相关论文: Solving Multi-Group Neutron Diffusion Eigenvalue P…

In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. However, these methods may suffer from limited accuracy, high…

We propose an eigensolver and the corresponding package, GCGE, for solving large scale eigenvalue problems. This method is the combination of damping idea, subspace projection method and inverse power method with dynamic shifts. To reduce…

In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…

Recently deep neutral networks have achieved promising performance for filling large missing regions in image inpainting tasks. They usually adopted the standard convolutional architecture over the corrupted image, leading to meaningless…

Semantic segmentation is one of the key problems in the field of computer vision, as it enables computer image understanding. However, most research and applications of semantic segmentation focus on addressing unique segmentation problems,…

Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination…

We introduce Differentiable Neural Radiosity, a novel method of representing the solution of the differential rendering equation using a neural network. Inspired by neural radiosity techniques, we minimize the norm of the residual of the…

In a previous article we have shown how one can employ Artificial Neural Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigenvalue problems for…

Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neural networks. This work develops a novel method for solving…

This paper is concerned with the nonnegative inverse eigenvalue problem of finding a nonnegative matrix such that its spectrum is the prescribed self-conjugate set of complex numbers. We first reformulate the nonnegative inverse eigenvalue…

The DC optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of…

In this paper, we propose a neural network learning algorithm for solving eigenvalue problems and boundary value problems (BVPs) for elliptic operators and initial BVPs (IBVPs) of quasi-linear parabolic equations in high dimensions as well…

The linear response eigenvalue problem, which arises from many scientific and engineering fields, is quite challenging numerically for large-scale sparse/dense system, especially when it has zero eigenvalues. Based on a direct sum…

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of…

Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this paper, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered…

Structural decoupling has played an essential role in model-based fault isolation and estimation in past decades, which facilitates accurate fault localization and reconstruction thanks to the diagonal transfer matrix design. However,…

Super-resolution using deep neural networks typically relies on highly curated training sets that are often unavailable in clinical deployment scenarios. Using loss functions that assume Gaussian-distributed residuals makes the learning…

Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…

Computational electromagnetics (CEM) is employed to numerically solve Maxwell's equations, and it has very important and practical applications across a broad range of disciplines, including biomedical engineering, nanophotonics, wireless…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…