用贝叶斯元学习建模动态系统，适应环境变化时仍保持高精度预测。
MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts
- 基于矩阵正态逆威沙特先验，实现对科普曼算子的闭式贝叶斯更新
- 在多种冬季极端工况下，多步预测误差降低18.7%，不确定性校准更优
- 适合自动驾驶、机器人等需应对分布偏移的实时控制场景
在分布偏移条件下建模与预测非线性动态是实现真实系统稳健决策的关键。本文提出MetaKoopman，一种基于贝叶斯元学习的框架，通过线性潜在表示建模非线性动态。该方法在科普曼算子上学习矩阵正态-逆威沙特（MNIW）先验，可基于近期轨迹段进行闭式贝叶斯更新，并提供未来状态轨迹的闭式后验预测分布，同时捕捉认知不确定性与随机不确定性。我们在全尺度自主卡车-挂车系统上评估了MetaKoopman，涵盖雪、冰及混合摩擦等多种严苛冬季场景，以及具有多样化分布偏移的模拟控制任务。结果表明，其在多步预测准确率、不确定性校准和分布偏移鲁棒性方面持续优于现有方法。实地实验进一步验证其在急避让与牵引极限工况下实现动态可行运动规划的有效性。
原文摘要 · Abstract (English)
Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose MetaKoopman, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (MNIW) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios, including snow, ice, and mixed-friction conditions, as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration, and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: https://mahmoud-selim.github.io/MetaKoopman/
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