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Graph neural networks are often used to model interacting dynamical systemssince they gracefully scale to systems with a varying and high number ofagents. While there has been much progress made for deterministic interactingsystems, modeling is much more challenging for stochastic systems in which oneis interested in obtaining a predictive distribution over future trajectories.Existing methods are either computationally slow since they rely on Monte Carlosampling or make simplifying assumptions such that the predictive distributionis unimodal. In this work, we present a deep state-space model which employsgraph neural networks in order to model the underlying interacting dynamicalsystem. The predictive distribution is multimodal and has the form of aGaussian mixture model, where the moments of the Gaussian components can becomputed via deterministic moment matching rules. Our moment matching schemecan be exploited for sample-free inference, leading to more efficient andstable training compared to Monte Carlo alternatives. Furthermore, we proposestructured approximations to the covariance matrices of the Gaussian componentsin order to scale up to systems with many agents. We benchmark our novelframework on two challenging autonomous driving datasets. Both confirm thebenefits of our method compared to state-of-the-art methods. We furtherdemonstrate the usefulness of our individual contributions in a carefullydesigned ablation study and provide a detailed runtime analysis of our proposedcovariance approximations. Finally, we empirically demonstrate thegeneralization ability of our method by evaluating its performance on unseenscenarios.

Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systems