Related papers: Basis set extrapolation from the vanishing counter…
Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…
Extrapolating treatment effects from related studies is a promising strategy for designing and analyzing clinical trials in situations where achieving an adequate sample size is challenging. Bayesian methods are well-suited for this…
Empirical Bayes estimators are based on minimizing the average risk with the hyper-parameters in the weighting function being estimated from observed data. The performance of an empirical Bayes estimator is typically evaluated by its mean…
We have investigated the title question for the W4-08 thermochemical benchmark using partial-wave truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root mean…
In this work, we study over-parameterization as a necessary condition for having the ability for the models to extrapolate outside the convex hull of training set. We specifically, consider classification models, e.g., image classification…
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in \cite{BCDDPW,DPW}, where…
In sufficiently complex models with many parameters that are unknown or undetermined from first principles, a small coupling or mass can naturally arise even if it is not protected by a symmetry or a result of some dynamics. For the…
This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's…
We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple…
A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation…
This article is a primer on concept extrapolation - the ability to take a concept, a feature, or a goal that is defined in one context and extrapolate it safely to a more general context. Concept extrapolation aims to solve model…
Spectroscopic measurements can show distorted spectral shapes arising from a mixture of absorbing and scattering contributions. These distortions (or baselines) often manifest themselves as non-constant offsets or low-frequency…
We study sparse principal component analysis in the high-dimensional, sample-limited regime, aiming to recover a leading component supported on a few coordinates. Despite extensive progress, most methods and analyses are tailored to the…
Reliable computational methodologies and basis sets for modeling x-ray spectra are essential for extracting and interpreting electronic and structural information from experimental x-ray spectra. In particular, the trade-off between…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
We present a bottom-up approach to the question of supersymmetry breaking in the MSSM. Starting with the experimentally measurable low energy supersymmetry breaking parameters which can take any values consistent with present experimental…
The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In…
We describe an all-electron implementation of the Bethe-Salpeter equation (BSE) for the calculation of optical absorption spectra in the full-potential linearized augmented-plane-wave (FLAPW) method. So far, FLAPW implementations have…
Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…