相关论文: A Time-spectral Approach to Numerical Weather Pred…

In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…

Post-processing typically takes the outputs of a Numerical Weather Prediction (NWP) model and applies linear statistical techniques to produce improve localized forecasts, by including additional observations, or determining systematic…

Forecasting univariate time series in the financial market is a challenging endeavor. While numerous statistical and machine learning models have been introduced to address this challenge, they typically concentrate solely on analyzing…

Seasonal forecasting remains challenging due to the inherent chaotic nature of atmospheric dynamics. This paper introduces DeepSeasons, a novel deep learning approach designed to enhance the accuracy and reliability of seasonal forecasts.…

We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…

Predictive models of the future are fundamental for an agent's ability to reason and plan. A common strategy learns a world model and unrolls it step-by-step at inference, where small errors can rapidly compound. Geometric Horizon Models…

We consider nonnegative time series forecasting framework. Based on recent advances in Nonnegative Matrix Factorization (NMF) and Archetypal Analysis, we introduce two procedures referred to as Sliding Mask Method (SMM) and Latent Clustered…

We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions. In contrast to previous work, we introduce a Gauss--Markov prior and…

Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…

This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…

Ultra-wideband (UWB) time difference of arrival(TDOA)-based localization has emerged as a low-cost and scalable indoor positioning solution. However, in cluttered environments, the performance of UWB TDOA-based localization deteriorates due…

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…

We consider difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$, $\beta$ and $\gamma$. By the method of energy inequalities, for the…

With a warming planet, tropical regions are expected to experience the brunt of climate change, with more intense and more volatile rainfall events. Currently, state-of-the-art numerical weather prediction (NWP) models are known to struggle…

The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm, using FCF-relaxation…

This paper deals with the state estimation of stochastic models with continuous dynamics. The aim is to incorporate spectral differentiation methods into the solution to the Fokker-Planck equation in grid-based state estimation routine,…

In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…

Attention-based architectures have become ubiquitous in time series forecasting tasks, including spatio-temporal (STF) and long-term time series forecasting (LTSF). Yet, our understanding of the reasons for their effectiveness remains…

Combining forecasts from multiple numerical weather prediction (NWP) models have shown substantial benefit over the use of individual forecast products. Although combination, in a broad sense, is widely used in meteorological forecasting,…

Simulation of unsteady creeping flows in complex geometries has traditionally required the use of a time-stepping procedure, which is typically costly and unscalable. To reduce the cost and allow for computations at much larger scales, we…