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Accurate weather forecasting holds significant importance to human activities. Currently, there are two paradigms for weather forecasting: Numerical Weather Prediction (NWP) and Deep Learning-based Prediction (DLP). NWP utilizes atmospheric…

Tropical cyclones (TCs) are among the most devastating natural hazards, yet their intensity remains notoriously difficult to predict. NWP models are constrained by both computational demands and intrinsic predictability, while…

We apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy…

Dynamic downscaling typically involves using numerical weather prediction (NWP) solvers to refine coarse data to higher spatial resolutions. Data-driven models such as FourCastNet have emerged as a promising alternative to the traditional…

Data-driven deep learning is considered a promising solution for ground-penetrating radar (GPR) full-waveform inversion (FWI), while its generalization ability is limited due to the heavy reliance on abundant labeled samples. In contrast,…

Data-driven models, such as FourCastNet (FCN), have shown exemplary performance in high-resolution global weather forecasting. This performance, however, is based on supervision on mesh-gridded weather data without the utilization of raw…

Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…

Deep learning is widely used to predict complex dynamical systems in many scientific and engineering areas. However, the black-box nature of these deep learning models presents significant challenges for carrying out simultaneous data…

We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and…

The rapid rise of air pollution events necessitates accurate, real-time monitoring for informed mitigation strategies. Data Assimilation (DA) methods provide promising solutions, but their effectiveness hinges heavily on optimal measurement…

Climate field reconstructions (CFR) attempt to estimate spatiotemporal fields of climate variables in the past using climate proxies such as tree rings, ice cores, and corals. Data Assimilation (DA) methods are a recent and promising new…

Data-driven machine learning (ML) models are reshaping weather forecasting and have shown the potential to accelerate and surpass traditional physics-based approaches, leading to a second revolution in the field after data assimilation.…

The short-term prediction of precipitation is critical in many areas of life. Recently, a large body of work was devoted to forecasting radar reflectivity images. The radar images are available only in areas with ground weather radars.…

Data assimilation techniques, developed in the last two decades mainly for weather prediction, produce better forecasts by taking advantage of both theoretical/numerical models and real-time observations. In this paper, we explore the…

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of about 40-100 km remains too coarse to resolve processes such as clouds and convection, which need to…

Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…

We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a non-abelian operator algebra, which provides a representation of…

Data Assimilation (DA) is a computational tool that uses value from the model and the real measurement to arrive to an optimally acceptable value. Rather, this technique relies on the idea of Kalman gain. We point out that DA has two…

Meteorological satellite imagery is critical for meteorologists. The data have played an important role in monitoring and analyzing weather and climate changes. However, satellite imagery is a kind of observation data and exists a…

An essential component of therapeutic drug/biomarker monitoring (TDM) is to combine patient data with prior knowledge for model-based predictions of therapy outcomes. Current Bayesian forecasting tools typically rely only on the most…