mlsanityData to 7 Oct 2026

Neural ODE Processes

arXiv 2103.12413 ↗First posted 23 Mar 2021cs.LGcited by 57

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Abstract (arXiv)

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few disadvantages. First, they are unable to adapt to incoming data points, a fundamental requirement for real-time applications imposed by the natural direction of time. Second, time series are often composed of a sparse set of measurements that could be explained by many possible underlying dynamics. NODEs do not capture this uncertainty. In contrast, Neural Processes (NPs) are a family of models providing uncertainty estimation and fast data adaptation but lack an explicit treatment of the flow of time. To address these problems, we introduce Neural ODE Processes (NDPs), a new class of stochastic processes determined by a distribution over Neural ODEs. By maintaining an adaptive data-dependent distribution over the underlying ODE, we show that our model can successfully capture the dynamics of low-dimensional systems from just a few data points. At the same time, we demonstrate that NDPs scale up to challenging high-dimensional time-series with unknown latent dynamics such as rotating MNIST digits.

Key facts. Cited by 57 papers in the map (data through 7 Oct 2026). Builds on 24 of its 31 references that are in the map. First posted on arXiv 23 Mar 2021.

Builds on

24 of 31 references.

References · 24

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  4. 2018Conditional Neural Processescited by 421
  5. 2019Augmented Neural ODEscited by 396
  6. 2018Neural Processescited by 307
  7. 2019Attentive Neural Processescited by 280
  8. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  9. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  10. 2019Latent ODEs for Irregularly-Sampled Time Seriescited by 182
  11. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  12. 2020Dissecting Neural ODEscited by 150
12 more
  1. 2019Neural Jump Stochastic Differential Equationscited by 147
  2. 2020Neural Rough Differential Equations for Long Time Seriescited by 140
  3. 2019Convolutional Conditional Neural Processescited by 139
  4. 2016Towards a Neural Statisticiancited by 119
  5. 2019Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noisecited by 98
  6. 2018Gaussian Process Prior Variational Autoencoderscited by 72
  7. 2020On Second Order Behaviour in Augmented Neural ODEscited by 68
  8. 2019Sequential Neural Processescited by 55
  9. 2020Modeling Continuous Stochastic Processes with Dynamic Normalizing Flowscited by 37
  10. 2019ODE2VAE: Deep generative second order ODEs with Bayesian neural networkscited by 36
  11. 2018The Variational Homoencoder: Learning to learn high capacity generative models from few examplescited by 23
  12. 2020Message Passing Neural Processescited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 14; 2022: 13; 2023: 8; 2024: 12; 2025: 8; 2026: 2.

57 papers.

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  1. 2021Efficient and Accurate Gradients for Neural SDEscited by 68
  2. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
  3. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  4. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  5. 2021Neural Point Process for Learning Spatiotemporal Event Dynamicscited by 42
  6. 2021LEADS: Learning Dynamical Systems that Generalize Across Environmentscited by 39
  7. 2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 34
  8. 2022The Neural Process Family: Survey, Applications and Perspectivescited by 23
  9. 2022On Numerical Integration in Neural Ordinary Differential Equationscited by 21
  10. 2023Normalizing Flow-based Neural Process for Few-Shot Knowledge Graph Completioncited by 19
  11. 2022What Matters For Meta-Learning Vision Regression Tasks?cited by 18
  12. 2022Latent Neural ODEs with Sparse Bayesian Multiple Shootingcited by 17
38 more
  1. 2024Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patchingcited by 16
  2. 2022SurvLatent ODE : A Neural ODE based time-to-event model with competing risks for longitudinal data improves cancer-associated Venous Thromboembolism (VTE) predictioncited by 13
  3. 2022Graph Sequential Neural ODE Process for Link Prediction on Dynamic and Sparse Graphscited by 13
  4. 2024Zero-shot Imputation with Foundation Inference Models for Dynamical Systemscited by 13
  5. 2023Improving Transferability for Cross-domain Trajectory Prediction via Neural Stochastic Differential Equationcited by 12
  6. 2021Continuous Latent Process Flowscited by 10
  7. 2022torchode: A Parallel ODE Solver for PyTorchcited by 10
  8. 2023Modulated Neural ODEscited by 10
  9. 2024Learning Physics Informed Neural ODEs With Partial Measurementscited by 9
  10. 2022Recognition Models to Learn Dynamics from Partial Observations with Neural ODEscited by 8
  11. 2024Beyond Kalman Filters: Deep Learning-Based Filters for Improved Object Trackingcited by 8
  12. 2022An end-to-end deep learning approach for extracting stochastic dynamical systems with α-stable L'evy noisecited by 7
  13. 2022Tripletformer for Probabilistic Interpolation of Irregularly sampled Time Seriescited by 6
  14. 2023Uncertainty and Structure in Neural Ordinary Differential Equationscited by 6
  15. 2024Rough Transformers for Continuous and Efficient Time-Series Modellingcited by 5
  16. 2024DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysiscited by 4
  17. 2024Latent Space Energy-based Neural ODEscited by 4
  18. 2025Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamicscited by 4
  19. 2025Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcationscited by 4
  20. 2021Segmenting Hybrid Trajectories using Latent ODEscited by 3
  21. 2022Compositional Law Parsing with Latent Random Functionscited by 3
  22. 2023Faster Training of Neural ODEs Using Gauss-Legendre Quadraturecited by 3
  23. 2024System-Aware Neural ODE Processes for Few-Shot Bayesian Optimizationcited by 3
  24. 2021Learning ODEs via Diffeomorphisms for Fast and Robust Integrationcited by 2
  25. 2023SpReME: Sparse Regression for Multi-Environment Dynamic Systemscited by 2
  26. 2023Learning Continuous Network Emerging Dynamics from Scarce Observations via Data-Adaptive Stochastic Processescited by 2
  27. 2024Reevaluating Meta-Learning Optimization Algorithms Through Contextual Self-Modulationcited by 2
  28. 2025Deep Neural Networks Inspired by Differential Equationscited by 2
  29. 2021Meta-learning using privileged information for dynamicscited by 1
  30. 2021Distributional Gradient Matching for Learning Uncertain Neural Dynamics Modelscited by 1
  31. 2021Heteroscedastic Temporal Variational Autoencoder For Irregular Time Seriescited by 1
  32. 2021Approximate Latent Force Model Inferencecited by 1
  33. 2023Adversarially Contrastive Estimation of Conditional Neural Processescited by 1
  34. 2021Multi-Task Neural Processescited by 0
  35. 2022Continuous-time Particle Filtering for Latent Stochastic Differential Equationscited by 0
  36. 2024Neural Controlled Differential Equations with Quantum Hidden Evolutionscited by 0
  37. 2024Predicting time-varying flux and balance in metabolic systems using structured neural-ODE processescited by 0
  38. 2024An Event-centric Framework for Predicting Crime Hotspots with Flexible Time Intervalscited by 0

50 most cited of 57 All 57 (JSON)