# Dissecting Neural ODEs

arXiv: https://arxiv.org/abs/2002.08071 · HTML: https://mlsanity.com/paper/2002.08071/

## Key facts

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

## Built on by (most cited first, 30 of 150)

- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Liquid Structural State-Space Models](https://mlsanity.com/paper/2209.12951/) (2022)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [Mechanistic Design and Scaling of Hybrid Architectures](https://mlsanity.com/paper/2403.17844/) (2024)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [MALI: A memory efficient and reverse accurate integrator for Neural ODEs](https://mlsanity.com/paper/2102.04668/) (2021)
- [Heavy Ball Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.04840/) (2021)
- [Learning Dynamic Alignment via Meta-filter for Few-shot Learning](https://mlsanity.com/paper/2103.13582/) (2021)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)
- [Deep Latent State Space Models for Time-Series Generation](https://mlsanity.com/paper/2212.12749/) (2022)
- [Momentum Residual Neural Networks](https://mlsanity.com/paper/2102.07870/) (2021)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Learning continuous models for continuous physics](https://mlsanity.com/paper/2202.08494/) (2022)
- [OCT-GAN: Neural ODE-based Conditional Tabular GANs](https://mlsanity.com/paper/2105.14969/) (2021)
- [Causal Navigation by Continuous-time Neural Networks](https://mlsanity.com/paper/2106.08314/) (2021)
- [LT-OCF: Learnable-Time ODE-based Collaborative Filtering](https://mlsanity.com/paper/2108.06208/) (2021)
- [On Numerical Integration in Neural Ordinary Differential Equations](https://mlsanity.com/paper/2206.07335/) (2022)
- [Generalization bounds for neural ordinary differential equations and deep residual networks](https://mlsanity.com/paper/2305.06648/) (2023)
- [Differentiable Multiple Shooting Layers](https://mlsanity.com/paper/2106.03885/) (2021)
- [Implicit regularization of deep residual networks towards neural ODEs](https://mlsanity.com/paper/2309.01213/) (2023)
- [Comprehensive Review of Neural Differential Equations for Time Series Analysis](https://mlsanity.com/paper/2502.09885/) (2025)
- [Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data](https://mlsanity.com/paper/2211.04234/) (2022)
- [Latent Neural ODEs with Sparse Bayesian Multiple Shooting](https://mlsanity.com/paper/2210.03466/) (2022)
- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)

## 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.