Tootfinder

This https://arxiv.org/abs/2501.16642 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation
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 goo…

This https://arxiv.org/abs/2407.11746 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Sparse data assimilation for under-resolved large-eddy simulations
The need for accurate and fast scale-resolving simulations of fluid flows, where turbulent dispersion is a crucial physical feature, is evident. Large-eddy simulations (LES) are computationally more affordable than direct numerical simulations, but their accuracy depends on sub-grid scale models and the quality of the computational mesh. In order to compensate related errors, a data assimilation approach for LES is devised in this work. The presented method is based on variational assimilatio…

Using Diffusion Models to do Data Assimilation
Daniel Hodyss, Matthias Morzfeld
https://arxiv.org/abs/2506.02249 https://arxiv.org/pd…

Using Diffusion Models to do Data Assimilation
The recent surge in machine learning (ML) methods for geophysical modeling has raised the question of how these same ML methods might be applied to data assimilation (DA). We focus on diffusion modeling (a form of generative artificial intelligence) and on systems that can perform the entire DA, rather than on ML-based tools that are used within an otherwise conventional DA system. We explain that there are (at least) three different types of diffusion-based DA systems and we show in detail tha…

This https://arxiv.org/abs/2506.03947 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Block Alpha-Circulant Preconditioners for All-at-Once Diffusion-Based Covariance Operators
Covariance matrices are central to data assimilation and inverse methods derived from statistical estimation theory. Previous work has considered the application of an all-at-once diffusion-based representation of a covariance matrix operator in order to exploit inherent parallellism in the underlying problem. In this paper, we provide practical methods to apply block $α$-circulant preconditioners to the all-at-once system for the case where the main diffusion operation matrix cannot be readil…

This https://arxiv.org/abs/2411.13443 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonlinear Assimilation via Score-based Sequential Langevin Sampling
This paper presents score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed method decomposes the assimilation process into alternating prediction and update steps, leveraging dynamic models for state prediction while incorporating observational data through score-based Langevin Monte Carlo during updates. To address challenges in posterior sampling, we introduce an annealing strategy within t…

This https://arxiv.org/abs/2303.00847 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Analysis of Four-Dimensional Variational Data Assimilation Problems in Low Regularity Spaces
We carry out a rigorous analysis of four-dimensional variational data assimilation ($4D$-VAR) problems for linear and semilinear parabolic partial differential equations. Continuity of the state with respect to the spatial variable is required since pointwise observations of the state variable appear in the cost functional. Using maximal parabolic regularity tools, we prove this regularity for initial conditions with $L^β$-regularity guaranteed by control constraints, rather than Sobolev regul…

Ocean-E2E: Hybrid Physics-Based and Data-Driven Global Forecasting of Extreme Marine Heatwaves with End-to-End Neural Assimilation
Ruiqi Shu, Yuan Gao, Hao Wu, Ruijian Gou, Yanfei Xiang, Fan Xu, Qingsong Wen, Xian Wu, Xiaomeng Huang
https://arxiv.org/abs/2505.22071

Ocean-E2E: Hybrid Physics-Based and Data-Driven Global Forecasting of Extreme Marine Heatwaves with End-to-End Neural Assimilation
This work focuses on the end-to-end forecast of global extreme marine heatwaves (MHWs), which are unusually warm sea surface temperature events with profound impacts on marine ecosystems. Accurate prediction of extreme MHWs has significant scientific and financial worth. However, existing methods still have certain limitations, especially in the most extreme MHWs. In this study, to address these issues, based on the physical nature of MHWs, we created a novel hybrid data-driven and numerical MH…

This https://arxiv.org/abs/2303.00847 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Analysis of Four-Dimensional Variational Data Assimilation Problems in Low Regularity Spaces
We carry out a rigorous analysis of four-dimensional variational data assimilation ($4D$-VAR) problems for linear and semilinear parabolic partial differential equations. Continuity of the state with respect to the spatial variable is required since pointwise observations of the state variable appear in the cost functional. Using maximal parabolic regularity tools, we prove this regularity for initial conditions with $L^β$-regularity guaranteed by control constraints, rather than Sobolev regul…

Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences
Jing-An Sun, Hang Fan, Junchao Gong, Ben Fei, Kun Chen, Fenghua Ling, Wenlong Zhang, Wanghan Xu, Li Yan, Pierre Gentine, Lei Bai
https://arxiv.org/abs/2505.22008

Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences
Data assimilation (DA) aims to estimate the full state of a dynamical system by combining partial and noisy observations with a prior model forecast, commonly referred to as the background. In atmospheric applications, this problem is fundamentally ill-posed due to the sparsity of observations relative to the high-dimensional state space. Traditional methods address this challenge by simplifying background priors to regularize the solution, which are empirical and require continual tuning for a…

Diff-FlowFSI: A GPU-Optimized Differentiable CFD Platform for High-Fidelity Turbulence and FSI Simulations
Xiantao Fan, Xinyang Liu, Meng Wang, Jian-Xun Wang
https://arxiv.org/abs/2505.23940

Diff-FlowFSI: A GPU-Optimized Differentiable CFD Platform for High-Fidelity Turbulence and FSI Simulations
Turbulent flows and fluid-structure interactions (FSI) are ubiquitous in scientific and engineering applications, but their accurate and efficient simulation remains a major challenge due to strong nonlinearities, multiscale interactions, and high computational demands. Traditional CFD solvers, though effective, struggle with scalability and adaptability for tasks such as inverse modeling, optimization, and data assimilation. Recent advances in machine learning (ML) have inspired hybrid modelin…