# Neural Ordinary Differential Equation based Recurrent Neural Network Model

arXiv: https://arxiv.org/abs/2005.09807 · HTML: https://mlsanity.com/paper/2005.09807/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2020.

## Built on by (most cited first, 12 of 12)

- [Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data](https://mlsanity.com/paper/2211.04234/) (2022)
- [Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2305.18687/) (2023)
- [Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces](https://mlsanity.com/paper/2308.08794/) (2023)
- [Parallel Training of GRU Networks with a Multi-Grid Solver for Long Sequences](https://mlsanity.com/paper/2203.04738/) (2022)
- [SeqLink: A Robust Neural-ODE Architecture for Modelling Partially Observed Time Series](https://mlsanity.com/paper/2212.03560/) (2022)
- [Neural Differential Recurrent Neural Network with Adaptive Time Steps](https://mlsanity.com/paper/2306.01674/) (2023)
- [ECG synthesis with Neural ODE and GAN models](https://mlsanity.com/paper/2111.00314/) (2021)
- [Multi-View Neural Differential Equations for Continuous-Time Stream Data in Long-Term Traffic Forecasting](https://mlsanity.com/paper/2408.06445/) (2024)
- [LERD: Latent Event-Relational Dynamics for Neurodegenerative Classification](https://mlsanity.com/paper/2602.18195/) (2026)
- [Recent Trends in Modelling the Continuous Time Series using Deep Learning: A Survey](https://mlsanity.com/paper/2409.09106/) (2024)
- [ODEStream: A Buffer-Free Online Learning Framework with ODE-based Adaptor for Streaming Time Series Forecasting](https://mlsanity.com/paper/2411.07413/) (2024)
- [VNODE: A Piecewise Continuous Volterra Neural Network](https://mlsanity.com/paper/2509.24659/) (2025)

## Abstract (arXiv)

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE) is explored with a new extension. The main goal of this work is to answer the following questions: (i)~can ODE be used to redefine the existing neural network model? (ii)~can Neural ODEs solve the irregular sampling rate challenge of existing neural network models for a continuous time series, i.e., length and dynamic nature, (iii)~how to reduce the training and evaluation time of existing Neural ODE systems? This work leverages the mathematical foundation of ODEs to redesign traditional RNNs such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The main contribution of this paper is to illustrate the design of two new ODE-based RNN models (GRU-ODE model and LSTM-ODE) which can compute the hidden state and cell state at any point of time using an ODE solver. These models reduce the computation overhead of hidden state and cell state by a vast amount. The performance evaluation of these two new models for learning continuous time series with irregular sampling rate is then demonstrated. Experiments show that these new ODE based RNN models require less training time than Latent ODEs and conventional Neural ODEs. They can achieve higher accuracy quickly, and the design of the neural network is simpler than, previous neural ODE systems.