DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants

TL;DR

DAISI introduces a scalable, generative-model-based data assimilation method that effectively handles complex, nonlinear, and noisy systems by combining inverse sampling with guidance-based conditional sampling.

Contribution

The paper presents DAISI, a novel filtering algorithm that uses flow-based generative models and inverse sampling to improve data assimilation in complex systems.

Findings

DAISI outperforms traditional methods on nonlinear systems.

It effectively handles sparse and noisy observations.

The approach is scalable and does not require retraining at each step.

Abstract

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical high-dimensional DA methods, such as the ensemble Kalman filter, rely on Gaussian approximations that are violated for complex dynamics or observation operators. To address this limitation, we introduce DAISI, a scalable filtering algorithm built on flow-based generative models that enables flexible probabilistic inference using data-driven priors. The core idea is to use a stationary, pre-trained generative prior that first incorporates forecast information through a novel inverse-sampling step, before assimilating observations via guidance-based conditional sampling. This allows us to leverage any forecasting model as part of the DA pipeline without having to retrain or fine-tune the generative prior at each assimilation step. Experiments on challenging nonlinear systems show that DAISI achieves accurate filtering results in regimes with sparse, noisy, and nonlinear observations where traditional methods struggle.