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Augmented Neural ODEs

arXiv 1904.01681 ↗First posted 2 Apr 2019stat.ML cs.LGcited by 396

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Abstract (arXiv)

We show that Neural Ordinary Differential Equations (ODEs) learn representations that preserve the topology of the input space and prove that this implies the existence of functions Neural ODEs cannot represent. To address these limitations, we introduce Augmented Neural ODEs which, in addition to being more expressive models, are empirically more stable, generalize better and have a lower computational cost than Neural ODEs.

Key facts. Cited by 396 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Apr 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 86; 2022: 66; 2023: 59; 2024: 63; 2025: 62; 2026: 60.

396 papers.

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  1. 2022Flow Matching for Generative Modelingcited by 5,426
  2. 2022Pseudo Numerical Methods for Diffusion Models on Manifoldscited by 695
  3. 2021Score-based Generative Modeling in Latent Spacecited by 634
  4. 2021GRAND: Graph Neural Diffusioncited by 258
  5. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  6. 2021Sinkformers: Transformers with Doubly Stochastic Attentioncited by 136
  7. 2022Liquid Structural State-Space Modelscited by 134
  8. 2021Neural Flows: Efficient Alternative to Neural ODEscited by 99
  9. 2024Normalizing Flows are Capable Generative Modelscited by 89
  10. 2021JFB: Jacobian-Free Backpropagation for Implicit Networkscited by 84
  11. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  12. 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 74
38 more
  1. 2021On Training Implicit Modelscited by 73
  2. 2022Multivariate Time Series Forecasting with Dynamic Graph Neural ODEscited by 72
  3. 2021Stabilizing Equilibrium Models by Jacobian Regularizationcited by 71
  4. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
  5. 2021Closed-form Continuous-time Neural Modelscited by 65
  6. 2022Deep Equilibrium Optical Flow Estimationcited by 63
  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. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
  11. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  12. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  13. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  14. 2021Survival Regression with Proper Scoring Rules and Monotonic Neural Networkscited by 42
  15. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  16. 2021Neural Point Process for Learning Spatiotemporal Event Dynamicscited by 42
  17. 2022Deep Equilibrium Approaches to Diffusion Modelscited by 42
  18. 2021Learning Dynamic Alignment via Meta-filter for Few-shot Learningcited by 41
  19. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  20. 2021Continuous-Time Model-Based Reinforcement Learningcited by 39
  21. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  22. 2022Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flowcited by 38
  23. 2021Momentum Residual Neural Networkscited by 36
  24. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  25. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  26. 2021Attentive Neural Controlled Differential Equations for Time-series Classification and Forecastingcited by 28
  27. 2021OCT-GAN: Neural ODE-based Conditional Tabular GANscited by 27
  28. 2022Do Residual Neural Networks discretize Neural Ordinary Differential Equations?cited by 27
  29. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 27
  30. 2021Neural Delay Differential Equationscited by 26
  31. 2023Recurrence without Recurrence: Stable Video Landmark Detection with Deep Equilibrium Modelscited by 26
  32. 2022Neural Laplace: Learning diverse classes of differential equations in the Laplace domaincited by 24
  33. 2021Causal Navigation by Continuous-time Neural Networkscited by 23
  34. 2023An overview of differentiable particle filters for data-adaptive sequential Bayesian inferencecited by 23
  35. 2022EXIT: Extrapolation and Interpolation-based Neural Controlled Differential Equations for Time-series Classification and Forecastingcited by 22
  36. 2022Online Deep Equilibrium Learning for Regularization by Denoisingcited by 22
  37. 2022Alternating Differentiation for Optimization Layerscited by 22
  38. 2023Generative learning for nonlinear dynamicscited by 22

50 most cited of 396 All 396 (JSON)