Score-based Data Assimilation
This addresses the data assimilation bottleneck for complex systems such as climate modeling, though it is incremental as it builds on existing score-based generative models.
The paper tackles the problem of identifying plausible state trajectories from noisy observations in stochastic dynamical systems, which is intractable for long horizons or high-dimensional systems like oceans, by introducing a score-based data assimilation method that learns a generative model and achieves inference in a non-autoregressive manner with zero-shot observation capabilities.
Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have been proposed to solve this problem, including particle-based and variational methods. However, most algorithms depend on the transition dynamics for inference, which becomes intractable for long time horizons or for high-dimensional systems with complex dynamics, such as oceans or atmospheres. In this work, we introduce score-based data assimilation for trajectory inference. We learn a score-based generative model of state trajectories based on the key insight that the score of an arbitrarily long trajectory can be decomposed into a series of scores over short segments. After training, inference is carried out using the score model, in a non-autoregressive manner by generating all states simultaneously. Quite distinctively, we decouple the observation model from the training procedure and use it only at inference to guide the generative process, which enables a wide range of zero-shot observation scenarios. We present theoretical and empirical evidence supporting the effectiveness of our method.