Reduced basis methods for time-dependent problems

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Reduced-order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics encompass the und ...

Recent years have been marked with the fast-pace diversification and increasing ubiquity of machine learning (ML) applications. Yet, a firm theoretical understanding of the surprising efficiency of neural networks (NNs) to learn from high-dimensional data ...

Approximate multipliers (AppMults) are widely employed in deep neural network (DNN) accelerators to reduce the area, delay, and power consumption. However, the inaccuracies of AppMults degrade DNN accuracy, necessitating a retraining process to recover acc ...

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potenti ...

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Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both theoretically and empi ...

Dynamic aperture is an important concept for the study of non-linear beam dynamics in circular accelerators. It describes the extent of the phase-space region where a particle's motion remains bounded over a given number of turns. Understanding the feature ...

Cross-view geo-localization aims at localizing a ground-level query image by matching it to its corresponding geo-referenced aerial view. In real-world scenarios, the task requires accommodating diverse ground images captured by users with varying orientat ...

Koopmans spectral functionals are a powerful extension of Kohn-Sham density-functional theory (DFT) that enables the prediction of spectral properties with state-of-the-art accuracy. The success of these functionals relies on capturing the effects of elect ...

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One approach for describing spatiotemporal chaos is to study the unstable invariant sets embedded in the chaotic attractor of the system. While equilibria, periodic orbits, and invariant tori can be computed using existing methods, the numerical identifica ...

Atomic simulations using machine learning interatomic potential (MLIP) have gained a lot of popularity owing to their accuracy in comparison to conventional empirical potentials. However, the transferability of MLIP to systems outside the training set pose ...

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

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Background: Cardiac output is essential for patient management in critically ill patients. The state-of-the-art for cardiac output monitoring bears limitations that pertain to the invasive nature of the method, high costs, and associated complications. Hen ...

Reduced basis methods for time-dependent problems

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High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

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