Related papers: Leak localisation with a measure source convection…
The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…
We propose a novel indicator function for reconstructing acoustic sources from multi-frequency near-field measurements. The theoretical basis is established by a formula relating the scattered field to the source function through the Radon…
Langevin diffusion (LD) is one of the main workhorses for sampling problems. However, its convergence rate can be significantly reduced if the target distribution is a mixture of multiple densities, especially when each component…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of the…
Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful reaction-transport systems remain limited. We apply…
We consider the problem of identifying a sparse initial source condition to achieve a given state distribution of a diffusion-advection partial differential equation after a given final time. The initial condition is assumed to be a finite…
Diffusion models have become emerging generative models. Their sampling process involves multiple steps, and in each step the models predict the noise from a noisy sample. When the models make prediction, the output deviates from the ground…
We establish a complete Widder Theory for the fractional fast diffusion equation. Our work focuses on nonnegative solutions satisfying a certain integral size condition at infinity. We prove that these solutions possess a Radon measure as…
The background caused by radon and its daughters is an important background in the low background liquid scintillator (LS) detectors. The study of the diffusion behaviour of radon in the LS contributes to the analysis of the related…
In this paper, we propose a data-driven leak localization method for water distribution networks (WDNs) which combines two complementary approaches: graph-based interpolation and dictionary classification. The former estimates the complete…
The paper presents an approach to olfactory search for a diffusive emitting source of tracer (e.g. aerosol, gas) in an environment with unknown map of randomly placed and shaped obstacles. The measurements of tracer concentration are…
In this paper, we consider a novel and robust maximum likelihood approach to localizing radiation sources with unknown statistics of the source signal strength. The result utilizes the smallest number of sensors required theoretically to…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare the standard Galerkin discretization using the linear…
Exciton diffusion length plays a vital role in the function of opto-electronic devices. Oftentimes, the domain occupied by an organic semiconductor is subject to surface measurement error. In many experiments, photoluminescence over the…
In this article we consider the numerical approximation of the convection-diffusion-reaction equation. One of the main challenges of designing a numerical method for this problem is that boundary layers occurring in the convection-dominated…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
We investigate the problem of optimal transport in the so-called Beckmann form, i.e. given two Radon measures on a compact set, we seek an optimal flow field which is a vector valued Radon measure on the same set that describes a flow…
Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the…
We study zero-shot conditional sampling with pretrained diffusion models for linear inverse problems, including inpainting and super-resolution. In these problems, the observation determines only part of the unknown signal. The remaining…