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Gaussian processes are widely used for the analysis of spatial data due to their nonparametric flexibility and ability to quantify uncertainty, and recently developed scalable approximations have facilitated application to massive datasets.…
In the study of nonlinear inverse scattering problems (ISPs), the traditional method for estimating the number of degrees of freedom (NDoF) of the scattered field does not consider the effect of the scatterer contrast. In this work, we…
It is shown that expressions for the global Lorentz force associated with a flaring active region derived by Fisher {\it et al.} (2012) can be used to estimate the Lorentz force changes for strong fields in large structures over…
In this paper a new technique for modeling non-linear force-free fields directly from line of sight magnetogram observations is presented. The technique uses sequences of magnetograms directly as lower boundary conditions to drive the…
For the past several decades, it has been popular to reconstruct Fourier imaging data using model-based approaches that can easily incorporate physical constraints and advanced regularization/machine learning priors. The most common…
In this paper, a potential field extrapolation and three nonlinear force-free (NLFF) field extrapolations (optimization, direct boundary integral (DBIE) and approximate vertical integration (AVI) methods) are used to study the spatial…
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…
Image restoration of biological structures in microscopy poses unique challenges for preserving fine textures and sharp edges. While recent GAN-based image restoration formulations have introduced frequency-domain losses for natural images,…
A uniform derivation is presented of the self-consistent field equations in a finite basis set. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional (DF) approximations are considered. The unitary…
Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate their hierarchical…
The magnetic fields in the solar corona are generally neither force-free nor axisymmetric and have complex dynamics that are difficult to characterize. Here we simulate the topological evolution of solar coronal magnetic field lines (MFLs)…
The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper, we systematically compute the solution landscapes of…
Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical…
Magnetars exhibit a variety of transient high-energy phenomena in the form of bursts, outbursts, and giant flares. It is a common belief that these events originate in the sudden release of magnetic energy due to the rearrangement of a…
A plethora of coronal models, from empirical to more complex magnetohydrodynamic (MHD) ones, are being used for reconstructing the coronal magnetic field topology and estimating the open magnetic flux. However, no individual solution fully…
Magnetohydrodynamic (MHD) simulations of the solar corona have become more popular with the increased availability of computational power. Modern computational plasma codes, relying upon Computational Fluid Dynamics (CFD) methods, allow for…
We investigate in details properties of stationary force-free magnetosphere of aligned rotator assuming the last closed field line lying in equatorial plane at large distances from pulsar. The pulsar equations is solved numerically using…
This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs) that focuses on hidden representations analysis rather than pure downstream task performance. Different from existing…
Given a known radial magnetic field distribution on the Sun's photospheric surface, there exist well-established methods for computing a potential magnetic field in the corona above. Such potential fields are routinely used as input to…
Solar magnetic fields are closely related to various physical phenomena on the sun, which can be extrapolated with different models from photospheric magnetograms. However, the Open Flux Problem (OFP), the underestimation of the magnetic…