Related papers: NEP: a module for the parallel solution of nonline…
Shape optimisation of thin-shell structures requires a flexible, differentiable geometric representation suitable for gradient-based optimisation. We propose a neural parametric representation (NRep) for the shell mid-surface based on a…
This paper concerns a class of monotone eigenvalue problems with eigenvector nonlinearities (mNEPv). The mNEPv is encountered in applications such as the computation of joint numerical radius of matrices, best rank-one approximation of…
We present a parallel profiling tool, GAPP, that identifies serialization bottlenecks in parallel Linux applications arising from load imbalance or contention for shared resources . It works by tracing kernel context switch events using…
In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite generalized eigenvalue problem lying in an interval on the real…
Submodular functions allow to model many real-world optimisation problems. This paper introduces approaches for computing diverse sets of high quality solutions for submodular optimisation problems. We first present diversifying greedy…
Nonlinear spectral problems arise across a range of fields, including mechanical vibrations, fluid-solid interactions, and photonic crystals. Discretizing infinite-dimensional nonlinear spectral problems often introduces significant…
The linear FEAST algorithm is a method for solving linear eigenvalue problems. It uses complex contour integration to calculate the eigenvectors whose eigenvalues that are located inside some user-defined region in the complex plane. This…
Spiking neural network (SNN), as the third generation of artificial neural networks, has been widely adopted in vision and audio tasks. Nowadays, many neuromorphic platforms support SNN simulation and adopt Network-on-Chips (NoC)…
We say that a list of complex numbers is "realisable" if it is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of characterising all realisable lists. Although the NIEP…
We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization. Our self-supervised models adapt to input operators using coarse spectral…
Eigenvalue problems for elliptic operators play an important role in science and engineering applications, where efficient and accurate numerical computation is essential. In this work, we propose a novel operator inference approach for…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
In this paper, an inexact Newton method for solving real-valued nonlinear eigenvalue problems with eigenvector dependency (NEPv) is introduced that is able to solve the problem on a matrix level. Our main contribution is to derive a variant…
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…
A dynamic method to solve the Non-linear Programming (NLP) problem with Equality Constraints (ECs) and Inequality Constraints (IECs) is proposed. Inspired by the Lyapunov continuous-time dynamics stability theory in the control field, the…
The last ten years have witnessed fast spreading of massively parallel computing clusters, from leading supercomputing facilities down to the average university computing center. Many companies in the private sector have undergone a similar…
Solving partial differential equations (PDEs) has been a fundamental problem in computational science and of wide applications for both scientific and engineering research. Due to its universal approximation property, neural network is…
Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…