Related papers: Automatic differentiation as an effective tool in …
In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time- convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in…
Algorithmic differentiation (AD) allows exact computation of derivatives given only an implementation of an objective function. Although many AD tools are available, a proper and efficient implementation of AD methods is not…
We consider the electrostatic inverse boundary value problem also known as electrical impedance tomography (EIT) for the case where the conductivity is a piecewise linear function on a domain $\Omega\subset\mathbb{R}^n$ and we show that a…
Solving inverse partial differential equation (PDE) problems is a fundamental topic in scientific research due to its broad significance across a wide range of real-world applications. Inverse PDE problems arise across medical imaging,…
We introduce a new geometric approach for the homogenization and inverse homogenization of the divergence form elliptic operator with rough conductivity coefficients $\sigma(x)$ in dimension two. We show that conductivity coefficients are…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
The Euler Characteristic Transform (ECT) of Turner et al. provides a way to statistically analyze non-diffeomorphic shapes without relying on landmarks. In applications, this transform is typically approximated by a discrete set of…
The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…
The success of deep neural networks often relies on a large amount of labeled examples, which can be difficult to obtain in many real scenarios. To address this challenge, unsupervised methods are strongly preferred for training neural…
Texture editing is a crucial task in 3D modeling that allows users to automatically manipulate the surface materials of 3D models. However, the inherent complexity of 3D models and the ambiguous text description lead to the challenge in…
Label-free tomographic microscopy offers a compelling means to visualize three-dimensional (3D) refractive index (RI) distributions from two-dimensional (2D) intensity measurements. However, limited forward-model accuracy and the ill-posed…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current.…
The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…
Visual Anomaly Detection (VAD) is a key task in industrial settings, where minimizing operational costs is essential. Deploying deep learning models within Internet of Things (IoT) environments introduces specific challenges due to limited…
The inverse problem of electrical impedance tomography is severely ill-posed. In particular, the resolution of images produced by impedance tomography deteriorates as the distance from the measurement boundary increases. Such depth…
Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) remains challenging. Because physical domains are naturally…
We investigate the automatic differentiation of dominant eigensolver where only a small proportion of eigenvalues and corresponding eigenvectors are obtained. Backpropagation through the dominant eigensolver involves solving certain…