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Quantum Circuits for the heat equation with physical boundary conditions via Schrödingerisation

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arXiv 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, CC BY-NC-ND.

关键词： Ordinary differential equations

Research on intelligent recognition and encryption algorithm of network big data image

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IOP Conference Series: Earth and Environmental Science 2021年第4期632卷

作者： Jubao Qu School of mathematics and computer Wuyi University Fujian 354300 China The Key Laboratory of Cognitive Computing and Intelligent Information Processing of Fujian Education Institutions (Wuyi University) Wuyi University Wuyishan Fujian 354300 China

In view of the identification and encryption of massive network information in the era of big data, this paper proposes to use intelligent image recognition technology to analyze the required information, then classify it according to the big data clustering method, and use pseudo pixel encryption algorithm for multiple encryption. The simulation results show that the algorithm has high recognition rate, good encryption effect, strong anti-interference ability and good ability to protect network image information.

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A Progressive Image Restoration Network for High-order Degradation Imaging in Remote Sensing

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arXiv 2024年

作者： Feng, Yujie Yang, Yin Fan, Xiaohong Zhang, Zhengpeng Bu, Lijing Zhang, Jianping School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory for Intelligent Computing and Information Processing of the Ministry of Education Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Xiangtan411105 China College of Mathematical Medicine Zhejiang Normal University Jinhua321004 China School of Automation and Electronic Information Xiangtan University Xiangtan411105 China

Recently, deep learning methods have gained remarkable achievements in the field of image restoration for remote sensing (RS). However, most existing RS image restoration methods focus mainly on conventional first-order degradation models, which may not effectively capture the imaging mechanisms of remote sensing images. Furthermore, many RS image restoration approaches that use deep learning are often criticized for their lacks of architecture transparency and model interpretability. To address these problems, we propose a novel progressive restoration network for high-order degradation imaging (HDI-PRNet), to progressively restore different image degradation. HDI-PRNet is developed based on the theoretical framework of degradation imaging, offering the benefit of mathematical interpretability within the unfolding network. The framework is composed of three main components: a module for image denoising that relies on proximal mapping prior learning, a module for image deblurring that integrates Neumann series expansion with dual-domain degradation learning, and a module for super-resolution. Extensive experiments demonstrate that our method achieves superior performance on both synthetic and real remote sensing images. Copyright © 2024, The Authors. All rights reserved.

关键词： Image reconstruction

Efficient and adaptive kernelization for nonlinear max-margin multi-view learning

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arXiv 2019年

作者： Du, Changying Jia He, B. Du, Changde Zhuang, Fuzhen He, Qing Long, Guoping Huawei Noah's Ark Lab Beijing100085 China Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China Institute of Software Chinese Academy of Sciences Beijing100190 China Research Center for Brain-Inspired Intelligence Institute of Automation CAS Beijing China University of Chinese Academy of Sciences Beijing100049 China

Existing multi-view learning methods based on kernel function either require the user to select and tune a single predefined kernel or have to compute and store many Gram matrices to perform multiple kernel learning. Apart from the huge consumption of manpower, computation and memory resources, most of these models seek point estimation of their parameters, and are prone to overfitting to small training data. This paper presents an adaptive kernel nonlinear max-margin multi-view learning model under the Bayesian framework. Specifically, we regularize the posterior of an efficient multi-view latent variable model by explicitly mapping the latent representations extracted from multiple data views to a random Fourier feature space where max-margin classification constraints are imposed. Assuming these random features are drawn from Dirichlet process Gaussian mixtures, we can adaptively learn shift-invariant kernels from data according to Bochners theorem. For inference, we employ the data augmentation idea for hinge loss, and design an efficient gradient-based MCMC sampler in the augmented space. Having no need to compute the Gram matrix, our algorithm scales linearly with the size of training set. Extensive experiments on real-world datasets demonstrate that our method has superior performance. Copyright © 2019, The Authors. All rights reserved.

