Related papers: A Deep Neural Network for Knot Placement in B-spli…
In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train…
This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does…
The problem of fixed knot approximation is convex and there are several efficient approaches to solve this problem, yet, when the knots joining the affine parts are also variable, finding conditions for a best Chebyshev approximation…
Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
This paper deals with the following important research question. Traditionally, the neural network employs non-linear activation functions concatenated with linear operators to approximate a given physical phenomenon. They "fill the space"…
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which…
Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…
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…
In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…
Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…
In this paper, a new approach to solve the cubic B-spline curve fitting problem is presented based on a meta-heuristic algorithm called " dolphin echolocation ". The method minimizes the proximity error value of the selected nodes that…
This paper presents a new approach to selecting knots at the same time as estimating the B-spline regression model. Such simultaneous selection of knots and model is not trivial, but our strategy can make it possible by employing a…
The personnel rostering problem is the problem of finding an optimal way to assign employees to shifts, subject to a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative…
Forward uncertainty quantification in dynamical systems is challenging due to non-smooth or locally oscillating nonlinear behaviors. Spline dimensional decomposition (SDD) addresses such nonlinearity by partitioning input coordinates via…
Deep Neural Networks require large amounts of labeled data for their training. Collecting this data at scale inevitably causes label noise.Hence,the need to develop learning algorithms that are robust to label noise. In recent years, k…
With the edge computing becoming an increasingly adopted concept in system architectures, it is expected its utilization will be additionally heightened when combined with deep learning (DL) techniques. The idea behind integrating demanding…
Numerical preprocessing remains an important component of tabular deep learning, where the representation of continuous features can strongly affect downstream performance. Although its importance is well established for classical…
Deep Neural Networks (DNNs) are a promising tool for Global Navigation Satellite System (GNSS) positioning in the presence of multipath and non-line-of-sight errors, owing to their ability to model complex errors using data. However,…