Graph neural networks are often used to model interacting dynamical systems
since they gracefully scale to systems with a varying and high number of
agents. While there has been much progress made for deterministic interacting
systems, modeling is much more challenging for stochastic systems in which one
is interested in obtaining a predictive distribution over future trajectories.
Existing methods are either computationally slow since they rely on Monte Carlo
sampling or make simplifying assumptions such that the predictive distribution
is unimodal. In this work, we present a deep state-space model which employs
graph neural networks in order to model the underlying interacting dynamical
system. The predictive distribution is multimodal and has the form of a
Gaussian mixture model, where the moments of the Gaussian components can be
computed via deterministic moment matching rules. Our moment matching scheme
can be exploited for sample-free inference, leading to more efficient and
stable training compared to Monte Carlo alternatives. Furthermore, we propose
structured approximations to the covariance matrices of the Gaussian components
in order to scale up to systems with many agents. We benchmark our novel
framework on two challenging autonomous driving datasets. Both confirm the
benefits of our method compared to state-of-the-art methods. We further
demonstrate the usefulness of our individual contributions in a carefully
designed ablation study and provide a detailed runtime analysis of our proposed
covariance approximations. Finally, we empirically demonstrate the
generalization ability of our method by evaluating its performance on unseen
scenarios.

本文提出了一种基于图神经网络的深度状态空间模型，用于建模交互式动态系统，且预测分布为多峰高斯混合模型，同时提出了结构化的协方差近似方法，可以适用于具有多个智能体的系统，并在自动驾驶数据集上进行了测试并与现有技术进行了比较。

交互动力系统的深度状态空间模型的廉价和确定性推理

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

We address the problem of forecasting pedestrian and vehicle trajectories in
unknown environments, conditioned on their past motion and scene structure.
Trajectory forecasting is a challenging problem due to the large variation in
scene structure and the multimodal distribution of future trajectories. Unlike
prior approaches that directly learn one-to-many mappings from observed context
to multiple future trajectories, we propose to condition trajectory forecasts
on plans sampled from a grid based policy learned using maximum entropy inverse
reinforcement learning (MaxEnt IRL). We reformulate MaxEnt IRL to allow the
policy to jointly infer plausible agent goals, and paths to those goals on a
coarse 2-D grid defined over the scene. We propose an attention based
trajectory generator that generates continuous valued future trajectories
conditioned on state sequences sampled from the MaxEnt policy. Quantitative and
qualitative evaluation on the publicly available Stanford drone and NuScenes
datasets shows that our model generates trajectories that are diverse,
representing the multimodal predictive distribution, and precise, conforming to
the underlying scene structure over long prediction horizons.

本文介绍一种基于最大熵逆强化学习 (MaxEnt IRL) 的计划采样方法，以提高对未知环境下行人和车辆运动轨迹的准确性和多样性，同时考虑多模式预测分布和场景结构的影响。在 Stanford drone 和 NuScenes 数据集上的实验表明，所提出的轨迹生成方法能够生成符合复杂场景结构的多元精确预测轨迹。