关键词： Bayesian networks

A Secure and Efficient Scheme for Digital Gift Certificates

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Journal of information Hiding and Multimedia Signal processing 2015年第3期6卷 416-429页

作者： Liu, Yanjun Chang, Chin-Chen Sun, Chin-Yu Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education Department of Electrical Engineering Anhui University 111 Jiu-Long road Hefei230039 China Department of Computer Science and Information Engineering Asia University 500 Liou-feng Road Taichung413 Taiwan Department of Information Engineering and Computer Science Feng Chia University 100 Wen-hwa Road Taichung407 Taiwan Department of Computer Science National Tsing-Hua University 101 Kuang-Fu Road Hsinchu300 Taiwan

With the increasingly rapid developments in e-commerce, schemes for digital gift certificates have become prevalent electronic payment systems due to their practicality and simplicity. In 2002, Chan and Chang introduced the concept of digital gift certificates and proposed the first scheme associated with them. Recently, Chang and Chang (2005) proposed a more practical scheme, called DGC-US (digital gift certificates with unconstrained spending), which can reduce the computational cost of all entities involved in Chan and Chang‘s scheme, especially the computational cost of the electronic department store. However, the asymmetric encryption/decryption operations required in the DGC-US scheme still waste a significant amount of time. In this paper, we propose a novel authentication scheme for digital gift certificates based on Chebyshev chaotic maps and the blind signature. Our proposed scheme can satisfy the essential security requirements and withstand various well-known attacks. Our analyses have shown that our proposed scheme maintains all of the merits of the DGC-US scheme but is more efficient in terms of computational cost. © 2015, Ubiquitous International. All rights reserved.

关键词： Authentication

ADEdgeDrop: Adversarial Edge Dropping for Robust Graph Neural Networks

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arXiv 2024年

作者： Chen, Zhaoliang Wu, Zhihao Sadikaj, Ylli Plant, Claudia Dai, Hong-Ning Wang, Shiping Cheung, Yiu-Ming Guo, Wenzhong College of Computer and Data Science Fuzhou University Fuzhou350116 China Department of Computer Science Hong Kong Baptist University Hong Kong Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing Fuzhou University Fuzhou350116 China Faculty of Computer Science and with the research network Data Science @ Uni Vienna University of Vienna Vienna1090 Austria

Although Graph Neural Networks (GNNs) have exhibited the powerful ability to gather graph-structured information from neighborhood nodes via various message-passing mechanisms, the performance of GNNs is limited by poor generalization and fragile robustness caused by noisy and redundant graph data. As a prominent solution, Graph Augmentation Learning (GAL) has recently received increasing attention in the literature. Among the existing GAL approaches, edge-dropping methods that randomly remove edges from a graph during training are effective techniques to improve the robustness of GNNs. However, randomly dropping edges often results in bypassing critical edges. Consequently, the effectiveness of message passing is weakened. In this paper, we propose a novel adversarial edgedropping method (ADEdgeDrop) that leverages an adversarial edge predictor guiding the removal of edges, which can be flexibly incorporated into diverse GNN backbones. Employing an adversarial training framework, the edge predictor utilizes the line graph transformed from the original graph to estimate the edges to be dropped, which improves the interpretability of the edge-dropping method. The proposed ADEdgeDrop is optimized alternately by stochastic gradient descent and projected gradient descent. Comprehensive experiments on eight graph benchmark datasets demonstrate that the proposed ADEdgeDrop outperforms state-of-the-art baselines across various GNN backbones, demonstrating improved generalization and robustness. Copyright © 2024, The Authors. All rights reserved.

关键词： Adversarial machine learning

Temperature prediction of generator carbon brush based on LSTM neural network

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Temperature prediction of generator carbon brush based on LS...

Chinese Automation Congress (CAC)

作者： Qing Zhang Tingyang Jiao Yinxing Ma Youmin Zhang Xiaohui Wu Pengyue Wu Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing Xi’an University of Technology Xi’an China The Faculty of Computing Science The University of Alberta Edmonton Alberta Canada Concordia University Montreal Canada Huaneng Weihai Power Generation Co. Ltd Wei’hai China Xi’an Thermal Power Research Institute Co. Ltd Xi’an China

