用端到端学习同时优化动力学模型与数据同化，提升稀疏观测下的建模鲁棒性。
Combined Optimization of Dynamics and Assimilation with End-to-End Learning on Sparse Observations
- 神经网络联合优化动力学参数与数据同化过程
- 可恢复初始状态并拟合未知参数，匹配观测与自洽约束
- 比传统方法更抗模型偏差，适合稀疏噪声数据场景
将非线性动力学模型拟合到稀疏且含噪的观测数据中具有根本性挑战。识别动力学需要数据同化（DA）来估计系统状态，但DA又依赖准确的动力学模型。为打破这一僵局，我们提出CODA——一种直接从稀疏含噪观测数据中联合学习动力学与数据同化的端到端优化方案。通过神经网络实现精确、高效且并行于时间的数据同化，同时优化动力系统中的自由参数。我们直接在观测数据上进行端到端学习，引入一种新颖的学习目标，结合了展开的自回归动力学与弱约束4Dvar DA中的数据一致性和自洽性项。通过考虑多个时间步中新旧模拟组件间的交互，CODA可恢复初始条件、拟合未知动力学参数，并学习基于神经网络的偏微分方程项，以同时匹配可用观测和自洽性约束。除了支持动力学的端到端学习并提供快速、摊销式、非序列化的数据同化外，相比经典方法，CODA对模型误设更具鲁棒性。
原文摘要 · Abstract (English)
Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this deadlock we present CODA, an end-to-end optimization scheme for jointly learning dynamics and DA directly from sparse and noisy observations. A neural network is trained to carry out data accurate, efficient and parallel-in-time DA, while free parameters of the dynamical system are simultaneously optimized. We carry out end-to-end learning directly on observation data, introducing a novel learning objective that combines unrolled auto-regressive dynamics with the data- and self-consistency terms of weak-constraint 4Dvar DA. By taking into account interactions between new and existing simulation components over multiple time steps, CODA can recover initial conditions, fit unknown dynamical parameters and learn neural network-based PDE terms to match both available observations and self-consistency constraints. In addition to facilitating end-to-end learning of dynamics and providing fast, amortized, non-sequential DA, CODA provides greater robustness to model misspecification than classical DA approaches.
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