Related papers: The Ensemble Schr{\"o}dinger Bridge filter for Non…

A Schr\"{o}dinger bridge establishes a dynamic transport map between two target distributions via a reference process, simultaneously solving an associated entropic optimal transport problem. We consider the setting where samples from the…

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding…

State estimation in multi-layer turbulent flow fields with only a single layer of partial observation remains a challenging yet practically important task. Applications include inferring the state of the deep ocean by exploiting surface…

At the core of modern generative modeling frameworks, including diffusion models, score-based models, and flow matching, is the task of transforming a simple prior distribution into a complex target distribution through stochastic paths in…

Inferring the state and unknown parameters of a network of coupled oscillators is of utmost importance. This task is made harder when only partial and noisy observations are available, which is a typical scenario in realistic…

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information…

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger bridge matching, effectively learn mappings…

Conditional generative models represent a significant advancement in the field of machine learning, allowing for the controlled synthesis of data by incorporating additional information into the generation process. In this work we introduce…

This paper presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool. It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves…

We introduce a score-based generative sampling method for solving the nonlinear filtering problem with robust accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low stability. To overcome this…

This paper proposes two practical implementations of Four-Dimensional Variational (4D-Var) Ensemble Kalman Filter (4D-EnKF) methods for non-linear data assimilation. Our formulations' main idea is to avoid the intrinsic need for adjoint…

Although data assimilation originates from control theory, the relationship between modern data assimilation methods in geoscience and model predictive control has not been extensively explored. In the present paper, I discuss that the…

A data-driven method for improving the correlation estimation in serial ensemble Kalman filters is introduced. The method finds a linear map that transforms, at each assimilation cycle, the poorly estimated sample correlation into an…

Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative…

Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that…

A hybrid data assimilation algorithm is developed for complex dynamical systems with partial observations. The method starts with applying a spectral decomposition to the entire spatiotemporal fields, followed by creating a machine learning…

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the…

This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data…