Related papers: A Refinement Algorithm for Generalized B-splines
In this paper we introduce a new method for automatically selecting knots in spline regression. The approach consists in setting a large number of initial knots and fitting the spline regression through a penalized likelihood procedure…
In this paper we introduce a novel method of gradient normalization and decay with respect to depth. Our method leverages the simple concept of normalizing all gradients in a deep neural network, and then decaying said gradients with…
Rationalizing which parts of a molecule drive the predictions of a molecular graph convolutional neural network (GCNN) can be difficult. To help, we propose two simple regularization techniques to apply during the training of GCNNs: Batch…
Recently the author and U. Reif introduced the concept of diversification of uniform tensor product B-splines. Based on this concept, we give a new constructive modification of non-uniform B-splines. The resulting spline spaces are…
We consider two-stage scattered data fitting with truncated hierarchical B-splines (THB-splines) for the adaptive reconstruction of industrial models. The first stage of the scheme is devoted to the computation of local least squares…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…
We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with…
This paper proposes the estimation of a smooth graphon model for network data analysis using principles of the EM algorithm. The approach considers both variability with respect to ordering the nodes of a network and smooth estimation of…
This paper presents the basic principles of partition of unity systems and B-splines. Analysis of these systems is performed using Fourier analysis, multi-resolution analysis, and wavelet analysis.
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the…
Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we…
In this work, we propose a new paradigm of iterative model-based reconstruction algorithms for providing real-time solution for zooming-in and refining a region of interest in medical and clinical tomographic images. This algorithmic…
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…
New algorithms for fast wavelet transforms with biorthogonal spline wavelets on nonuniform grids are presented. In contrary to classical wavelet transforms, the algorithms are not based on filter coefficients, but on algorithms for B-spline…
Methods for choosing a fixed set of knot locations in additive spline models are fairly well established in the statistical literature. While most of these methods are in principle directly extendable to non-additive surface models, they…
In this work we present a new WENO b-spline based quasi-interpolation algorithm. The novelty of this construction resides in the application of the WENO weights to the b-spline functions, that are a partition of unity, instead to the…
G-splines are a generalization of B-splines that deals with extraordinary points by imposing G^1 constraints across their spoke edges, thus obtaining a continuous tangent plane throughout the surface. Using the isoparametric concept and the…
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By…
How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model…