Related papers: Adversarial neural network methods for topology op…

We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…

We show the sup-norm convergence of deep neural network estimators with a novel adversarial training scheme. For the nonparametric regression problem, it has been shown that an estimator using deep neural networks can achieve better…

Recently, machine learning has been introduced in the inverse design of physical devices, i.e., the automatic generation of device geometries for a desired physical response. In particular, generative adversarial networks have been proposed…

We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the obstacle problem (which is an elliptic variational…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Recently, substantial progress has been made in language modeling by using deep neural networks. However, in practice, large scale neural language models have been shown to be prone to overfitting. In this paper, we present a simple yet…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…

Despite the high performance achieved by deep neural networks on various tasks, extensive studies have demonstrated that small tweaks in the input could fail the model predictions. This issue of deep neural networks has led to a number of…

Adversarial neural networks solve many important problems in data science, but are notoriously difficult to train. These difficulties come from the fact that optimal weights for adversarial nets correspond to saddle points, and not…

In the past few years, it has become increasingly evident that deep neural networks are not resilient enough to withstand adversarial perturbations in input data, leaving them vulnerable to attack. Various authors have proposed strong…

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables…

Automatic music transcription is considered to be one of the hardest problems in music information retrieval, yet recent deep learning approaches have achieved substantial improvements on transcription performance. These approaches commonly…

Automated machine learning (AutoML) methods improve upon existing models by optimizing various aspects of their design. While present methods focus on hyperparameters and neural network topologies, other aspects of neural network design can…

Recent work has proposed neural network pruning techniques to reduce the size of a network while preserving robustness against adversarial examples, i.e., well-crafted inputs inducing a misclassification. These methods, which we refer to as…

The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…

A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…

Adversarial attack has recently become a tremendous threat to deep learning models. To improve the robustness of machine learning models, adversarial training, formulated as a minimax optimization problem, has been recognized as one of the…