Learning multi-agent dynamics is a core AI problem with broad applications in robotics and autonomous driving. While most existing works focus on deterministic prediction, producing probabilistic forecasts to quantify uncertainty and assess risks is critical for downstream decision-making tasks such as motion planning and collision avoidance. Multi-agent dynamics often contains internal symmetry. By leveraging symmetry, specifically rotation equivariance, we can improve not only the prediction accuracy but also uncertainty calibration. We introduce Energy Score, a proper scoring rule, to evaluate probabilistic predictions. We propose a novel deep dynamics model, Probabilistic Equivariant Continuous COnvolution (PECCO) for probabilistic prediction of multi-agent trajectories. PECCO extends equivariant continuous convolution to model the joint velocity distribution of multiple agents. It uses dynamics integration to propagate the uncertainty from velocity to position. On both synthetic and real-world datasets, PECCO shows significant improvements in accuracy and calibration compared to non-equivariant baselines.

翻译：学习多智能体动力学是一个核心的人工智能问题，广泛应用于机器人技术和自动驾驶领域。现有工作大多侧重于确定性预测，而生成概率性预测以量化不确定性和评估风险，对于运动规划、碰撞避免等下游决策任务至关重要。多智能体动力学通常包含内部对称性，通过利用对称性（特别是旋转等变性），我们不仅能提升预测准确性，还能改善不确定性校准效果。本文引入能量评分（Energy Score）这一恰当评分规则来评估概率预测，并提出一种新颖的深度动力学模型——概率等变连续卷积（Probabilistic Equivariant Continuous COnvolution, PECCO），用于多智能体轨迹的概率预测。PECCO将等变连续卷积扩展至多智能体联合速度分布的建模，并通过动力学积分将不确定性从速度传播至位置。在合成数据集和真实世界数据集上，与非等变基线方法相比，PECCO在准确性和校准效果方面均表现出显著提升。