Related papers: 4D-Var using Hessian approximation and backpropaga…
Precipitation governs Earth's hydroclimate, and its daily spatiotemporal fluctuations have major socioeconomic effects. Advances in Numerical weather prediction (NWP) have been measured by the improvement of forecasts for various physical…
The demand for high-resolution information on climate change is critical for accurate projections and decision-making. Presently, this need is addressed through high-resolution climate models or downscaling. High-resolution models are…
We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to…
Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has…
Over the past few years, machine learning-based data-driven weather prediction has been transforming operational weather forecasting by providing more accurate forecasts while using a mere fraction of computing power compared to traditional…
We propose an automatic algorithm for 3D inverse electromagnetic scattering based on the combination of topological derivatives and regularized Gauss-Newton iterations. The algorithm is adapted to decoding digital holograms. A hologram is a…
The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a…
Accurate precipitation estimates at individual locations are crucial for weather forecasting and spatial analysis. This study presents a paradigm shift by leveraging Deep Neural Networks (DNNs) to surpass traditional methods like Kriging…
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are probabilistic and non-parametric…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…
This paper addresses variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic…
Precipitation prediction has undergone a profound transformation. A notable limitation of traditional NWP is the need for extensive statistical post-processing. To address this challenge, neural network-based approaches were developed.…
Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate…
The forecasting skill of numerical weather prediction (NWP) models critically depends on the accurate initial conditions, also known as analysis, provided by data assimilation (DA). Traditional DA methods often face a trade-off between…
In numerical weather prediction (NWP), a large number of observations are used to create initial conditions for weather forecasting through a process known as data assimilation. An assessment of the value of these observations for NWP can…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…
The growing impact of global climate change amplifies the need for accurate and reliable weather forecasting. Traditional autoregressive approaches, while effective for temporal modeling, suffer from error accumulation in long-term…