As artificial intelligence (AI) continues to rapidly evolve, the realm of Earth and atmospheric
sciences is increasingly adopting data-driven models, powered by progressive …

Neural networks suffer from spectral bias and have difficulty representing the high-frequency
components of a function, whereas relaxation methods can resolve high frequencies …

Neural operator learning models have emerged as very effective surrogates in data-driven
methods for partial differential equations (PDEs) across different applications from …

Numerical simulations are computationally demanding in three-dimensional (3D) settings
but they are often required to accurately represent physical phenomena. Neural operators …

Materials simulations based on direct numerical solvers are accurate but computationally
expensive for predicting materials evolution across length-and time-scales, due to the …

Iterative solvers of linear systems are a key component for the numerical solutions of partial
differential equations (PDEs). While there have been intensive studies through past decades …

Recent advances in machine learning establish the ability of certain neural-network
architectures called neural operators to approximate maps between function spaces …

Neural operators have emerged as a powerful tool for learning the mapping between infinite-
dimensional parameter and solution spaces of partial differential equations (PDEs). In this …

Physics-informed machine learning (PIML) has emerged as a promising alternative to
classical methods for predicting dynamical systems, offering faster and more generalizable …

Machine learning and deep learning methods have been widely explored in understanding
the chaotic behavior of the atmosphere and furthering weather forecasting. There has been …