用随机标签生成物理系统多路径轨迹，避免预测平均化。
Stochastic Lifting for Generating Trajectories of Stochastic Physical Systems
- 为状态转移附加高维随机标签，建模多可能未来。
- 单步网络评估即可生成多样轨迹，计算高效。
- 适合需要多样性模拟的物理系统建模任务。
许多随机物理系统随时间平滑演化，状态分布变化规律。当前状态到下一状态的转移常可建模为平滑映射与显式随机源的组合。随机提升方法通过在训练数据的状态转移中附加独立的高维随机标签，使用标准回归损失拟合从当前状态和标签到下一状态的转移映射。这些标签作为辅助坐标，使模型能从相似当前状态中表示多个合理下一状态，避免在有限样本下塌缩为均值预测。推理时，每一步采样新标签，通过自回归方式滚动前推，仅需每步一次网络评估即可生成多样化轨迹。
原文摘要 · Abstract (English)
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a smooth map and an explicit source of randomness. Stochastic Lifting exploits this structure by attaching an independent, high-dimensional random label to each state transition in the training data and fitting a transition map from the current state and label to the next state using a standard regression loss. The labels act as auxiliary coordinates that let the model represent multiple plausible next states from similar current states, avoiding collapse to a mean prediction in the finite-sample size regime. At inference, fresh labels are sampled at each time step and the learned map is rolled forward autoregressively, generating diverse trajectories with a single network evaluation per time step.
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