This repository provides a PyTorch implementation of Hierarchical Deep-Learning Neural Networks (HiDeNN) for the Finite Element Method (FEM), based on Zhang et al., “Hierarchical Deep-Learning Neural ...

Abstract: The Galerkin FEM based on GBCs over polygon or polyhedron are heavily time consuming. In light of the simple shape functions in simple geometric elements, such as triangle, tetrahedron, a ...

Abstract: Lagrange interpolation is widely used in signal processing; however, high-order interpolation is affected by Runge phenomenon and the inflexible basis function construction. In this paper, ...

Fractal interpolation functions (FIFs) represent an innovative class of methods for modelling and approximating complex data. Derived from iterated function systems, these functions enable the ...

Interpolation is essential to most studies of spatial patterns in ecology. However, there has been a lack of quantitative techniques for interpolation of spatial data. This paper introduces a new ...

We study mean-value interpolation of Hermite type by a polynomial of degree m in z−1 and n in z. We show that the interpolation problem corresponding to the integrals over the segments of the form ...

./code/PD_Impute_interp+knn_test.R <- source this file to run the imputation on the TEST set data with linear interpolation first and then the KNN algorithm; please ...