Deep Generative Models For Stochastic Multi--Object Dynamical Systems

Real-world dynamical systems often consist of multiple stochastic objects that inter-act with each other.Modeling and forecasting the behavior of such dynamics are gener-ally not easy,due to the inherent hardness in understanding the complicated interactions and evolutions of their constituents.In this work,we introduce two approaches that de-sign deep generative models(DGMs)empowered by graph neural networks(GNNs)for multi-object dynamics modeling.For the first approach,we propose the relational state-space model(R-SSM),which simulates the joint state transitions of multiple correlated objects with GNNs.For the second approach,we propose the CGNF-IT(conditional graph normalizing flow for interacting trajectories)model,which model the joint distri-bution of multistep trajectories using normalizing flows and run GNNs parallel-in-time to capture the correlation among objects.By tightly connecting GNNs and DGMs,R-SSM provides a flexible way to incorporate relational information into the modeling of multi-object dynamics,and CGNF-IT enables efficiently predicting multistep trajecto-ries of interacting objects in a joint manner.The effectiveness of R-SSM and CGNF-IT is empirically evaluated on synthetic and real time series datasets.