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Graph neural networks (GNNs) which apply the deep neural networks to graph data have achieved significant performance for the task of semi-supervised node classification. However, only few work has addressed the adversarial robustness of…

Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…

Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary modeling, but often suffer from sensitivity to parameter…

This paper proposes a novel image segmentation approachthat integrates fully convolutional networks (FCNs) with a level setmodel. Compared with a FCN, the integrated method can incorporatesmoothing and prior information to achieve an…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Deep Neural Networks (DNNs) have become increasingly popular in computer vision, natural language processing, and other areas. However, training and fine-tuning a deep learning model is computationally intensive and time-consuming. We…

Deep Neural Networks (DNNs) are typically trained by backpropagation in a batch learning setting, which requires the entire training data to be made available prior to the learning task. This is not scalable for many real-world scenarios…

We present PFNN, a penalty-free neural network method, to efficiently solve a class of second-order boundary-value problems on complex geometries. To reduce the smoothness requirement, the original problem is reformulated to a weak form so…

Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…

Deep Neural Networks (DNNs) are capable of solving complex problems in domains related to embedded systems, such as image and natural language processing. To efficiently implement DNNs on a specific FPGA platform for a given cost criterion,…

Recently, deep neural networks (DNNs) have shown advantages in accelerating optimization algorithms. One approach is to unfold finite number of iterations of conventional optimization algorithms and to learn parameters in the algorithms.…

We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully…

Complex design problems are common in the scientific and industrial fields. In practice, objective functions or constraints of these problems often do not have explicit formulas, and can be estimated only at a set of sampling points through…

To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…

With the edge computing becoming an increasingly adopted concept in system architectures, it is expected its utilization will be additionally heightened when combined with deep learning (DL) techniques. The idea behind integrating demanding…

Deep-unfolding neural networks (NNs) have received great attention since they achieve satisfactory performance with relatively low complexity. Typically, these deep-unfolding NNs are restricted to a fixed-depth for all inputs. However, the…

Deep learning based methods hold state-of-the-art results in image denoising, but remain difficult to interpret due to their construction from poorly understood building blocks such as batch-normalization, residual learning, and feature…

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

In this paper, we propose a novel algorithm called Neuron-wise Parallel Subspace Correction Method (NPSC) for the finite neuron method that approximates numerical solutions of partial differential equations (PDEs) using neural network…

This work investigates the electrical impedance tomography (EIT) problem when only limited boundary measurements are available, which is known to be challenging due to the extreme ill-posedness. Based on the direct sampling method (DSM), we…