Related papers: The Ensemble Schr{\"o}dinger Bridge filter for Non…
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…
We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary data distributions i.e. they generalize…
Nonlinear adaptive filtering allows for modeling of some additional aspects of a general system and usually relies on highly complex algorithms, such as those based on the Volterra series. Through the use of the Kronecker product and some…
A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the…
This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new…
Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…
Scientists often want to make predictions beyond the observed time horizon of "snapshot" data following latent stochastic dynamics. For example, in time course single-cell mRNA profiling, scientists have access to cellular transcriptional…
This paper introduces filtered finite difference methods for numerically solving a dispersive evolution equation with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled nonlinear Schr\"odinger…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…
Glacier modeling is crucial for quantifying the evolution of cryospheric processes. At the same time, uncertainties hamper process understanding and predictive accuracy. Here, we suggest improving glacier mass balance simulations for the…
In this paper we combine the non-linear filtering capabilities of particle filters with the transdimensional inference of the reversible-jump Markov chain Monte Carlo method for a data assimilation methodology over dynamic problems with…
We report on a number of careful numerical experiments motivated by the semiclassical (zero-dispersion, \epsilon\downarrow 0) limit of the focusing nonlinear Schr\"odinger equation. Our experiments are designed to study the evolution of a…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more…
Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…