Related papers: 4D-Var using Hessian approximation and backpropaga…
In three-dimensional variational data assimilation (3DVar) for numerical weather prediction (NWP), the observation operator $\mathcal{H}$ plays a central role by mapping model state variables to an observation equivalent. For weather radar,…
To quantify the uncertainty in numerical weather prediction (NWP) forecasts, ensemble prediction systems are utilized. Although NWP forecasts continuously improve, they suffer from systematic bias and dispersion errors. To obtain well…
Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
The task of sampling efficiently the Gibbs-Boltzmann distribution of disordered systems is important both for the theoretical understanding of these models and for the solution of practical optimization problems. Unfortunately, this task is…
Despite continuous improvements, precipitation forecasts are still not as accurate and reliable as those of other meteorological variables. A major contributing factor to this is that several key processes affecting precipitation…
Methods to deal with systematic model errors are an increasingly important component of modern data assimilation systems and their effectiveness has increased in recent years thanks to advances in methodology and the quality and density of…
There is growing awareness that errors in the model equations cannot be ignored in data assimilation methods such as four-dimensional variational assimilation (4D-Var). If allowed for, more information can be extracted from observations,…
There is growing interest in data-driven weather prediction (DDWP), for example using convolutional neural networks such as U-NETs that are trained on data from models or reanalysis. Here, we propose 3 components to integrate with commonly…
We demonstrate that automatic differentiation (AD), which has become commonly available in machine learning frameworks, is an efficient way to explore ideas that lead to algorithmic improvement in multi-scale affine image registration and…
This paper addresses the impact of assimilating data from the Earth Networks Total Lightning Network (ENTLN) during two cases of severe weather. Data from the ENTLN serve as a substitute for those from the upcoming launch of the GOES…
3D Gaussian Splatting (3DGS) has become a competitive approach for novel view synthesis (NVS) due to its advanced rendering efficiency through 3D Gaussian projection and blending. However, Gaussians are treated equally weighted for…
Due to insufficient local area information, numerical weather prediction (NWP) may yield biases for specific areas. Previous studies correct biases mainly by employing handcrafted features or applying data-driven methods intuitively,…
Nonlinear vector autoregression (NVAR) and reservoir computing (RC) have shown promise in forecasting chaotic dynamical systems, such as the Lorenz-63 model and El Nino-Southern Oscillation. However, their reliance on fixed nonlinear…
We present practical Levenberg-Marquardt variants of Gauss-Newton and natural gradient methods for solving non-convex optimization problems that arise in training deep neural networks involving enormous numbers of variables and huge data…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
Through sequential construction of posteriors on observing data online, Bayes' theorem provides a natural framework for continual learning. We develop Variational Auto-Regressive Gaussian Processes (VAR-GPs), a principled posterior updating…
Numerical weather predictions (NWP) are systematically subject to errors due to the deterministic solutions used by numerical models to simulate the atmosphere. Statistical postprocessing techniques are widely used nowadays for NWP…
Numerical weather forecasting using high-resolution physical models often requires extensive computational resources on supercomputers, which diminishes their wide usage in most real-life applications. As a remedy, applying deep learning…
I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I present a hybrid of expectation propagation called Variational Expectation…