让数据同化算法自动学习状态、动力学和参数，提升精度与适应性。
Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms
- 通过自动微分联合优化状态、动力学与滤波器参数。
- 在航空航天、气象、生物系统上均实现更优估计性能。
- 适合需高精度建模且有观测噪声的科研与工程场景。
数据同化算法从部分观测中估计动态系统的状态，其性能高度依赖于昂贵的参数调优和精确的动力学模型。本文提出一种自可微滤波框架，通过梯度优化联合学习状态、动力学及滤波算法参数。该框架基于理论驱动的损失函数，利用自动微分从部分、含噪观测中进行学习。我们进一步展示了多个经典数据同化方法可在该框架下被学习或调优。为验证其通用性，我们在多个科学领域动态系统上开展实验，包括航空航天中的Clohessy-Wiltshire方程、大气科学中的Lorenz-96系统以及系统生物学中的广义Lotka-Volterra方程。最后，为实践者提供定制框架的指导，可根据观测模型、精度要求与计算预算灵活调整。
原文摘要 · Abstract (English)
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics. This paper introduces a framework for jointly learning the state, dynamics, and parameters of filtering algorithms in data assimilation through a process we refer to as auto-differentiable filtering. The framework leverages a theoretically motivated loss function that enables learning from partial, noisy observations via gradient-based optimization using auto-differentiation. We further demonstrate how several well-known data assimilation methods can be learned or tuned within this framework. To underscore the versatility of auto-differentiable filtering, we perform experiments on dynamical systems spanning multiple scientific domains, such as the Clohessy-Wiltshire equations from aerospace engineering, the Lorenz-96 system from atmospheric science, and the generalized Lotka-Volterra equations from systems biology. Finally, we provide guidelines for practitioners to customize our framework according to their observation model, accuracy requirements, and computational budget.
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