Related papers: Fourier Neural Operators for Arbitrary Resolution …
This work presents a systematic framework for improving the predictions of statistical quantities for turbulent systems, with a focus on correcting climate simulations obtained by coarse-scale models. While high resolution simulations or…
Regional high-resolution climate projections are crucial for many applications, such as agriculture, hydrology, and natural hazard risk assessment. Dynamical downscaling, the state-of-the-art method to produce localized future climate…
Addressing complex meteorological processes at a fine spatial resolution requires substantial computational resources. To accelerate meteorological simulations, researchers have utilized neural networks to downscale meteorological variables…
Human activities accelerate consumption of fossil fuels and produce greenhouse gases, resulting in urgent issues today: global warming and the climate change. These indirectly cause severe natural disasters, plenty of lives suffering and…
Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socio-economic impacts of anthropogenic climate change, but are computationally too expensive to be run at sufficiently high…
Based on a previously introduced downscaling data assimilation algorithm, which employs a nudging term to synchronize the coarse mesh spatial scales, we construct a determining map for recovering the full trajectories from their…
We present a method to downscale idealized geophysical fluid simulations using generative models based on diffusion maps. By analyzing the Fourier spectra of images drawn from different data distributions, we show how one can chain together…
Data assimilation (DA) is crucial for enhancing solutions to partial differential equations (PDEs), such as those in numerical weather prediction, by optimizing initial conditions using observational data. Variational DA methods are widely…
Modern deep learning techniques, which mimic traditional numerical weather prediction (NWP) models and are derived from global atmospheric reanalysis data, have caused a significant revolution within a few years. In this new paradigm, our…
Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…
We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by…
Observing system simulation experiments (OSSEs) have been widely used as a rigorous and cost-effective way to guide development of new observing systems, and to evaluate the performance of new data assimilation algorithms. Nature runs…
Running high-resolution physical models is computationally expensive and essential for many disciplines. Agriculture, transportation, and energy are sectors that depend on high-resolution weather models, which typically consume many hours…
Climate models are limited by heavy computational costs, often producing outputs at coarse spatial resolutions, while many climate change impact studies require finer scales. Statistical downscaling bridges this gap, and we adapt the…
Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…
Recent progress in AI has established neural operators as powerful tools that can predict the evolution of partial differential equations, such as the Navier-Stokes equations. Some complex problems rely on sophisticated algorithms to deal…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
Due to the computational complexity of 3D medical image segmentation, training with downsampled images is a common remedy for out-of-memory errors in deep learning. Nevertheless, as standard spatial convolution is sensitive to variations in…
A central challenge in climate science and applied mathematics is developing data-driven models of multiscale systems that capture both stationary statistics and responses to external perturbations. Current neural climate emulators aim to…
This paper focuses on investigating the learning operators for identifying weak solutions to the Navier-Stokes equations. Our objective is to establish a connection between the initial data as input and the weak solution as output. To…