Related papers: 4D-Var using Hessian approximation and backpropaga…
Reliable 4D aircraft trajectory prediction, whether in a real-time setting or for analysis of counterfactuals, is important to the efficiency of the aviation system. Toward this end, we first propose a highly generalizable efficient…
State estimates from weak constraint 4D-Var data assimilation can vary significantly depending on the data and model error covariances. As a result, the accuracy of these estimates heavily depends on the correct specification of both model…
We propose a certified reduced basis approach for the strong- and weak-constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. While the standard strong-constraint 4D-Var approach uses the…
Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…
Machine Learning (ML) has shown great promise in revolutionizing weather forecasting, yet most ML systems still rely on initial conditions generated by Numerical Weather Prediction (NWP) systems. End-to-end ML models aim to eliminate this…
Adverse weather conditions, particularly convective phenomena, pose significant challenges to Air Traffic Management, often requiring real-time rerouting decisions that impact efficiency and safety. This study introduces a 3-D Gaussian…
Numerical Weather Prediction (NWP), is widely used in precipitation forecasting, based on complex equations of atmospheric motion requires supercomputers to infer the state of the atmosphere. Due to the complexity of the task and the huge…
While widely recognized as one of the most substantial weather forecasting methodologies, Numerical Weather Prediction (NWP) usually suffers from relatively coarse resolution and inevitable bias due to tempo-spatial discretization, physical…
The nudging data assimilation algorithm is a powerful tool used to forecast phenomena of interest given incomplete and noisy observations. Machine learning is becoming increasingly popular in data assimilation given its ease of computation…
Weather forecasting is a crucial yet highly challenging task. With the maturity of Artificial Intelligence (AI), the emergence of data-driven weather forecasting models has opened up a new paradigm for the development of weather forecasting…
Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…
4D-variational data assimilation is applied to the Lorenz '63 model to introduce a new method for parameter estimation in chaotic climate models. The approach aims to optimise an Earth system model (ESM), for which no adjoint exists, by…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
Non linear regression models are a standard tool for modeling real phenomena, with several applications in machine learning, ecology, econometry... Estimating the parameters of the model has garnered a lot of attention during many years. We…
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…
Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
Numerical weather prediction (NWP) and machine learning (ML) methods are popular for solar forecasting. However, NWP models have multiple possible physical parameterizations, which requires site-specific NWP optimization. This is further…
The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and…
A major problem in numerical weather prediction (NWP) is the estimation of high-dimensional covariance matrices from a small number of samples. Maximum likelihood estimators cannot provide reliable estimates when the overall dimension is…