arXiv subjects

Hristo G. Chipilski

Publications and source records attributed to Hristo G. Chipilski.

9 recordsLinked to original sources

arXiv2026

From Variational Optimization to Flow-Based Transport: Posterior-Geometry Regularization for Ill-Conditioned Data Assimilation

Variational data assimilation computes a Bayesian update through optimization on a fixed posterior geometry, whose conditioning is determined by the prior covariance and the observation operator. In strongly anisotropic, weakly observed, or highly informative regimes, this geometry can become severely ill conditioned, leading to substantial sensitivity to solver design and preconditioning. This work investigates an alternative computational route based on flow-based transport, using the ensemble score filter as a training-free realization. Rather than repeatedly optimizing over the full posterior geometry, the flow-based update transports the predictive distribution through a sequence of intermediate distributions whose covariance and curvature are progressively regularized before reaching the target posterior. In the linear-Gaussian setting, we characterize this mechanism through the evolution of the diffused posterior covariance and the associated time-dependent curvature, revealing a continuation from a near-isotropic reference geometry to the ill-conditioned posterior geometry targeted by variational assimilation. Numerical stress tests show that this geometric regularization makes the flow-based method substantially less sensitive to severe ill-conditioning than the variational method, while a heterogeneous $10^4$-dimensional Lorenz-96 benchmark demonstrates improved robustness and lower delivered computational cost. These results identify posterior-geometry regularization as a key mechanism distinguishing transport-based from optimization-based data assimilation.

math.NA↗

arXiv2026

Global Attention with Linear Complexity for Exascale Generative Data Assimilation in Earth System Prediction

Accurate Earth system prediction requires state inference from incomplete observations, but conventional two-stage data assimilation (DA) is computationally prohibitive because repeated PDE-based ensemble forecasts, observation updates, and intermediate data movement limit ensemble size at high resolution. We introduce STORM, a one-stage generative AI framework that reformulates DA as diffusion-based Bayesian posterior sampling, replacing online PDE ensemble forecasts with scalable AI inference. It further combines a spatiotemporal transformer with a global-attention algorithm that reduces complexity from quadratic to linear through scalable gradient propagation, enabling high-resolution, long-context Earth modeling. STORM scales to 74,400 GPUs on Frontier with 96--99\% strong-scaling efficiency and up to 6 ExaFLOPs sustained BF16 throughput, while enabling 32,768-member ensembles for uncertainty quantification in 34 seconds on 4,096 GPUs. It scales to 20 billion spatiotemporal tokens and 177,000 temporal frames. Hurricane tracking and long-term climate reanalysis demonstrate improved accuracy, including benefits from longer temporal context and recovery of temperature extremes missed by forecast-only predictions.

cs.LG↗

arXiv2026

A Two-Step Ensemble Score Filter for Data Assimilation in Partially Observed Systems

Data assimilation blends model forecasts with observations to estimate the evolving state of complex dynamical systems, but sparse observing networks remain challenging because unobserved state variables are not directly constrained by observations. In this work, we introduce the Ensemble Score Filter with Linear Regression (EnSF-LR), a two-step filtering method for partially observed nonlinear systems. At each analysis time, EnSF-LR first applies the Ensemble Score Filter (EnSF) to update the observed state components using a nonlinear score-based analysis update. It then computes the resulting observed-state analysis increments and maps these corrections to the unobserved components through the ensemble-based prior covariance matrix. The latter amounts to the same linear regression mechanism used by Ensemble Kalman Filters (EnKFs). We evaluate EnSF-LR using the Lorenz-63 and 40-dimensional Lorenz-96 systems with sparse linear and nonlinear observations. The method is compared with the original EnSF and with the classical stochastic EnKF. In the linear-observation experiments, EnSF-LR produces accuracy comparable to the EnKF baseline while substantially reducing error relative to the original EnSF. In the nonlinear-observation experiments, EnSF-LR achieves lower full-state root-mean-square error than both the original EnSF and the EnKF reference. These results suggest that hybridizing score-based and EnKF analysis schemes provides an effective strategy for assimilating sparse and nonlinear observations.

