相关论文: DeepTV: A neural network approach for total variat…

From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared…

We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functions representing by deep neural networks are…

In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

We propose an adaptive version of the total variation algorithm proposed in [3] for computing the balanced cut of a graph. The algorithm from [3] used a sequence of inner total variation minimizations to guarantee descent of the balanced…

We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…

Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…

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…

Fitting a function by using linear combinations of a large number $N$ of `simple' components is one of the most fruitful ideas in statistical learning. This idea lies at the core of a variety of methods, from two-layer neural networks to…

Recent studies showed that the generalization of neural networks is correlated with the sharpness of the loss landscape, and flat minima suggests a better generalization ability than sharp minima. In this paper, we propose a novel method…

We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…

We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…

Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort…

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…

In this paper, we seek to tackle a challenge in training low-precision networks: the notorious difficulty in propagating gradient through a low-precision network due to the non-differentiable quantization function. We propose a solution by…

Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…

Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the…

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…

We motivate the use of neural networks for the construction of numerical solutions to differential equations. We prove that there exists a feed-forward neural network that can arbitrarily minimise an objective function that is zero at the…