Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations

TL;DR

This paper introduces LG-ODE, a novel model that learns continuous system dynamics from irregular, partial observations of multi-agent systems with known graph structures, overcoming limitations of regular sampling assumptions.

Contribution

It is the first to learn system dynamics from irregularly-sampled partial data using a graph neural network and neural ODEs for multi-agent systems.

Findings

Effective on motion capture, spring, and charged particle datasets.

Outperforms existing methods in modeling complex dynamics.

Learns high-dimensional trajectories and latent dynamics simultaneously.

Abstract

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.