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

This paper proposes a novel Generalized Non-Standard Finite Difference (GNSFD) scheme for the numerical solution of a class of fractional partial differential equations (FrPDEs). The formulation of the method is grounded in optimization and…

Data driven weather models now approach traditional numerical weather prediction (NWP) skill at short to medium lead times, but their dynamical consistency during autoregressive rollout remains uncertain.

Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from…

The Generalized Integral Representation Method (GIRM) for Space-Time-Separated Method (STSM) and Space-Time-Unified Method (STUM) are discussed. STSM and STUM give explicit and implicit time evolutions, respectively. The algorithm of STSM…

Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…

This work is aimed to develop a new class of methods for the BGK model of the Boltzmann equation. This technique allows to get high order of accuracy both in space and time, theoretically without CFL stability limitation. It's based on a…

Global warming leads to the increase in frequency and intensity of climate extremes that cause tremendous loss of lives and property. Accurate long-range climate prediction allows more time for preparation and disaster risk management for…

As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes can be a…

Time-harmonic solutions to the wave equation can be computed in the frequency or in the time domain. In the frequency domain, one solves a discretized Helmholtz equation, while in the time domain, the periodic solutions to a discretized…

This work is dedicated to simultaneous continuous-time trajectory estimation and mapping based on Gaussian Processes (GP). State-of-the-art GP-based models for Simultaneous Localization and Mapping (SLAM) are computationally efficient but…

Long-term stability stands as a crucial requirement in data-driven medium-range global weather forecasting. Spectral bias is recognized as the primary contributor to instabilities, as data-driven methods difficult to learn small-scale…

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…

The accuracy of solving partial differential equations (PDEs) on coarse grids is greatly affected by the choice of discretization schemes. In this work, we propose to learn time integration schemes based on neural networks which satisfy…

In the current context of Big Data, the nature of many forecasting problems has changed from predicting isolated time series to predicting many time series from similar sources. This has opened up the opportunity to develop competitive…

Financial market forecasting is inherently uncertain, yet most deep learning approaches rely on point predictions that provide only single-value estimates without quantifying uncertainty. Such predictions are insufficient for risk-aware…

This paper introduces filtered finite difference methods for numerically solving a dispersive evolution equation with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled nonlinear Schr\"odinger…

Complex time series models such as (the sum of) ARMA$(p,q)$ models with additional noise, random walks, rounding errors and/or drifts are increasingly used for data analysis in fields such as biology, ecology, engineering and economics…

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…

We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…