发表机构
Inria Paris; DI ENS; PSL Research University; Renault Group（巴黎Inria研究所; 巴黎高等师范学校计算机科学系; 巴黎文理研究大学; 雷诺集团）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出EnJoi，一种基于扩散模型的数据同化算法，通过学习联合状态分布并改进En4DVar，动态平衡当前状态与观测置信度，在稀疏非均匀观测下提升重建性能。
AI 中文摘要
数据同化（DA）旨在恢复仅被部分观测的动态系统的完整状态。一种解决方案是使用基于分数的模型来生成与观测一致的物理上合理的轨迹。这些自回归扩散模型通过基于先前状态的条件进行训练；然而，它们并未考虑其过去预测的不确定性。我们提出了一种新的基于扩散的同化算法，该算法动态平衡当前状态与新观测之间的置信度。关键在于，我们选择学习包含过去和未来的联合状态的分布。这使得我们能够使用En4DVar的改进版本，En4DVar是一种经典的数据同化算法，依赖于粒子集成的协方差。在流体和交通流模拟上的实验表明，重建性能得到了改善，尤其是在观测稀疏且非均匀的情况下。
英文摘要
Data Assimilation (DA) aims to recover the full state of a dynamical system that is only partially observed. A solution is to use Score-based models to generate physically consistent trajectories that agree with the observations. These Autoregressive Diffusion models are trained by conditioning on the previous state; however, they do not take into account the uncertainty of their past predictions. We propose a new diffusion-based assimilation algorithm that dynamically balances the confidence in the current state and the new observations. Crucially, we choose to learn the distribution of the joint state containing both the past and future. This allows us to use a modified version of En4DVar, a classical DA algorithm that relies on the covariance of an ensemble of particles. Experiments on fluid and traffic flow simulations show improved reconstruction performance, especially in situations where observations are sparse and non-homogeneous.
