FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation
This addresses data assimilation for systems with unknown or partially known dynamics, such as weather forecasting, offering a more flexible alternative to traditional model-driven approaches.
The paper tackles the problem of data assimilation for PDE-governed systems where full knowledge of true dynamics is unavailable, introducing FlowDAS, a framework that uses stochastic interpolants to learn state transition dynamics step-by-step from data. Experiments on Lorenz-63, Navier-Stokes, and large-scale weather forecasting show it surpasses model-driven methods, neural operators, and score-based baselines in accuracy and physical plausibility.
Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in practice, while purely data-driven solvers learn a deterministic mapping between observations and states and therefore miss the intrinsic stochasticity of real processes. Recently, score-based diffusion models learn a global diffusion prior and provide a good modeling of the stochastic dynamics, showing new potential for DA. However, their all-at-once generation rather than step-by-step transition limits their performance when dealing with highly complex stochastic processes and lacks physical interpretability. To tackle these drawbacks, we introduce FlowDAS, a generative DA framework that uses stochastic interpolants to directly learn state transition dynamics and achieve step-by-step transition to better model the real dynamics. We also improve the framework by combining the observation, better suiting the DA settings. Directly learning the underlying dynamics from collected data removes restrictive dynamical assumptions, and conditioning on observations at each interpolation step yields stable, measurement-consistent forecasts. Experiments on Lorenz-63, Navier-Stokes super-resolution/sparse-observation scenarios, and large-scale weather forecasting -- where dynamics are partly or wholly unknown -- show that FlowDAS surpasses model-driven methods, neural operators, and score-based baselines in accuracy and physical plausibility.