  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.

Machine Learning;Machine Learning