Related papers: Wavelet Algorithm for Circuit Simulation

This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, which makes adaptivity essential in improving the simulation…

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…

The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…

This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…

This work presents a deep learning-based framework for the solution of partial differential equations on complex computational domains described with computer-aided design tools. To account for the underlying distribution of the training…

In this paper we focus on nonparametric estimators in inverse problems for Poisson processes involving the use of wavelet decompositions. Adopting an adaptive wavelet Galerkin discretization, we find that our method combines the well-known…

Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…

New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…

We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…

We study fully discrete linearized Galerkin finite element approximations to a nonlinear gradient flow, applications of which can be found in many areas. Due to the strong nonlinearity of the equation, existing analyses for implicit schemes…

Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…

Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…

This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…

Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…

We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of…

Gottesman-Knill theorem states that computations on stabilizer circuits can be simulated on a classical computer, conventional simulation algorithms extensively use linear algebra over bit strings. For instance, given a non-adaptive…

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…

Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…