Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …

We demonstrate how incorporating physics constraints into convolutional neural networks
(CNNs) enables learning subgrid-scale (SGS) closures for stable and accurate large-eddy …

We present a data-driven approach for forecasting global weather using graph neural
networks. The system learns to step forward the current 3D atmospheric state by six hours …

Partial differential equations (PDEs) see widespread use in sciences and engineering to
describe simulation of physical processes as scalar and vector fields interacting and …

Partial differential equations (PDEs) are central to describing complex physical system
simulations. Their expensive solution techniques have led to an increased interest in deep …

High-dimensional dynamical systems often require computationally intensive physics-based
simulations, making full physical space data assimilation impractical. Latent data …

There is a growing interest in developing data‐driven reduced‐order models for
atmospheric and oceanic flows that are trained on data obtained either from high‐resolution …

Data assimilation (DA) is a key component of many forecasting models in science and
engineering. DA allows one to estimate better initial conditions using an imperfect dynamical …

Weather forecasting is crucial for scientific research and society. Recently, deep learning
(DL) methods have achieved significant advancements in medium-range weather …

This book enables readers to understand, model, and predict complex dynamical systems
using new methods with stochastic tools. The author presents a unique combination of …