Related papers: A PINNs approach for the computation of eigenvalue…

In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding…

Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonlinear eigenvalue problems. We present a natural generalization…

We propose gradient-enhanced PINNs based on transfer learning (TL-gPINNs) for inverse problems of the function coefficient discovery in order to overcome deficiency of the discrete characterization of the PDE loss in neural networks and…

Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &\Delta {\mathbf u}+ \alpha{\rm grad}(\text{div}{\mathbf…

We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep…

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…

Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…

We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network which is trained under the guidance of a probabilistic…

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…

In this paper the author introduces a new domain decomposition method for the solution of discretised integral equation eigenvalue problems. The new domain decomposition method is motivated by the so-called automated multi-level…

This paper is concerned with the Dirichlet eigenvalue problem associated to the $\infty$-Laplacian in metric spaces. We establish a direct PDE approach to find the principal eigenvalue and eigenfunctions in a proper geodesic space without…

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao et.al. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…

Generalized eigenvalue problems involving a singular pencil are very challenging to solve, both with respect to accuracy and efficiency. The existing package Guptri is very elegant but may sometimes be time-demanding, even for small and…

The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…

We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally…

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the…