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Dissecting Neural ODEs

arXiv 2002.08071 ↗First posted 19 Feb 2020cs.LG cs.NE stat.MLcited by 150

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Abstract (arXiv)

Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a novel perspective. However, deciphering the inner working of these models is still an open challenge, as most applications apply them as generic black-box modules. In this work we "open the box", further developing the continuous-depth formulation with the aim of clarifying the influence of several design choices on the underlying dynamics.

Key facts. Cited by 150 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 38; 2022: 33; 2023: 19; 2024: 32; 2025: 19; 2026: 9.

150 papers.

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  1. 2023Hyena Hierarchy: Towards Larger Convolutional Language Modelscited by 388
  2. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
  3. 2022Liquid Structural State-Space Modelscited by 134
  4. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 87
  5. 2024ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEscited by 78
  6. 2021Closed-form Continuous-time Neural Modelscited by 65
  7. 2021Neural ODE Processescited by 57
  8. 2024Mechanistic Design and Scaling of Hybrid Architecturescited by 57
  9. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  10. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  11. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  12. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
38 more
  1. 2021Learning Dynamic Alignment via Meta-filter for Few-shot Learningcited by 41
  2. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  3. 2022Deep Latent State Space Models for Time-Series Generationcited by 37
  4. 2021Momentum Residual Neural Networkscited by 36
  5. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
  6. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  7. 2022Learning continuous models for continuous physicscited by 28
  8. 2021OCT-GAN: Neural ODE-based Conditional Tabular GANscited by 27
  9. 2021Causal Navigation by Continuous-time Neural Networkscited by 23
  10. 2021LT-OCF: Learnable-Time ODE-based Collaborative Filteringcited by 21
  11. 2022On Numerical Integration in Neural Ordinary Differential Equationscited by 21
  12. 2023Generalization bounds for neural ordinary differential equations and deep residual networkscited by 21
  13. 2021Differentiable Multiple Shooting Layerscited by 20
  14. 2023Implicit regularization of deep residual networks towards neural ODEscited by 20
  15. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  16. 2022Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Datacited by 19
  17. 2022Latent Neural ODEs with Sparse Bayesian Multiple Shootingcited by 17
  18. 2023CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systemscited by 16
  19. 2023Latent SDEs on Homogeneous Spacescited by 16
  20. 2021ACE-NODE: Attentive Co-Evolving Neural Ordinary Differential Equationscited by 15
  21. 2021Stateful ODE-Nets using Basis Function Expansionscited by 14
  22. 2022Neural Ordinary Differential Equations for Nonlinear System Identificationcited by 14
  23. 2024Continuous Temporal Domain Generalizationcited by 14
  24. 2021Sparse Flows: Pruning Continuous-depth Modelscited by 13
  25. 2021Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equationscited by 13
  26. 2022Reachability Analysis of a General Class of Neural Ordinary Differential Equationscited by 13
  27. 2022A Neural ODE Interpretation of Transformer Layerscited by 13
  28. 2021Convergent Graph Solverscited by 11
  29. 2021Globally Convergent Multilevel Training of Deep Residual Networkscited by 11
  30. 2021Second-Order Neural ODE Optimizercited by 11
  31. 2024Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methodscited by 11
  32. 2025Neural Motion Simulator: Pushing the Limit of World Models in Reinforcement Learningcited by 11
  33. 2021How Does Momentum Benefit Deep Neural Networks Architecture Design? A Few Case Studiescited by 10
  34. 2022Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order modelscited by 10
  35. 2022Dynamical systems' based neural networkscited by 10
  36. 2022On the Forward Invariance of Neural ODEscited by 10
  37. 2022torchode: A Parallel ODE Solver for PyTorchcited by 10
  38. 2021The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learningcited by 9

50 most cited of 150 All 150 (JSON)