为什么我们应当基于过去观测窗口对去噪扩散生成模型进行条件化

中文摘要 AI 辅助

数据同化（DA）传统上是一个循环过程，依赖于随时间变化的先验，将过去观测的信息传播到未来的循环中。使用去噪扩散生成模型进行数据同化具有挑战性，因为标准方法使用固定的训练数据集，这导致静态先验忽略了来自过去观测的信息。由于过去观测被忽略，具有静态先验的数据同化系统比循环数据同化系统产生更大的后验误差。然而，将随时间变化的先验纳入生成模型需要昂贵且频繁的重新训练。受线性系统理论的启发——其中卡尔曼滤波预测对过去观测的依赖呈指数衰减——我们对扩散模型基于过去观测的短窗口进行条件化。具体而言，我们描述了两种框架的训练过程：一种扩散数据同化系统，根据一组过去观测预测当前状态；以及一种扩散“直接观测预测”（DOP）系统，根据一组过去观测预测未来观测。使用一个典型线性系统，我们表明，只要时间窗口足够长，两种系统都能达到完全循环数据同化/DOP系统的最小后验误差特征，而无需重新训练。线性设置确保了解析可处理性，避免了混淆神经网络训练误差，并确认了基于过去观测窗口的条件化对于高效准确的基于扩散的数据同化或直接观测预测是必需的。

英文摘要

Data assimilation (DA) is, traditionally, a cycling process that relies on time-dependent priors to propagate information from past observations to future cycles. Using denoising diffusion generative modeling for DA is challenging because standard approaches use a fixed training data set, which in turn leads to a static prior that ignores information from past observations. Because past observations are ignored, DA systems with static priors lead to larger posterior errors than cycling DA systems. Incorporating time-dependent priors into generative models, however, requires expensive and frequent retraining. Motivated by linear systems theory - where the dependence of a prediction of a Kalman filter on past observations decays exponentially - we condition diffusion models on short windows of past observations. Specifically, we describe training procedures for two frameworks: a diffusion DA system predicting the current state given a set of past observations, and a diffusion ``direct observation prediction'' (DOP) system, predicting future observations given a set of past observations. Using a canonical linear system, we show that both systems can achieve the minimal posterior error characteristic of a fully-cycled DA/DOP system, without re-training, provided the time windows are long enough. The linear setup ensures analytical tractability, avoids confounding neural network training errors, and confirms that conditioning on windows of past observations is required for efficient and accurate diffusion-based DA or DOP.

发表机构

• Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California, San Diego（西克利普斯海洋学院，加利福尼亚大学圣地亚哥分校）
• U.S. Naval Research Laboratory（美国海军研究实验室）

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