相关论文: A two-stage method for reconstruction of parameter…

The focus of this paper is on the concurrent reconstruction of both the diffusion and potential coefficients present in an elliptic/parabolic equation, utilizing two internal measurements of the solutions. A decoupled algorithm is…

We propose a double obstacle phase field approach to the recovery of piece-wise constant diffusion coefficients for elliptic partial differential equations. The approach to this inverse problem is that of optimal control in which we have a…

This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…

We revisit the inverse problem of reconstructing a spatially varying diffusion coefficient in stationary elliptic equations from boundary Cauchy data. From a theoretical perspective, we introduce a gradient-weighted modification of the…

We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex…

Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…

The flux reconstruction (FR) method has gained popularity within the research community. The approach has been demonstrated to recover high-order methods such as the discontinuous Galerkin (DG) method. Stability analyses have been conducted…

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…

This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…

We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here we develop a two-stage super-resolution method using spectral filtering to restore the high-wavenumber…

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…

A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

Diffusion and flow models achieve high generative quality but remain computationally expensive due to slow multi-step sampling. Distillation methods accelerate them by training fast student generators, yet most existing objectives lack a…

In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…

In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at…

In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…

This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…

The Kramers-Kronig (KK) algorithm, useful for retrieving the phase of a spectrum based on the known spectral amplitude, is applied to reconstruct the impulse response of a diffusive medium. It is demonstrated by a simulation of a 1D…

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…