorithms via Stability type: paper-conference URL: http://arxiv.org/abs/1609.08397 volume: '10' - 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: michaelbeyond2022 author: - family: Bronstein given: Michael citation-key: michaelbeyond2022 container-title: The Gradient issued: - year: 2022 title: >- Beyond message passing: a physics-inspired paradigm for graph neural networks type: article-journal URL: >- https://thegradient.pub/graph-neural-networks-beyond-message-passing-and-weisfeiler-lehman - 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: OpschoorDeep2020 accessed: - year: 2023 month: 9 day: 6 author: - family: Opschoor given: Joost A. A. - family: Petersen given: Philipp C. - family: Schwab given: Christoph citation-key: OpschoorDeep2020 container-title: Analysis and Applications container-title-short: Anal. Appl. DOI: 10.1142/S0219530519410136 ISSN: 0219-5305 issue: '05' issued: - year: 2020 month: 9 page: 715-770 publisher: World Scientific Publishing Co. title: Deep ReLU networks and high-order finite element methods type: article-journal URL: https://www.worldscientific.com/doi/abs/10.1142/S0219530519410136 volume: '18' - 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: 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: 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: 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: RobertsPrinciples2021 accessed: - year: 2021 month: 10 day: 23 author: - family: Roberts given: Daniel A. - family: Yaida given: Sho - family: Hanin given: Boris citation-key: RobertsPrinciples2021 container-title: arXiv:2106.10165 [hep-th, stat] issued: - year: 2021 month: 8 day: 24 title: The Principles of Deep Learning Theory type: article-journal URL: http://arxiv.org/abs/2106.10165 - 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: RuheGeometric2023 author: - family: Ruhe given: David - family: Gupta given: Jayesh K - family: Keninck given: Steven non-dropping-particle: de - family: Welling given: Max - family: Brandstetter given: Johannes citation-key: RuheGeometric2023 container-title: arXiv preprint arXiv:2302.06594 issued: - year: 2023 title: Geometric clifford algebra networks type: paper-conference URL: http://arxiv.org/abs/2302.06594 - 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: SchoenholzDeep2017 accessed: - year: 2022 month: 10 day: 30 author: - family: Schoenholz given: Samuel S. - family: Gilmer given: Justin - family: Ganguli given: Surya - family: Sohl-Dickstein given: Jascha citation-key: SchoenholzDeep2017 event-title: International Conference on Learning Representations issued: - year: 2017 language: en title: Deep Information Propagation type: paper-conference URL: https://arxiv.org/abs/1611.01232v2 - 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: VenturiMoriZwanzig2022 accessed: - year: 2022 month: 9 day: 15 author: - family: Venturi given: Daniele - family: Li given: Xiantao citation-key: VenturiMoriZwanzig2022 DOI: 10.48550/arXiv.2209.05544 issued: - year: 2022 month: 9 day: 12 number: arXiv:2209.05544 publisher: arXiv title: The Mori-Zwanzig formulation of deep learning type: article URL: http://arxiv.org/abs/2209.05544 - 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: 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: WiatowskiEnergy2018 author: - family: Wiatowski given: Thomas - family: Grohs given: Philipp - family: Bölcskei given: Helmut citation-key: WiatowskiEnergy2018 container-title: IEEE Transactions on Information Theory DOI: 10.1109/TIT.2017.2756880 ISSN: 0018-9448 issue: '7' issued: - year: 2018 page: 1-1 title: Energy Propagation in Deep Convolutional Neural Networks type: article-journal URL: http://arxiv.org/abs/1704.03636 volume: '64' - id: WiatowskiMathematical2015 accessed: - year: 2016 month: 1 day: 2 author: - family: Wiatowski given: Thomas - family: Bölcskei given: Helmut citation-key: WiatowskiMathematical2015 container-title: Proceedings of IEEE International Symposium on Information Theory event-title: IEEE International Symposium on Information Theory issued: - year: 2015 month: 12 day: 19 title: >- A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction type: paper-conference URL: http://arxiv.org/abs/1512.06293 - id: YegenogluEnsemble2020 accessed: - year: 2022 month: 9 day: 20 author: - family: Yegenoglu given: Alper - family: Krajsek given: Kai - family: Pier given: Sandra Diaz - family: Herty given: Michael citation-key: YegenogluEnsemble2020 container-title: Machine Learning, Optimization, and Data Science DOI: 10.1007/978-3-030-64580-9_7 editor: - family: Nicosia given: Giuseppe - family: Ojha given: Varun - family: La Malfa given: Emanuele - family: Jansen given: Giorgio - family: Sciacca given: Vincenzo - family: Pardalos given: Panos - family: Giuffrida given: Giovanni - family: Umeton given: Renato event-place: Cham ISBN: 978-3-030-64579-3 978-3-030-64580-9 issued: - year: 2020 language: en page: 78-92 publisher: Springer International Publishing publisher-place: Cham title: >- Ensemble Kalman Filter Optimizing Deep Neural Networks: An Alternative Approach to Non-performing Gradient Descent type: chapter URL: http://link.springer.com/10.1007/978-3-030-64580-9_7 volume: '12566' - 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 ...