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In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…
The spatio-temporal graph learning is becoming an increasingly important object of graph study. Many application domains involve highly dynamic graphs where temporal information is crucial, e.g. traffic networks and financial transaction…
Numerical simulation of multi-phase fluid dynamics in porous media is critical to a variety of geoscience applications. Data-driven surrogate models using Convolutional Neural Networks (CNNs) have shown promise but are constrained to…
We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…
In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography (EIT), where the goal is to recover the conductivity in a medium from boundary current-to-voltage measurements, i.e., the…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
Electron tomography (ET) has become a standard technique for 3D characterization of materials at the nano-scale. Traditional reconstruction algorithms such as weighted back projection suffer from disruptive artifacts with insufficient…
Mammography is a specific type of breast imaging that uses low-dose X-rays to detect cancer in early stage. During the exam, the women breast is compressed between two plates until a nearly uniform breast thickness is obtained. This…
U-Nets are a go-to, state-of-the-art neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper,…
Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…
In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…
U-Net has been the go-to architecture for medical image segmentation tasks, however computational challenges arise when extending the U-Net architecture to 3D images. We propose the Implicit U-Net architecture that adapts the efficient…
Learning universal graph representations across heterogeneous domains is difficult because graph datasets differ in topology, node-attribute semantics, feature dimensions, and even attribute availability. We propose GraphVec, a…
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…
Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…
To study the fundamental physics of complex multiphase flow systems using advanced measurement techniques, especially the electrical capacitance tomography (ECT) approach, this article carries out an initial literature review of the ECT…
Artificial intelligence in construction increasingly depends on structured representations such as Building Information Models and knowledge graphs, yet early-stage building designs are predominantly created as flexible…
Deep neural networks have been widely used in medical image analysis and medical image segmentation is one of the most important tasks. U-shaped neural networks with encoder-decoder are prevailing and have succeeded greatly in various…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
Deep learning-based methods have revolutionized the field of imaging inverse problems, yielding state-of-the-art performance across various imaging domains. The best performing networks incorporate the imaging operator within the network…