DAWIS: Data Assimilation with Windowed Inverse Sampling via Multitask Interpolants

2026-10-02

AI Summary

This study addresses the error accumulation problem in existing data assimilation filters, which cannot leverage new observations to correct historical states. To this end, we propose a unified framework integrating filtering and smoothing. Methodologically, efficient state estimation for high-dimensional non-Gaussian systems is achieved via windowed reverse sampling. Furthermore, we introduce a novel multi-task interpolator that assigns independent flow times, seamlessly incorporating forecasting into the assimilation cycle and enabling dynamic correction of historical states without requiring additional predictive models. The technical core relies on flow/diffusion generative models, inference-time guidance, and multi-task stochastic interpolation. Experimental results demonstrate that the proposed method significantly outperforms conventional baselines under nonlinear, sparse, and noisy observation conditions, effectively mitigating long-term error accumulation.

Abstract

Flow- and diffusion-based generative models have recently emerged as flexible and highly efficient forecasting models for dynamical systems. When combined with inference-time guidance, they offer a promising route to high-dimensional non-Gaussian data assimilation (DA), the problem of combining forecasts with observations to estimate latent system states. Existing filters, however, condition on a fixed history and assimilate only the most recent observation, leaving them unable to revise past states when new observations arrive. Estimates then stay tethered to a history that later observations may contradict, and errors accumulate over the assimilation run. To this end, we introduce **DAWIS**, a unified DA method covering filtering, fixed-lag smoothing, and block smoothing within a single framework. DAWIS replaces the single flow time of a state-level prior with a multitask stochastic interpolant over a window of consecutive states, assigning a separate flow time to each. An assimilation cycle inverts the window to a vector of per-state turning points and regenerates it under observation guidance, with the turning points controlling how strongly each state is held fixed, revised, or generated from scratch. The same construction can also absorb the forecast into the assimilation cycle, removing the need for a separate forecasting model. Experiments on challenging nonlinear systems show that DAWIS improves on both filtering and smoothing baselines under sparse, noisy, and nonlinear observations. The code for DAWIS is available at https://github.com/Erik-Wikingsson/DAWIS

Problem

• data assimilation
• dynamical systems
• filtering
• smoothing
• non-Gaussian

Innovation

• Data Assimilation
• Stochastic Interpolants
• Multitask Learning
• Generative Models
• Smoothing