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Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…
In Helio- and asteroseismology, it is important to have continuous, uninterrupted, data sets. However, seismic observations usually contain gaps and we need to take them into account. In particular, if the gaps are not randomly distributed,…
A widely recognized limitation of molecular prediction models is their reliance on structures observed in the training data, resulting in poor generalization to out-of-distribution compounds. Yet in drug discovery, the compounds most…
This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on…
Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…
We discuss the interpolation of the electric and magnetic fields within a charge-conserving Particle-In-Cell scheme. The choice of the interpolation procedure for the fields acting on a particle can be constrained by analyzing conservation…
Uncertainty quantification (UQ) in mathematical models is essential for accurately predicting system behavior under variability. This study provides guidance on method selection for reliable UQ across varied functional behaviors in…
This chapter provides an introduction to Hybrid High-Order (HHO) methods. These are new generation numerical methods for PDEs with several advantageous features: the support of arbitrary approximation orders on general polyhedral meshes,…
This paper introduces a method for spatial interpolation of extreme values, and in particular targets the case in which conventional data, resulting from a measurement for example, are available at only a few locations. To overcome this the…
This paper is concerned with high-order numerical methods for hyperbolic systems of balance laws. Such methods are typically based on high-order piecewise polynomial reconstructions (interpolations) of the computed discrete quantities.…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
Predicting the evolution of spatiotemporal physical systems from sparse and scattered observational data poses a significant challenge in various scientific domains. Traditional methods rely on dense grid-structured data, limiting their…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
The configuration of physical parameterization schemes in Numerical Weather Prediction (NWP) models plays a critical role in determining the accuracy of the forecast. However, existing parameter calibration methods typically treat each…
The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes…
Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
Nowadays, climate models rely on couplers. Each complete climate model is broken into different sub-models (oceanic, atmospheric,...), each one working on a different grid. The coupler brings these models together and interpolates the…
Accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating in supercapacitors during charging/discharging cycles. However, numerical methods that can faithfully capture entropy variation in…
This note presents an approach for estimating the spatial distribution of static properties in reservoir modeling using a nearest-neighbor neural network. The method leverages the strengths of neural networks in approximating complex,…