Related papers: A. hexahedron element formulation with a new multi…
This paper proposes Deep Hyperalignment (DHA) as a regularized, deep extension, scalable Hyperalignment (HA) method, which is well-suited for applying functional alignment to fMRI datasets with nonlinearity, high-dimensionality (broad ROI),…
Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for…
Model merging offers a scalable alternative to multi-task learning but often yields suboptimal performance on classification tasks. We attribute this degradation to a geometric misalignment between the merged encoder and static…
In this article we introduce Line Smoothness-Increasing Accuracy-Conserving Multi-Resolution Analysis\linebreak (LSIAC-MRA). This is a procedure for exploiting convolution kernel post-processors for obtaining more accurate multi-dimensional…
In this paper, the notion of {\em $p$-adic multiresolution analysis (MRA)} is introduced. We use a ``natural'' refinement equation whose solution (a refinable function) is the characteristic function of the unit disc. This equation reflects…
An Iterative Reanalysis Approximation (IRA) is integrated with the Moving Morphable Components (MMCs) based topology optimization (IRA-MMC) in this study. Compared with other classical topology optimization methods, the Finite Element (FE)…
In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…
Recovering high-resolution structural and compositional information from coherent X-ray measurements involves solving coupled, nonlinear, and ill-posed inverse problems. Ptychography reconstructs a complex transmission function from…
Multiresolution approximation (MRA) of the vector fields on T^3 is studied. We introduced in the Fourier space a triad of vector fields called helical vectors which derived from the spherical coordinate system basis. Utilizing the helical…
We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which…
In the past two decades, extensive research has been conducted on the (co)homology of various models of random simplicial complexes. So far, it has always been examined merely as a list of groups. This paper expands upon this by describing…
This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
We propose a novel deep learning framework for fast prediction of boundaries of two-dimensional simply connected domains using wavelets and Multi Resolution Analysis (MRA). The boundaries are modelled as (piecewise) smooth closed curves…
Magnetic resonance imaging (MRI) acquisition, reconstruction, and segmentation are usually processed independently in the conventional practice of MRI workflow. It is easy to notice that there are significant relevances among these tasks…
Predicting how the microstructure governs the mechanical response of heterogeneous materials is essential for optimizing design and performance. Yet this task remains difficult due to the complex, high dimensional nature of microstructural…
The multi-scale entanglement renormalization ansatz (MERA) provides a natural description of the ground state of a quantum critical Hamiltonian on the lattice. From an optimized MERA, one can extract the scaling dimensions of the underlying…