Related papers: A Least-Squares-Based Regularity-Conforming Neural…

We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing with either variational and non-variational problems, and…

The single image super-resolution(SISR) algorithms under deep learning currently have two main models, one based on convolutional neural networks and the other based on Transformer. The former uses the stacking of convolutional layers with…

Most neural network pruning methods, such as filter-level and layer-level prunings, prune the network model along one dimension (depth, width, or resolution) solely to meet a computational budget. However, such a pruning policy often leads…

We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…

With the improvement of the pattern recognition and feature extraction of Deep Neural Networks (DPNNs), image-based design and optimization have been widely used in multidisciplinary researches. Recently, a Reconstructive Neural Network…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…

In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of…

Recently, methods for neural surface representation and rendering, for example NeuS, have shown that learning neural implicit surfaces through volume rendering is becoming increasingly popular and making good progress. However, these…

We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Line segment detection is a fundamental low-level task in computer vision, and improvements in this task can impact more advanced methods that depend on it. Most new methods developed for line segment detection are based on Convolutional…

This paper investigates whether sequence models can learn to perform numerical algorithms, e.g. gradient descent, on the fundamental problem of least squares. Our goal is to inherit two properties of standard algorithms from numerical…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks…

Deep convolutional neural networks (CNNs) have brought breakthroughs in processing clinical electrocardiograms (ECGs), speaker-independent speech and complex images. However, typical CNNs require a fixed input size while it is common to…

This work develops robust diffusion recursive least squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Phase unwrapping is a classical ill-posed problem which aims to recover the true phase from wrapped phase. In this paper, we introduce a novel Convolutional Neural Network (CNN) that incorporates a Spatial Quad-Directional Long Short Term…

Foundation models and their checkpoints have significantly advanced deep learning, boosting performance across various applications. However, fine-tuned models often struggle outside their specific domains and exhibit considerable…