Related papers: Bridging and Improving Theoretical and Computation…
This work presents a data-driven framework for fast forward and inverse analysis in topology optimization (TO) by combining Rank Reduction Autoencoders (RRAEs) with neural latent-space mappings. The methodology targets the efficient…
Electrical Impedance Tomography (EIT) is a noninvasive imaging technique that does not use ionizing radiation, with application both in environmental sciences and in health. Image reconstruction is performed by solving an inverse problem…
Electrical impedance tomography (EIT) enables non-invasive, spatially continuous reconstruction of internal conductivity distributions, providing full field sensing beyond conventional point measurements. Here, we report the first in situ…
This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper…
Electrical impedance tomography (EIT) provides an attractive solution for large-area tactile sensing due to its minimal wiring and shape flexibility, but its nonlinear inverse problem often leads to severe artifacts and inaccurate contact…
When and why can evolutionary multi-objective optimization (EMO) algorithms cover the entire Pareto set? That is a major concern for EMO researchers and practitioners. A recent theoretical study revealed that (roughly speaking) if the…
Parallel-beam X-ray computed tomography (CT) and electrical impedance tomography (EIT) are two imaging modalities which stem from completely different underlying physics, and for decades have been thought to have little in common either…
Accurate plasma state reconstruction will be crucial for the success of ITER and future fusion plants, but the harsh conditions of a burning plasma will make diagnostic operation more challenging than in current machines. Integrated data…
Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact…
Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we…
In computational inverse problems, the optimal experimental design (OED) problem seeks the best locations in time and space at which to take measurements. We investigate the nonlinear OED problem in the context of continuously-indexed…
The regularized D-bar method is a popular method for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It utilizes the low-pass truncated scattering data in the non-linear Fourier domain to solve…
We propose a control-oriented optimal experimental design (cOED) approach for linear PDE-constrained Bayesian inverse problems. In particular, we consider optimal control problems with uncertain parameters that need to be estimated by…
This work examines two ways of using proper orthogonal decomposition (POD) to enhance the prior work of EITPose, a device which uses electrical impedance tomography (EIT) to detect posture by way of a band of electrodes on the forearm.…
We consider the problem of computing the topology and describing the geometry of a parametric curve in $\mathbb{R}^n$. We present an algorithm, PTOPO, that constructs an abstract graph that is isotopic to the curve in the embedding space.…
This paper considers the problem of noise-robust neural operator approximation for the solution map of Calder\'on's inverse conductivity problem. In this continuum model of electrical impedance tomography (EIT), the boundary measurements…
We provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint based solution of partial differential equation (PDE) constrained optimization. This…
We consider optimal experimental design (OED) problems in selecting the most informative observation sensors to estimate model parameters in a Bayesian framework. Such problems are computationally prohibitive when the…