physics.ao-ph↗

arXiv2026

Two Localization Strategies for Sequential MCMC Data Assimilation with Applications to Nonlinear Non-Gaussian Geophysical Models

We present a localized data assimilation (DA) scheme based on the sequential Markov Chain Monte Carlo (SMCMC) technique [Ruzayqat et al., 2024], a provably convergent method for filtering high-dimensional, nonlinear, and potentially non-Gaussian state-space models. Unlike particle filters, which are exact methods for nonlinear non-Gaussian models, SMCMC does not assign weights to samples and therefore avoids weight degeneracy in small-ensemble regimes. We design two localization approaches within the SMCMC framework that exploit spatial sparsity of observations to reduce the effective degrees of freedom and improve efficiency. The first variant collects observed blocks into a single reduced domain and runs parallel MCMC chains over this combined region. The second variant further reduces the per-chain state dimension by decomposing the observed region into independent blocks, each augmented with a compact halo, and applying Gaspari--Cohn observation-noise tapering to smoothly down-weight distant observations. When the observation model is linear and Gaussian, we show that our approximate filtering density reduces to a Gaussian mixture from which independent samples can be drawn exactly. For nonlinear or non-Gaussian observation models, we employ an MCMC kernel. We test on high-dimensional ($d \sim 10^4 - 10^5$) state-space models, including a linear Gaussian model and a nonlinear multilayer shallow water equation with both linear and nonlinear observation operators. We consider Gaussian and non-Gaussian (Student-$t$) observation noise, showing that LSMCMC naturally handles heavy-tailed errors that cause ensemble Kalman methods to diverge. Observations include synthetic and real data from the Surface Water and Ocean Topography (SWOT) mission (NASA) and ocean drifter data (NOAA). We compare the two variants against each other and the local ensemble transform Kalman filter (LETKF).

stat.CO↗

arXiv2025

On the sensitivity of different ensemble filters to the type of assimilated observation networks

Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods depends on the observation network characteristics. In this study, we present initial experiments with the surface quasi-geostrophic model, in which we compare a recently developed AI-based ensemble filter with the standard Local Ensemble Transform Kalman Filter (LETKF). Our results show that the analysis solutions respond differently to the number, spatial distribution, and nonlinear fraction of assimilated observations. We also find notable changes in the multiscale characteristics of the analysis errors. Given that standard DA techniques will be eventually replaced by more advanced methods, we hope this study sets the ground for future efforts to reassess the value of Earth observation systems in the context of newly emerging algorithms.

physics.ao-ph↗

arXiv2025

Exact nonlinear state estimation

The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric, particle-based DA algorithms have superior accuracy, but their application to high-dimensional models still poses operational challenges. Drawing inspiration from recent advances in the field of generative artificial intelligence (AI), this article introduces a new nonlinear estimation theory which attempts to bridge the existing gap in DA methodology. Specifically, a Conjugate Transform Filter (CTF) is derived and shown to generalize the celebrated Kalman filter to arbitrarily non-Gaussian distributions. The new filter has several desirable properties, such as its ability to preserve statistical relationships in the prior state and convergence to highly accurate observations. An ensemble approximation of the new theory (ECTF) is also presented and validated using idealized statistical experiments that feature bounded quantities with non-Gaussian distributions, a prevalent challenge in Earth system models. Results from these experiments indicate that the greatest benefits from ECTF occur when observation errors are small relative to the forecast uncertainty and when state variables exhibit strong nonlinear dependencies. Ultimately, the new filtering theory offers exciting avenues for improving conventional DA algorithms through their principled integration with AI techniques.

stat.ME↗

arXiv2025

Ensemble score filter with image inpainting for data assimilation in tracking surface quasi-geostrophic dynamics with partial observations

