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As artificial intelligence (AI), including machine learning (ML) models and foundation models (FMs), is increasingly deployed in high-stakes domains, ensuring their trustworthiness has become a central challenge. However, the core…
The objective is to provide clear and well-motivated guidance to Machine Learning (ML) teams, founded on our experience in empirical turbulence modeling. Guidance is also needed for modeling outside ML. ML is not yet successful in…
Explainable AI methods facilitate the understanding of model behaviour, yet, small, imperceptible perturbations to inputs can vastly distort explanations. As these explanations are typically evaluated holistically, before model deployment,…
Artificial intelligence (AI) - and specifically machine learning (ML) - applications for climate prediction across timescales are proliferating quickly. The emergence of these methods prompts a revisit to the impact of data preprocessing, a…
Understanding how droughts may change in the future is essential for anticipating and mitigating their adverse impacts. However, robust climate projections require large amounts of high-resolution climate simulations, particularly for…
By combining AI and fluid physics, we discover a closed-form closure for 2D turbulence from small direct numerical simulation (DNS) data. Large-eddy simulation (LES) with this closure is accurate and stable, reproducing DNS statistics…
Extreme weather events pose significant challenges, thereby demanding techniques for accurate analysis and precise forecasting to mitigate its impact. In recent years, deep learning techniques have emerged as a promising approach for…
The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at…
Global deep-learning weather prediction models have recently been shown to produce forecasts that rival those from physics-based models run at operational centers. It is unclear whether these models have encoded atmospheric dynamics, or…
The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…
Reynolds-averaged Navier-Stokes simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such situation, machine learning…
Since the weather is chaotic, forecasts aim to predict the distribution of future states rather than make a single prediction. Recently, multiple data driven weather models have emerged claiming breakthroughs in skill. However, these have…
We analyze the linear stability of monoclinal traveling waves on a constant incline, which connect uniform flowing regions of differing depths. The classical shallow-water equations are employed, subject to a general resistive drag term.…
The recipe behind the success of deep learning has been the combination of neural networks and gradient-based optimization. Understanding the behavior of gradient descent however, and particularly its instability, has lagged behind its…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…
Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…
When simulating multiscale systems, where some fields cannot be fully prescribed despite their effects on the simulation's accuracy, closure models are needed. This phenomenon is observed in turbulent fluid dynamics, where Large Eddy…
In operational weather models, the effects of turbulence in the atmospheric boundary layer (ABL) on the resolved flow are modeled using turbulence parameterizations. These parameterizations typically use a predetermined set of model…
Learning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. These systems exhibit positive Lyapunov exponents, which…
Country instability is a global issue, with unpredictably high levels of instability thwarting socio-economic growth and possibly causing a slew of negative consequences. As a result, uncertainty prediction models for a country are becoming…