ISBN: (纸本)9781665426480

In order to improve the prediction accuracy of the carbon brush temperature trend of the generator, analyzing the operating state of the generator more accurately, and reduce other accidents like the unplanned outage caused by carbon brush failure of the generator in the power plant. A multi-step temperature prediction model based on the LSTM (Long Short-Term Memory) neural network is proposed. The data comes from real operating carbon brush temperature of Weihai Power Plant in ten days. Then the temperature prediction model is established to achieve an accurate prediction of the carbon brush temperature in the future day. The prediction error is stable within 0.4 °C. By comparing the predicted results of the BP model and Elman model, the error between the predicted results of each model and the actual temperature data is analyzed. By comparing the indicators and analyzing the actual curves, the results show that LSTM neural network has higher accuracy in predicting the temperature of generator carbon brush. This method is of reference significance for the accurate analysis of the operation state of the generator and the load analysis of the excitation system.

关键词： Analytical models Temperature distribution Brushes Neural networks Predictive models Market research Generators

Learning data-adaptive non-parametric kernels

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2020年第1期21卷 8590-8628页

作者： Fanghui Liu Xiaolin Huang Chen Gong Jie Yang Li Li Department of Electrical Engineering ESAT-STADIUS KU Leuven Belgium Institute of Image Processing and Pattern Recognition Institute of Medical Robotics Shanghai Jiao Tong University Shanghai China PCA Lab Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education School of Computer Science and Engineering Nanjing University of Science and Technology China and Department of Computing Hong Kong Polytechnic University Hong Kong SAR China Department of Automation BNRist Tsinghua University China

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise scheme. Learning this data-adaptive matrix in a formulation-free strategy enlarges the margin between classes and thus improves the model flexibility. The introduced two constraints are imposed either exactly (on small data sets) or approximately (on large data sets) in our model, which provides a controllable trade-off between model flexibility and complexity with theoretical demonstration. In algorithm optimization, the objective function of our learning framework is proven to be gradient-Lipschitz continuous. Thereby, kernel and classifier/regressor learning can be efficiently optimized in a unified framework via Nesterov's acceleration. For the scalability issue, we study a decomposition-based approach to our model in the large sample case. The effectiveness of this approximation is illustrated by both empirical studies and theoretical guarantees. Experimental results on various classification and regression benchmark data sets demonstrate that our non-parametric kernel learning framework achieves good performance when compared with other representative kernel learning based algorithms.

关键词： support vector machines non-parametric kernel learning gradient-Lipschitz continuous

A Novel Preference-Driven Dynamic Multi-Objective Evolutionary Algorithm for Solving Dynamic Multi-Objective Problems

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SSRN

SSRN 2023年

作者： Wang, Xueqing Zheng, Jinhua Hou, Zhanglu Liu, Yuan Zou, Juan Xia, Yizhang Yang, Shengxiang Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Computer Science School of Cyberspace Science Xiangtan University Hunan Province Xiangtan China School of Computer Science School of Cyberspace Science of Xiangtan University Xiangtan411105 China School of Computer Science and Informatics De Montfort University LeicesterLE1 9BH United Kingdom

Most research on dynamic multi-objective optimization primarily concentrates on tracking the true Pareto optimal front (POF) and Pareto optimal set (POS) quickly and accurately when the environment undergoes changes. However, there are real-world scenarios where it is necessary to simultaneously solve changing objective functions and satisfy the preference of Decision Makers (DMs). Specifically, the DMs may be only interested in a partial region of the POF, known as the region of interest (ROI), rather than requiring the entire POF. To meet the challenge of simultaneously predicting a changing POF and/or POS and dynamic ROI, this paper proposes a new dynamic multi-objective evolutionary algorithm (DMOEAs) based on the preference. The proposed algorithm comprises three main components: an evolutionary direction adjustment strategy based on changing reference points to accommodate preference shifts, an angle-based search strategy for tracking the varying ROI, and a hybrid prediction strategy combining linear prediction models and population manifold estimation within the ROI to ensure convergence and distribution in unchanged preference scenarios. Experimental studies conducted on 16 widely used benchmark problems and empirical results demonstrate the significant advantages of the proposed algorithm over existing state-of-the-art DMOEAs. © 2023, The Authors. All rights reserved.

关键词： Evolutionary algorithms