# Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations

arXiv: https://arxiv.org/abs/2011.03880 · HTML: https://mlsanity.com/paper/2011.03880/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2020.

## Built on by (most cited first, 30 of 61)

- [Towards Better Dynamic Graph Learning: New Architecture and Unified Library](https://mlsanity.com/paper/2303.13047/) (2023)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
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- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases](https://mlsanity.com/paper/2308.13212/) (2023)
- [Multilingual Knowledge Graph Completion with Self-Supervised Adaptive Graph Alignment](https://mlsanity.com/paper/2203.14987/) (2022)
- [Generalizing Graph ODE for Learning Complex System Dynamics across Environments](https://mlsanity.com/paper/2307.04287/) (2023)
- [MTP-GO: Graph-Based Probabilistic Multi-Agent Trajectory Prediction with Neural ODEs](https://mlsanity.com/paper/2302.00735/) (2023)
- [A Survey on Graph Neural Network Acceleration: Algorithms, Systems, and Customized Hardware](https://mlsanity.com/paper/2306.14052/) (2023)
- [DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs](https://mlsanity.com/paper/2408.06966/) (2024)
- [CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2306.11216/) (2023)
- [Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series](https://mlsanity.com/paper/2410.14030/) (2024)
- [On latent dynamics learning in nonlinear reduced order modeling](https://mlsanity.com/paper/2408.15183/) (2024)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [BrainODE: Dynamic Brain Signal Analysis via Graph-Aided Neural Ordinary Differential Equations](https://mlsanity.com/paper/2405.00077/) (2024)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [Temporal Graph ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/2404.19508/) (2024)
- [HOT: Higher-Order Dynamic Graph Representation Learning with Efficient Transformers](https://mlsanity.com/paper/2311.18526/) (2023)
- [Towards Scene Graph Anticipation](https://mlsanity.com/paper/2403.04899/) (2024)
- [Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling](https://mlsanity.com/paper/2410.06366/) (2024)
- [Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs](https://mlsanity.com/paper/2305.12334/) (2023)
- [Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamics](https://mlsanity.com/paper/2312.11198/) (2023)
- [Causal Graph ODE: Continuous Treatment Effect Modeling in Multi-agent Dynamical Systems](https://mlsanity.com/paper/2403.00178/) (2024)
- [Temporal Graph Neural Networks for Irregular Data](https://mlsanity.com/paper/2302.08415/) (2023)
- [PGODE: Towards High-quality System Dynamics Modeling](https://mlsanity.com/paper/2311.06554/) (2023)
- [Concept2Box: Joint Geometric Embeddings for Learning Two-View Knowledge Graphs](https://mlsanity.com/paper/2307.01933/) (2023)
- [DuSEGO: Dual Second-order Equivariant Graph Ordinary Differential Equation](https://mlsanity.com/paper/2411.10000/) (2024)
- [Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs](https://mlsanity.com/paper/2205.11894/) (2022)
- [Stability-Informed Initialization of Neural Ordinary Differential Equations](https://mlsanity.com/paper/2311.15890/) (2023)

## Abstract (arXiv)

Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding and predicting the dynamics based on observed trajectories of objects become a critical research problem in many domains. Most existing algorithms, however, assume the observations are regularly sampled and all the objects can be fully observed at each sampling time, which is impractical for many applications. In this paper, we propose to learn system dynamics from irregularly-sampled partial observations with underlying graph structure for the first time. To tackle the above challenge, we present LG-ODE, a latent ordinary differential equation generative model for modeling multi-agent dynamic system with known graph structure. It can simultaneously learn the embedding of high dimensional trajectories and infer continuous latent system dynamics. Our model employs a novel encoder parameterized by a graph neural network that can infer initial states in an unsupervised way from irregularly-sampled partial observations of structural objects and utilizes neuralODE to infer arbitrarily complex continuous-time latent dynamics. Experiments on motion capture, spring system, and charged particle datasets demonstrate the effectiveness of our approach.