# PGODE: Towards High-quality System Dynamics Modeling

arXiv: https://arxiv.org/abs/2311.06554 · HTML: https://mlsanity.com/paper/2311.06554/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 73 of its 105 references that are in the map.
- First posted on arXiv 11 Nov 2023.

## Builds on (most cited first, 30 of 73)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [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)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [COMBO: Conservative Offline Model-Based Policy Optimization](https://mlsanity.com/paper/2102.08363/) (2021)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2005.08514/) (2020)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)

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

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation](https://mlsanity.com/paper/2505.18647/) (2025)
- [System-Aware Neural ODE Processes for Few-Shot Bayesian Optimization](https://mlsanity.com/paper/2406.02352/) (2024)
- [Graph Fourier Neural ODEs: Modeling Spatial-temporal Multi-scales in Molecular Dynamics](https://mlsanity.com/paper/2411.01600/) (2024)
- [DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEs](https://mlsanity.com/paper/2603.01762/) (2026)
- [Learning System Dynamics without Forgetting](https://mlsanity.com/paper/2407.00717/) (2024)
- [Generalizing Dynamics Modeling More Easily from Representation Perspective](https://mlsanity.com/paper/2603.22655/) (2026)

## Abstract (arXiv)

This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are then captured by powerful graph neural networks (GNNs). However, predicting interacting dynamics in challenging scenarios such as out-of-distribution shift and complicated underlying rules remains unsolved. In this paper, we propose a new approach named Prototypical Graph ODE (PGODE) to address the problem. The core of PGODE is to incorporate prototype decomposition from contextual knowledge into a continuous graph ODE framework. Specifically, PGODE employs representation disentanglement and system parameters to extract both object-level and system-level contexts from historical trajectories, which allows us to explicitly model their independent influence and thus enhances the generalization capability under system changes. Then, we integrate these disentangled latent representations into a graph ODE model, which determines a combination of various interacting prototypes for enhanced model expressivity. The entire model is optimized using an end-to-end variational inference framework to maximize the likelihood. Extensive experiments in both in-distribution and out-of-distribution settings validate the superiority of PGODE compared to various baselines.