Related papers: Hessian Spectral Analysis at Foundation Model Scal…
We explore the diagnostic potential of the H$\alpha$ line for probing the chromospheric magnetic field using a realistic 3D radiative magnetohydrodynamic (rMHD) model. The Stokes profiles of the H$\alpha$ line are synthesized through full…
Spectral variability significantly impacts the accuracy and convergence of hyperspectral unmixing algorithms. Many methods address complex spectral variability; yet large-scale distortions to the scale of the observed pixel signatures due…
Hyperspectral imaging provides detailed spectral information, offering significant potential for monitoring greenhouse gases like CH4 and NO2. However, its application is constrained by limited spatial coverage and infrequent revisit times.…
Many PDEs involving fractional Laplacian are naturally set in unbounded domains with underlying solutions decay very slowly, subject to certain power laws. Their numerical solutions are under-explored. This paper aims at developing accurate…
The high resolution spectrograph ESPRESSO on the VLT allows measurements of fundamental constants at unprecedented precision and hence enables tests for spacetime variations predicted by some theories. In a series of recent papers, we…
We present an algorithm for reliably and systematically proving the existence of spectral gaps in Hamiltonians with quasicrystalline order, based on numerical calculations on finite domains. We apply this algorithm to prove that the…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal…
In the present article we consider an accurate modeling of spectrograph with cascade of volume-phase holographic gratings. The proposed optical scheme allows to detect spectra in an extended wavelength range without gaps providing…
Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate…
In this work we develop a Hessian-based sampling method for the construction of goal-oriented reduced order models with high-dimensional parameter inputs. Model reduction is known very challenging for high-dimensional parametric problems…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
We consider an initial boundary value problem of the space fractional Allen-Cahn equation with logarithmic Flory-Huggins potential. As an approximation technique, first-order weighted and shifted Grunwald difference formulae of the left and…
We present a scalable Bayesian framework for the analysis of confocal fluorescence spectroscopy data, addressing key limitations in traditional fluorescence correlation spectroscopy methods. Our framework captures molecular motion,…
We present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing…
The fidelity per site between two ground states of a quantum lattice system corresponding to different values of the control parameter defines a surface embedded in a Euclidean space. The Gaussian curvature naturally quantifies quantum…
Absorption line systems detected in quasar spectra can be used to compare the value of the fine-structure constant, {\alpha}, measured today on Earth with its value in distant galaxies. In recent years, some evidence has emerged of small…
The eigenvalue distribution of the Hessian matrix plays a crucial role in understanding the optimization landscape of deep neural networks. Prior work has attributed the well-documented ``bulk-and-spike'' spectral structure, where a few…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the…