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Predictions of global climate models typically operate on coarse spatial scales due to the large computational costs of climate simulations. This has led to a considerable interest in methods for statistical downscaling, a similar process…
The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…
Uniformity plays an important role in evaluating learned representations, providing insights into self-supervised learning. In our quest for effective uniformity metrics, we pinpoint four principled properties that such metrics should…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
We introduce a new unbinned two sample test statistic sensitive to CP violation utilizing the optimal transport plan associated with the Wasserstein (earth mover's) distance. The efficacy of the test statistic is shown via two examples of…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
Distinguishing quantum states with minimal sampling overhead is of fundamental importance to teach quantum data to an algorithm. Recently, the quantum Wasserstein distance emerged from the theory of quantum optimal transport as a promising…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
This is the second part of a series of two articles focused on the development and evaluation of the ARP-GEM1 global atmosphere model. The first paper introduced the model's new physics and speedup improvements. In this second part, we…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
A comprehensive understanding of the behaviours of the various geophysical processes and an effective evaluation of time series (else referred to as "stochastic") simulation models require, among others, detailed investigations across…
Previous studies showed that hydro-climate processes are stochastic and complex systems, and it is difficult to discover the hidden patterns in the all non-stationary data and thoroughly understand the hydro-climate relationships. For the…
Kilometer-scale weather data is crucial for real-world applications but remains computationally intensive to produce using traditional weather simulations. An emerging solution is to use deep learning models, which offer a faster…
Rapid changes in Earth's cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets.…
Extreme weather is one of the main mechanisms through which climate change will directly impact human society. Coping with such change as a global community requires markedly improved understanding of how global warming drives extreme…
Global Climate Models (GCMs) are the primary tool to simulate climate evolution and assess the impacts of climate change. However, they often operate at a coarse spatial resolution that limits their accuracy in reproducing local-scale…
Spatio-temporal forecasting is challenging attributing to the high nonlinearity in temporal dynamics as well as complex location-characterized patterns in spatial domains, especially in fields like weather forecasting. Graph convolutions…
The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded…
Climate change is a non-uniform phenomenon. This paper proposes a new quantitative methodology to characterize, measure, and test the existence of climate change heterogeneity. It consists of three steps. First, we introduce a new testable…
Motivated by the 2D class averaging problem in single-particle cryo-electron microscopy (cryo-EM), we present a k-means algorithm based on a rotationally-invariant Wasserstein metric for images. Unlike existing methods that are based on…