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Contemporary approaches to instance segmentation in cell science use 2D or 3D convolutional networks depending on the experiment and data structures. However, limitations in microscopy systems or efforts to prevent phototoxicity commonly…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication…
We design and analyze several Finite Element Methods (FEMs) applied to the Caffarelli-Silvestre extension that localizes the fractional powers of symmetric, coercive, linear elliptic operators in bounded domains with Dirichlet boundary…
In this paper, an enhanced Virtual Element Method (VEM) formulation is proposed for plane elasticity. It is based on the improvement of the strain representation within the element, without altering the degree of the displacement…
Spectral residual methods are powerful tools for solving nonlinear systems of equations without derivatives. In a recent paper, it was shown that an acceleration technique based on the Sequential Secant Method can greatly improve its…
The Phase Extraction Neural Network (PhENN) is a computational architecture, based on deep machine learning, for lens-less quantitative phase retrieval from raw intensity data. PhENN is a deep convolutional neural network trained through…
Diffusion-weighted Magnetic Resonance Imaging (dMRI) is an essential tool in neuroimaging. It is arguably the sole noninvasive technique for examining the microstructural properties and structural connectivity of the brain. Recent years…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
Spacecraft Pose Estimation (SPE) is a fundamental capability for autonomous space operations such as rendezvous, docking, and in-orbit servicing. Hybrid pipelines that combine object detection, keypoint regression, and Perspective-n-Point…
Surface integral equation (SIE) methods are of great interest for the efficient electromagnetic modeling of various devices, from integrated circuits to antenna arrays. Existing acceleration algorithms for SIEs, such as the adaptive…
This research presents a comprehensive assessment of pan-sharpening techniques for satellite imagery, focusing on the critical aspects of spectral fidelity and spatial enhancement. Motivated by the need for informed algorithm selection in…
In this paper, a non-polynomial spectral Petrov-Galerkin method and associated collocation method for substantial fractional differential equations (FDEs) are proposed, analyzed, and tested. We extend a class of generalized Laguerre…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
Foundation models pre-trained on large-scale data have been widely witnessed to achieve success in various natural imaging downstream tasks. Parameter-efficient fine-tuning (PEFT) methods aim to adapt foundation models to new domains by…
In the last few years, large improvements in image clustering have been driven by the recent advances in deep learning. However, due to the architectural complexity of deep neural networks, there is no mathematical theory that explains the…
Astrophysical explorations are underpinned by large-scale stellar spectroscopy surveys, necessitating a paradigm shift in spectral fitting techniques. Our study proposes three enhancements to transcend the limitations of the current…
This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…