# Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series

arXiv: https://arxiv.org/abs/2410.14030 · HTML: https://mlsanity.com/paper/2410.14030/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series](https://mlsanity.com/paper/2202.07857/) (2022)
- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [On Low Rank Directed Acyclic Graphs and Causal Structure Learning](https://mlsanity.com/paper/2006.05691/) (2020)
- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)
- [Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology](https://mlsanity.com/paper/1508.01775/) (2015)
- [Inferring dynamic regulatory interaction graphs from time series data with perturbations](https://mlsanity.com/paper/2306.07803/) (2023)

## Built on by (most cited first, 15 of 15)

- [Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline](https://mlsanity.com/paper/2505.11250/) (2025)
- [HyperIMTS: Hypergraph Neural Network for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.17431/) (2025)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Bridging Time and Frequency: A Joint Modeling Framework for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.00582/) (2026)
- [ASTGI: Adaptive Spatio-Temporal Graph Interactions for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2509.23313/) (2025)
- [TiWeaver: Unified Temporal Dynamics Modeling via Contextual Patching](https://mlsanity.com/paper/2606.03121/) (2026)
- [Towards Robust Real-World Multivariate Time Series Forecasting: A Unified Framework for Dependency, Asynchrony, and Missingness](https://mlsanity.com/paper/2506.08660/) (2025)
- [MM-ISTS: Cooperating Irregularly Sampled Time Series Forecasting with Multimodal Vision-Text LLMs](https://mlsanity.com/paper/2603.05997/) (2026)
- [One-Step Graph-Structured Neural Flows for Irregular Multivariate Time Series Classification](https://mlsanity.com/paper/2605.10179/) (2026)
- [Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework](https://mlsanity.com/paper/2607.28035/) (2026)
- [Learning Recursive Multi-Scale Representations for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2602.21498/) (2026)
- [MissHyper: Restoring Clinical Synchronicity in Missingness-Guided Hypergraph Forecasting](https://mlsanity.com/paper/2607.21922/) (2026)
- [Rethinking Irregular Time Series Forecasting from the Perspective of Basis Functions](https://mlsanity.com/paper/2608.17284/) (2026)
- [BITS: Rethinking Fair and Comprehensive Evaluation for Irregular Time Series Forecasting](https://mlsanity.com/paper/2609.33303/) (2026)
- [QiYao-I: A Manifold Based Foundation Model for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2610.06936/) (2026)

## Abstract (arXiv)

Interacting systems are prevalent in nature. It is challenging to accurately predict the dynamics of the system if its constituent components are analyzed independently. We develop a graph-based model that unveils the systemic interactions of time series observed at irregular time points, by using a directed acyclic graph to model the conditional dependencies (a form of causal notation) of the system components and learning this graph in tandem with a continuous-time model that parameterizes the solution curves of ordinary differential equations (ODEs). Our technique, a graph neural flow, leads to substantial enhancements over non-graph-based methods, as well as graph-based methods without the modeling of conditional dependencies. We validate our approach on several tasks, including time series classification and forecasting, to demonstrate its efficacy.