发表机构
Institute for Functional Intelligent Materials; National University of Singapore; School of Mathematical Sciences（功能智能材料研究所; 新加坡国立大学; 数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对多对一、隐式等复杂观测机制下的数据同化问题，提出集成控制流滤波器（EnCF），通过随机控制流及伴随匹配学习依赖观测的控制，该方法在处理非高斯等复杂观测模型时表现更佳。
AI 中文摘要
数据同化从模型预测和传入观测中估计动态系统的状态。然而，许多观测机制是多对一、隐式、非光滑的，或只能通过模拟访问，且无需提供现有集成滤波器所需的残差结构或似然引导。我们引入隐式数据同化，其中分析律被定义为预测分布的能量倾斜。然后我们提出集成控制流滤波器（EnCF），它通过随机控制流实现此更新，并通过终端能量梯度的伴随匹配学习依赖观测的控制。对于模拟器定义的观测，EnCF-LF从样本中学习替代条件能量并应用相同的控制流求解器。我们证明了理想精确性，推导了一步误差分解，并在滤波器稳定性下建立了局部误差的非累积性。数值结果表明，对于光滑加性高斯观测，卡尔曼型滤波器仍然更可取，而所提出的方法更适合非高斯、多对一、多模态和隐式观测模型。
英文摘要
Data assimilation estimates the state of a dynamical system from model forecasts and incoming observations. Many observation mechanisms, however, are many-to-one, implicit, non-smooth, or accessible only through simulation, and need not provide the residual structures or likelihood guidance required by existing ensemble filters. We introduce implicit data assimilation, in which the analysis law is defined as an energy tilt of the forecast distribution. We then propose the Ensemble Controlled-flow Filter (EnCF), which realizes this update through a stochastic controlled flow and learns the observation-dependent control by adjoint matching from terminal energy gradients. For simulator-defined observations, EnCF-LF learns a surrogate conditional energy from samples and applies the same controlled-flow solver. We prove ideal exactness, derive a one-step error decomposition, and establish non-accumulation of local errors under filter stability. Numerical results show that Kalman-type filters remain preferable for smooth additive-Gaussian observations, while the proposed methods are better suited to non-Gaussian, many-to-one, multimodal, and implicit observation models.
Comments26 pages
