# Learning Continuous Network Emerging Dynamics from Scarce Observations via Data-Adaptive Stochastic Processes

arXiv: https://arxiv.org/abs/2310.16466 · HTML: https://mlsanity.com/paper/2310.16466/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 72 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 29 of 29)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [Data-driven discovery of intrinsic dynamics](https://mlsanity.com/paper/2108.05928/) (2021)
- [Nonparametric inference of interaction laws in systems of agents from trajectory data](https://mlsanity.com/paper/1812.06003/) (2018)
- [Neural Dynamics on Complex Networks](https://mlsanity.com/paper/1908.06491/) (2019)
- [Joint Modeling of Local and Global Temporal Dynamics for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/1911.10273/) (2019)
- [Generalizing Graph ODE for Learning Complex System Dynamics across Environments](https://mlsanity.com/paper/2307.04287/) (2023)
- [A General Deep Learning Framework for Network Reconstruction and Dynamics Learning](https://mlsanity.com/paper/1812.11482/) (2018)
- [Deep learning of contagion dynamics on complex networks](https://mlsanity.com/paper/2006.05410/) (2020)
- [Data-Driven Control of Complex Networks](https://mlsanity.com/paper/2003.12189/) (2020)
- [Message Passing Neural Processes](https://mlsanity.com/paper/2009.13895/) (2020)
- [How Neural Processes Improve Graph Link Prediction](https://mlsanity.com/paper/2109.14894/) (2021)
- [Graph Neural Processes: Towards Bayesian Graph Neural Networks](https://mlsanity.com/paper/1902.10042/) (2019)
- [Enhanced spatio-temporal electric load forecasts using less data with active deep learning](https://mlsanity.com/paper/2012.04407/) (2020)
- [Conditional Graph Neural Processes: A Functional Autoencoder Approach](https://mlsanity.com/paper/1812.05212/) (2018)
- [Autoregressive GNN-ODE GRU Model for Network Dynamics](https://mlsanity.com/paper/2211.10594/) (2022)
- [Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks?](https://mlsanity.com/paper/2305.12185/) (2023)
- [Group Sparse Bayesian Learning for Active Surveillance on Epidemic Dynamics](https://mlsanity.com/paper/1712.00328/) (2017)

## Built on by (most cited first, 2 of 2)

- [Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression](https://mlsanity.com/paper/2411.06833/) (2024)
- [Structural Inference under Hidden Agents](https://mlsanity.com/paper/2609.18045/) (2026)

## Abstract (arXiv)

Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at learning network dynamic behaviors generated by a specific ordinary differential equation instance, resulting in ineffectiveness for new ones, and generally require dense observations. The observed data, especially from network emerging dynamics, are usually difficult to obtain, which brings trouble to model learning. Therefore, how to learn accurate network dynamics with sparse, irregularly-sampled, partial, and noisy observations remains a fundamental challenge. We introduce Neural ODE Processes for Network Dynamics (NDP4ND), a new class of stochastic processes governed by stochastic data-adaptive network dynamics, to overcome the challenge and learn continuous network dynamics from scarce observations. Intensive experiments conducted on various network dynamics in ecological population evolution, phototaxis movement, brain activity, epidemic spreading, and real-world empirical systems, demonstrate that the proposed method has excellent data adaptability and computational efficiency, and can adapt to unseen network emerging dynamics, producing accurate interpolation and extrapolation with reducing the ratio of required observation data to only about 6% and improving the learning speed for new dynamics by three orders of magnitude.