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We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

We propose the Linearly Adaptive Cross Entropy Loss function. This is a novel measure derived from the information theory. In comparison to the standard cross entropy loss function, the proposed one has an additional term that depends on…

Recently, many deep-learning techniques have been applied to various weather-related prediction tasks, including precipitation nowcasting (i.e., predicting precipitation levels and locations in the near future). Most existing…

Quantifying the impacts of anthropogenic global warming requires accurate Earth system model (ESM) simulations. Statistical bias correction and downscaling can be applied to reduce errors and increase the resolution of ESMs. However,…

In most machine learning training paradigms a fixed, often handcrafted, loss function is assumed to be a good proxy for an underlying evaluation metric. In this work we assess this assumption by meta-learning an adaptive loss function to…

To facilitate effective decision-making, precipitation datasets should include uncertainty estimates. Quantile regression with machine learning has been proposed for issuing such estimates. Distributional regression offers distinct…

In recent years, the growing frequency and severity of natural disasters have increased the need for effective tools to manage catastrophe risk. Catastrophe (CAT) bonds allow the transfer of part of this risk to investors, offering an…

The earth system is exceedingly complex and often chaotic in nature, making prediction incredibly challenging: we cannot expect to make perfect predictions all of the time. Instead, we look for specific states of the system that lead to…

Recently, deep-learning weather forecasting models have surpassed traditional numerical models in terms of the accuracy of meteorological variables. However, there is considerable potential for improvements in precipitation forecasts,…

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This…

Deep learning models have achieved remarkable progress in precipitation prediction. However, they still face significant challenges in accurately capturing spatial details of radar images, particularly in regions of high precipitation…

Optical turbulence, driven by fluctuations of the atmospheric refractive index, poses a significant challenge to ground-based optical systems, as it distorts the propagation of light. This degradation affects both astronomical observations…

This paper provides an outlook on the future of operational weather prediction given the recent evolution in science, computing and machine learning. In many parts, this evolution strongly deviates from the strategy operational centres have…

Decision-makers rely on weather forecasts to plant crops, manage wildfires, allocate water and energy, and prepare for weather extremes. Today, such forecasts enjoy unprecedented accuracy out to two weeks thanks to steady advances in…

In a recent development in the literature, a new temporal rainfall model, based on the Bartlett-Lewis clustering mechanism and intended for sub-hourly application, was introduced. That model replaced the rectangular rain cells of the…

Deep learning models for meteorological forecasting often fail in rare but high-impact events such as typhoons, where relevant data is scarce. Existing fine-tuning methods typically face a trade-off between overlooking these extreme events…

We propose a theoretical framework for an adaptive learning rate policy for the Mean Absolute Error loss function and Quantile loss function and evaluate its effectiveness for regression tasks. The framework is based on the theory of…

Optimization in the presence of sharp (non-Lipschitz), unpredictable (w.r.t. time and amount) changes is a challenging and largely unexplored problem of great significance. We consider the class of piecewise Lipschitz functions, which is…

Data assimilation (DA) plays a pivotal role in numerical weather prediction by systematically integrating sparse observations with model forecasts to estimate optimal atmospheric initial condition for forthcoming forecasts. Traditional…

Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…