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Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
We propose a novel image sampling method for differentiable image transformation in deep neural networks. The sampling schemes currently used in deep learning, such as Spatial Transformer Networks, rely on bilinear interpolation, which…
We introduce a new method for robust beamforming, where the goal is to estimate a signal from array samples when there is uncertainty in the angle of arrival. Our method offers state-of-the-art performance on narrowband signals and is…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot's model with frequency-independant coefficients. The coexistence of a propagating fast wave and a diffusive slow…
We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach…
In this study, a Fourier-based, split-step Pad\'e (SSP) method for solving the parabolic wave equation with applications in guided wave propagation in ocean acoustics is presented. Traditional SSP implementations rely in finite-difference…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a…
Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
We introduce a novel reflection-mode diffraction tomography technique that enables simultaneous recovery of forward and backward scattering information for high-resolution 3D refractive index reconstruction. Our technique works by imaging a…
A new scaling law model for propagation of optical beams through atmospheric turbulence is presented and compared to a common scalar stochastic waveoptics technique. This methodology tracks the evolution of the important beam wavefront and…
We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation…
The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the…
In geophysics, wave propagation in elastic media is a crucial subject. In this context, seismology has made significant progress as a result of numerous advances, among these stands out the advancement of numerical methods such as the…
We have shown that the wave scattering by a soliton occurs in a peculiar way. The nonlinear interaction leads to the generation of waves with frequencies that are multiples of the frequency of the incident wave, minus the frequency of the…