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We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
Most methods for estimating configurational entropy from molecular simulation data yield upper limits except for harmonic systems where they are exact. Problems arise at diffusive systems and the presence of conformational transitions.…
This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to…
Deploying deep learning (DL) models in medical applications relies on predictive performance and other critical factors, such as conveying trustworthy predictive uncertainty. Uncertainty estimation (UE) methods provide potential solutions…
A nonconformal domain decomposition method based on the hybrid surface integral equation partial differential equation (SIE-PDE) formulation is proposed to solve the transverse magnetic electromagnetic problems. In the hybrid SIE-PDE…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…
We propose a universal image reconstruction method to represent detailed images purely from binary sparse edge and flat color domain. Inspired by the procedures of painting, our framework, based on generative adversarial network, consists…
In this paper, we propose a mesh-free numerical method for solving elliptic PDEs on unknown manifolds, identified with randomly sampled point cloud data. The PDE solver is formulated as a spectral method where the test function space is the…
In deep reinforcement learning (DRL), an agent is trained from a stream of experience. In a continual learning setting, such agents can suffer from plasticity loss: their ability to learn new skills from new experiences diminishes over…
Network embedding aims to learn low-dimensional representations of nodes in a network, while the network structure and inherent properties are preserved. It has attracted tremendous attention recently due to significant progress in…
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory…
An eigenmode projection technique (EPT) is developed and employed to solve problems of electromagnetic resonance in closed cavities and scattering from discontinuities in guided-wave structures. The EPT invokes the eigenmodes of a canonical…
Partial Differential Equation (PDE)-based approaches have gained significant attention in image despeckling due to their strong capability to preserve structural details while suppressing noise. However, conventional second-order PDE models…
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…
Fracture is a very challenging and complicated problem with various applications in engineering and physics. Although it has been extensively studied within the context of mesh-based numerical techniques, such as the finite element method…
We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach.…
Implicit neural representations (INRs) are increasingly being used as tools to map coordinates to signals, encompassing applications from neural fields to texture compression, shape representations, and beyond. Most INR methods are based on…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. Combined with explicit…
We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of…