# Temporal Graph Neural Networks for Irregular Data

arXiv: https://arxiv.org/abs/2302.08415 · HTML: https://mlsanity.com/paper/2302.08415/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 16 Feb 2023.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Tackling Climate Change with Machine Learning](https://mlsanity.com/paper/1906.05433/) (2019)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [Transformer Networks for Trajectory Forecasting](https://mlsanity.com/paper/2003.08111/) (2020)
- [Neural Jump Stochastic Differential Equations](https://mlsanity.com/paper/1905.10403/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Graph-Guided Network for Irregularly Sampled Multivariate Time Series](https://mlsanity.com/paper/2110.05357/) (2021)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Probabilistic Forecasting with Temporal Convolutional Neural Network](https://mlsanity.com/paper/1906.04397/) (2019)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Chickenpox Cases in Hungary: a Benchmark Dataset for Spatiotemporal Signal Processing with Graph Neural Networks](https://mlsanity.com/paper/2102.08100/) (2021)
- [Continuous-Depth Neural Models for Dynamic Graph Prediction](https://mlsanity.com/paper/2106.11581/) (2021)
- [Deep Learning for Predicting Dynamic Uncertain Opinions in Network Data](https://mlsanity.com/paper/1910.05640/) (2019)
- [GraphVid: It Only Takes a Few Nodes to Understand a Video](https://mlsanity.com/paper/2207.01375/) (2022)

## Built on by (most cited first, 7 of 7)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [Diffusion-Based Environment-Aware Trajectory Prediction](https://mlsanity.com/paper/2403.11643/) (2024)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Evaluation of Differentially Constrained Motion Models for Graph-Based Trajectory Prediction](https://mlsanity.com/paper/2304.05116/) (2023)
- [Irregularity-Informed Time Series Analysis: Adaptive Modelling of Spatial and Temporal Dynamics](https://mlsanity.com/paper/2410.12257/) (2024)
- [Sampling-guided Heterogeneous Graph Neural Network with Temporal Smoothing for Scalable Longitudinal Data Imputation](https://mlsanity.com/paper/2411.04899/) (2024)

## Abstract (arXiv)

This paper proposes a temporal graph neural network model for forecasting of graph-structured irregularly observed time series. Our TGNN4I model is designed to handle both irregular time steps and partial observations of the graph. This is achieved by introducing a time-continuous latent state in each node, following a linear Ordinary Differential Equation (ODE) defined by the output of a Gated Recurrent Unit (GRU). The ODE has an explicit solution as a combination of exponential decay and periodic dynamics. Observations in the graph neighborhood are taken into account by integrating graph neural network layers in both the GRU state update and predictive model. The time-continuous dynamics additionally enable the model to make predictions at arbitrary time steps. We propose a loss function that leverages this and allows for training the model for forecasting over different time horizons. Experiments on simulated data and real-world data from traffic and climate modeling validate the usefulness of both the graph structure and time-continuous dynamics in settings with irregular observations.