Related papers: PFNN: A Penalty-Free Neural Network Method for Sol…
Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…
Convolutional Neural Networks (CNNs) have a large number of parameters and take significantly large hardware resources to compute, so edge devices struggle to run high-level networks. This paper proposes a novel method to reduce the…
Deep neural networks (DNNs) have demonstrated remarkable success in various fields. However, the large number of floating-point operations (FLOPs) in DNNs poses challenges for their deployment in resource-constrained applications, e.g.,…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…
Fourier phase retrieval (FPR) is a challenging task widely used in various applications. It involves recovering an unknown signal from its Fourier phaseless measurements. FPR with few measurements is important for reducing time and hardware…
Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…
Nonconvex optimization problems such as the ones in training deep neural networks suffer from a phenomenon called saddle point proliferation. This means that there are a vast number of high error saddle points present in the loss function.…
Probabilistic Neural Network (PNN) is a feed-forward artificial neural network developed for solving classification problems. This paper proposes a hardware implementation of an approximated PNN (APNN) algorithm in which the conventional…
This paper introduces a novel two-stream deep model based on graph convolutional network (GCN) architecture and feed-forward neural networks (FFNN) for learning the solution of nonlinear partial differential equations (PDEs). The model aims…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically…
In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty re-formulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a non-zero…
Deep learning approaches for partial differential equations (PDEs) have received much attention in recent years due to their mesh-freeness and computational efficiency. However, most of the works so far have concentrated on time-dependent…
This paper presents a high-order deferred correction algorithm combined with penalty iteration for solving free and moving boundary problems, using a fourth-order finite difference method. Typically, when free boundary problems are solved…
Precise representation of large-scale undirected network is the basis for understanding relations within a massive entity set. The undirected network representation task can be efficiently addressed by a symmetry non-negative latent factor…
Deep neural networks (DNNs) are usually over-parameterized to increase the likelihood of getting adequate initial weights by random initialization. Consequently, trained DNNs have many redundancies which can be pruned from the model to…
A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…
In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…