Data assimilation plays a pivotal role in understanding and predicting turbulent systems within geoscience and weather forecasting, where data assimilation is used to address three fundamental challenges, i.e., high-dimensionality, nonlinearity, and partial observations. Recent advances in machine learning (ML)-based data assimilation methods have demonstrated encouraging results. In this work, we develop an ensemble score filter (EnSF) that integrates image inpainting to solve the data assimilation problems with partial observations. The EnSF method exploits an exclusively designed training-free diffusion models to solve high-dimensional nonlinear data assimilation problems. Its performance has been successfully demonstrated in the context of having full observations, i.e., all the state variables are directly or indirectly observed. However, because the EnSF does not use a covariance matrix to capture the dependence between the observed and unobserved state variables, it is nontrivial to extend the original EnSF method to the partial observation scenario. In this work, we incorporate various image inpainting techniques into the EnSF to predict the unobserved states during data assimilation. At each filtering step, we first use the diffusion model to estimate the observed states by integrating the likelihood information into the score function. Then, we use image inpainting methods to predict the unobserved state variables. We demonstrate the performance of the EnSF with inpainting by tracking the Surface Quasi-Geostrophic (SQG) model dynamics under a variety of scenarios. The successful proof of concept paves the way to more in-depth investigations on exploiting modern image inpainting techniques to advance data assimilation methodology for practical geoscience and weather forecasting problems.

physics.ao-ph↗

arXiv2024

A Scalable Real-Time Data Assimilation Framework for Predicting Turbulent Atmosphere Dynamics

The weather and climate domains are undergoing a significant transformation thanks to advances in AI-based foundation models such as FourCastNet, GraphCast, ClimaX and Pangu-Weather. While these models show considerable potential, they are not ready yet for operational use in weather forecasting or climate prediction. This is due to the lack of a data assimilation method as part of their workflow to enable the assimilation of incoming Earth system observations in real time. This limitation affects their effectiveness in predicting complex atmospheric phenomena such as tropical cyclones and atmospheric rivers. To overcome these obstacles, we introduce a generic real-time data assimilation framework and demonstrate its end-to-end performance on the Frontier supercomputer. This framework comprises two primary modules: an ensemble score filter (EnSF), which significantly outperforms the state-of-the-art data assimilation method, namely, the Local Ensemble Transform Kalman Filter (LETKF); and a vision transformer-based surrogate capable of real-time adaptation through the integration of observational data. The ViT surrogate can represent either physics-based models or AI-based foundation models. We demonstrate both the strong and weak scaling of our framework up to 1024 GPUs on the Exascale supercomputer, Frontier. Our results not only illustrate the framework's exceptional scalability on high-performance computing systems, but also demonstrate the importance of supercomputers in real-time data assimilation for weather and climate predictions. Even though the proposed framework is tested only on a benchmark surface quasi-geostrophic (SQG) turbulence system, it has the potential to be combined with existing AI-based foundation models, making it suitable for future operational implementations.

cs.LG↗

arXiv2024

Nonlinear ensemble filtering with diffusion models: Application to the surface quasi-geostrophic dynamics

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed \textit{Ensemble Score Filter (EnSF)} is completely training-free and can efficiently generate a set of analysis ensemble members. In this study, we apply the EnSF to a surface quasi-geostrophic model and compare its performance against the popular Local Ensemble Transform Kalman Filter (LETKF), which makes Gaussian assumptions on the posterior distribution. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that EnSF achieves competitive performance relative to LETKF in the case of linear observations, but leads to significant advantages when the state is nonlinearly observed and the numerical model is subject to unexpected shocks. A spectral decomposition of the analysis results shows that the largest improvements over LETKF occur at large scales (small wavenumbers) where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity is very encouraging, and motivates further developments of the algorithm for more realistic problems.

math-ph↗