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A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

Neural and Evolutionary Computing · Computer Science 2022-09-02 Toni Schneidereit , Michael Breuß

The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually converges slowly. To speed up the convergence of this…

Numerical Analysis · Mathematics 2025-07-10 Wenhan Gao , Chunmei Wang

With rapid progress and significant successes in a wide spectrum of applications, deep learning is being applied in many safety-critical environments. However, deep neural networks have been recently found vulnerable to well-designed input…

Machine Learning · Computer Science 2018-07-10 Xiaoyong Yuan , Pan He , Qile Zhu , Xiaolin Li

Artificial neural networks have been successfully used for many different classification tasks including malware detection and distinguishing between malicious and non-malicious programs. Although artificial neural networks perform very…

Machine Learning · Computer Science 2019-09-12 Robert Podschwadt , Hassan Takabi

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

Numerical Analysis · Mathematics 2025-04-24 Yifan Wang , Zhongshuo Lin , Hehu Xie

Though deep neural networks have achieved state-of-the-art performance in visual classification, recent studies have shown that they are all vulnerable to the attack of adversarial examples. Small and often imperceptible perturbations to…

Machine Learning · Computer Science 2018-06-05 Pinlong Zhao , Zhouyu Fu , Ou wu , Qinghua Hu , Jun Wang

With the popularity of 3D sensors in self-driving and other robotics applications, extensive research has focused on designing novel neural network architectures for accurate 3D point cloud completion. However, unlike in point cloud…

Computer Vision and Pattern Recognition · Computer Science 2023-01-24 Mengxi Wu , Hao Huang , Yi Fang

Deep neural networks (DNNs) have been widely used in the fields such as natural language processing, computer vision and image recognition. But several studies have been shown that deep neural networks can be easily fooled by artificial…

Computer Vision and Pattern Recognition · Computer Science 2019-01-23 Long Zhang , Xuechao Sun , Yong Li , Zhenyu Zhang

With the increasing amount of available data and advances in computing capabilities, deep neural networks (DNNs) have been successfully employed to solve challenging tasks in various areas, including healthcare, climate, and finance.…

Machine Learning · Computer Science 2023-01-12 Marcele O. K. Mendonça , Javier Maroto , Pascal Frossard , Paulo S. R. Diniz

Deep Neural Networks (DNNs) have recently made significant progress in many fields. However, studies have shown that DNNs are vulnerable to adversarial examples, where imperceptible perturbations can greatly mislead DNNs even if the full…

Computer Vision and Pattern Recognition · Computer Science 2023-05-09 Zhaoxia Yin , Shaowei Zhu , Hang Su , Jianteng Peng , Wanli Lyu , Bin Luo

Deep Neural Networks (DNNs) have been widely applied in various recognition tasks. However, recently DNNs have been shown to be vulnerable against adversarial examples, which can mislead DNNs to make arbitrary incorrect predictions. While…

Cryptography and Security · Computer Science 2018-10-15 Chaowei Xiao , Ruizhi Deng , Bo Li , Fisher Yu , Mingyan Liu , Dawn Song

Neural network (NN) interatomic potentials provide fast prediction of potential energy surfaces, closely matching the accuracy of the electronic structure methods used to produce the training data. However, NN predictions are only reliable…

Machine Learning · Computer Science 2021-08-31 Daniel Schwalbe-Koda , Aik Rui Tan , Rafael Gómez-Bombarelli

We propose to generate adversarial samples by modifying activations of upper layers encoding semantically meaningful concepts. The original sample is shifted towards a target sample, yielding an adversarial sample, by using the modified…

Machine Learning · Computer Science 2022-03-22 Johannes Schneider , Giovanni Apruzzese

We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…

Numerical Analysis · Mathematics 2024-04-15 Zhaodong Xu , Zhiqiang Sheng

With the development of high computational devices, deep neural networks (DNNs), in recent years, have gained significant popularity in many Artificial Intelligence (AI) applications. However, previous efforts have shown that DNNs were…

Computation and Language · Computer Science 2019-04-12 Wei Emma Zhang , Quan Z. Sheng , Ahoud Alhazmi , Chenliang Li

Incorporating encoding-decoding nets with adversarial nets has been widely adopted in image generation tasks. We observe that the state-of-the-art achievements were obtained by carefully balancing the reconstruction loss and adversarial…

Computer Vision and Pattern Recognition · Computer Science 2018-01-23 Zhifei Zhang , Yang Song , Hairong Qi

We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…

Machine Learning · Statistics 2016-11-29 Dilin Wang , Qiang Liu

Adversarial training has become the primary method to defend against adversarial samples. However, it is hard to practically apply due to many shortcomings. One of the shortcomings of adversarial training is that it will reduce the…

Machine Learning · Computer Science 2021-08-31 Zhishen Nie , Ying Lin , Sp Ren , Lan Zhang

Learning by contrasting positive and negative samples is a general strategy adopted by many methods. Noise contrastive estimation (NCE) for word embeddings and translating embeddings for knowledge graphs are examples in NLP employing this…

Computation and Language · Computer Science 2018-08-06 Avishek Joey Bose , Huan Ling , Yanshuai Cao

We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…

Methodology · Statistics 2021-08-02 Amanda Lenzi , Julie Bessac , Johann Rudi , Michael L. Stein