A Liouville Equation-Based Hybrid Method for Uncertainty-Aware Vehicle Motion Prediction
Abstract
Robust prediction of the uncertain motion states of surrounding vehicles remains a fundamental challenge in autonomous driving. To address this challenge, we introduce the Liouville Equation (LE) into motion prediction to characterize the evolution of uncertain states governed by probability conservation, and propose a hybrid mechanism-learning paradigm. Specifically, we establish the LE as the mechanistic framework to ensure the physical consistency of state evolution. To provide the required dynamic driving force within this framework, we design a Transformer-based architecture to learn an adaptive context-conditioned state vector field (SVF), thereby overcoming the limitations of purely mechanistic methods in capturing system dynamics under complex driving scenarios. During the LE-based evolution of uncertain motion states, the learned SVF governs their geometric transport in the state space, while the divergence of the SVF dynamically adjusts the probabilistic weight associated with each motion state. Experimental results on both simulation and real-world data demonstrate that the proposed method achieves robust prediction performance, effectively captures potential collision risks, and thereby improves the safety of downstream planned trajectories.