Related papers: 4D-Var using Hessian approximation and backpropaga…

A Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and…

Earth system modeling presents a fundamental challenge in scientific computing: capturing complex, multiscale nonlinear dynamics in computationally efficient models while minimizing forecast errors caused by necessary simplifications. Even…

This paper examines the application of adaptive mesh refinement (AMR) in the field of numerical weather prediction (NWP). We implement and assess two distinct AMR approaches and evaluate their performance through standard NWP benchmarks. In…

Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

Weather forecasting is critical for a range of human activities including transportation, agriculture, industry, as well as the safety of the general public. Machine learning models have the potential to transform the complex weather…

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

Several numerical approximation strategies for the expectation-propagation algorithm are studied in the context of large-scale learning: the Laplace method, a faster variant of it, Gaussian quadrature, and a deterministic version of…

Recent advancements in evaluating matrix-exponential functions have opened the doors to the practical use of exponential time-integration methods in numerical weather prediction (NWP). The success of exponential methods in shallow water…

Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The…

We propose an extension of quasi-Newton methods, and investigate the convergence and the robustness properties of the proposed update formulae for the approximate Hessian matrix. Fletcher has studied a variational problem which derives the…

We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a…

Weather Forecasting is an attractive challengeable task due to its influence on human life and complexity in atmospheric motion. Supported by massive historical observed time series data, the task is suitable for data-driven approaches,…

In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

Accurate weather prediction is essential for many aspects of life, notably the early warning of extreme weather events such as rainstorms. Short-term predictions of these events rely on forecasts from numerical weather models, in which,…

Accurate wind power forecasts depend on reliable wind speed forecasts. Numerical Weather Predictions (NWPs) utilize huge amounts of computing time, but still have rather low spatial and temporal resolution. However, stochastic wind speed…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

We derive the adjoint path-kernel method for computing parameter-gradients (linear responses) of SDEs. Its cost is almost independent of the number of parameters, and it works for non-hyperbolic systems with parameter-controlled…

We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…