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To foster trust in machine learning models, explanations must be faithful and stable for consistent insights. Existing relevant works rely on the $\ell_p$ distance for stability assessment, which diverges from human perception. Besides,…
Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…
Accurate estimation of global terrestrial evapotranspiration (ET) is essential to understanding changes in the water cycle, which are expected to intensify in the context of climate change. Current global ET products are derived from…
Recent research in clustering face embeddings has found that unsupervised, shallow, heuristic-based methods -- including $k$-means and hierarchical agglomerative clustering -- underperform supervised, deep, inductive methods. While the…
The reconstruction of ocean subsurface temperature (OST) using satellite remote sensing data holds significant scientific value for advancing the understanding of ocean dynamics and climate variability. However, the scarcity of subsurface…
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…
The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use…
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…
Compared to common density functionals, ab initio wave function methods can provide greater reliability and accuracy, which could prove useful when modeling adsorbates or defects of otherwise periodic systems. However, the breaking of…
Test-time adaptation (TTA) seeks to tackle potential distribution shifts between training and test data by adapting a given model w.r.t. any test sample. Although recent TTA has shown promising performance, we still face two key challenges:…
Soot is an important material with impacts that depend on particle morphology. Transmission electron microscopy (TEM) represents one of the most direct routes to qualitatively assess particle characteristics. However, producing quantitative…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
Climate change increases the frequency of extreme rainfall, placing a significant strain on urban infrastructures, especially Combined Sewer Systems (CSS). Overflows from overburdened CSS release untreated wastewater into surface waters,…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the…
We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…
The increased computerization in recent years has resulted in the production of a variety of different software, however measures need to be taken to ensure that the produced software isn't defective. Many researchers have worked in this…
The article is devoted to the resampling approach application to the reliability problems. This approach to reliability problems was first proposed by Ivnitsky (1967). Resampling is intensive statistical computer method, which is…
The effect of the relative entropy asymmetry is analyzed in the empirical risk minimization with relative entropy regularization (ERM-RER) problem. A novel regularization is introduced, coined Type-II regularization, that allows for…
Entropy integrals are widely used as a powerful empirical process tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimation and regression. The upper…