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Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…
This paper investigates the problem of reconstructing a random source from statistical phaseless data for the two-dimensional Helmholtz equation. The major challenge of this problem is non-uniqueness, which we overcome through a reference…
We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate and the temperature…
Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a…
We present a unified technique for sequential estimation of convex divergences between distributions, including integral probability metrics like the kernel maximum mean discrepancy, $\varphi$-divergences like the Kullback-Leibler…
Magnetic properties of 2D systems of magnetic nanoobjects (2D regular lattices of the magnetic nanoparticles or magnetic nanostripes) are considered. The analytical calculation of the hysteresis curve of the system with interaction between…
We present a general methodology for addressing the infinite hierarchy problem that arises in measurement-induced dynamics of replicated quantum systems. Our approach introduces trace-preserving replica cutoffs using tomographic-like…
Controlled interventions provide the most direct source of information for learning causal effects. In particular, a dose-response curve can be learned by varying the treatment level and observing the corresponding outcomes. However,…
Learning complex physical dynamics purely from data is challenging due to the intrinsic properties of systems to be satisfied. Incorporating physics-informed priors, such as in Hamiltonian Neural Networks (HNNs), achieves high-precision…
Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a…
Variational methods in imaging are nowadays developing towards a quite universal and flexible tool, allowing for highly successful approaches on tasks like denoising, deblurring, inpainting, segmentation, super-resolution, disparity, and…
The traditional magnetic storage mechanisms (both analog and digital) apply an external field signal H(t) to a hysteretic magnetic material, and read the remanent magnetization M(t), which is (roughly) proportional to H(t). We propose a new…
The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle…
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…
We demonstrate the existence of an open set of data which exhibits \textit{reversal} and \textit{recirculation} for the stationary Prandtl equations (data is taken in an appropriately defined product space due to the simultaneous forward…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
Amorphous materials are solids that lack long-range atomic order but possess complex short- and medium-range order. Unlike crystalline materials that can be described by unit cells containing few up to hundreds of atoms, amorphous materials…
A new approach for functional data description is proposed in this paper. It consists of a regression model with a discrete hidden logistic process which is adapted for modeling curves with abrupt or smooth regime changes. The model…