相关论文: Data Assimilation in Optimal Transport Framework

The Kalman filter and its extensions are used in a vast number of aerospace and navigation applications for nonlinear state estimation of time series. In the literature, different approaches have been proposed to exploit the structure of…

In this work we propose a framework to address the issue of state dependent nonlinear equality-constrained state estimation using Bayesian filtering. This framework is constructed specifically for a linear approximation of Bayesian…

We propose a method to identify and characterize distribution shifts in classification datasets based on optimal transport. It allows the user to identify the extent to which each class is affected by the shift, and retrieves corresponding…

The combined use of data from different sources can be critical in emergencies, where accurate models are needed to make real-time decisions, but high-fidelity representations and detailed information are simply unavailable. This study…

Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention. Building upon recent advances in computational optimal transport, we develop an optimal transport non-negative matrix…

Data Assimilation (DA) is a computational tool that uses value from the model and the real measurement to arrive to an optimally acceptable value. Rather, this technique relies on the idea of Kalman gain. We point out that DA has two…

We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…

Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…

We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…

Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…

A Kalman filter based sequential estimator is presented in the present work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state…

Accurate and timely prediction of crop growth is of great significance to ensure crop yields and researchers have developed several crop models for the prediction of crop growth. However, there are large difference between the simulation…

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…

This paper presents an approach to tackle the problem of tram localization through utilizing a custom processing of Global Navigation Satellite System (GNSS) observables and the track map. The method is motivated by suboptimal performance…

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…

Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…

This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in…

We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an…

The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…

We present a toolkit of directed distances between quantile functions. By employing this, we solve some new optimal transport (OT) problems which e.g. considerably flexibilize some prominent OTs expressed through Wasserstein distances.