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A hybrid FEM-PINN method for time-dependent partial differential equations

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arXiv 2024年

作者： Feng, Xiaodong Shangguan, Haojiong Tang, Tao Wan, Xiaoliang Zhou, Tao Division of Science and Technology BNU-HKBU United International College Zhuhai519087 China School of Electrical and Computer Engineering Guangzhou Nanfang College Guangzhou510970 China Department of Mathematics Center for Computation and Technology Louisiana State University Baton Rouge70803 United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based formulation where the neural network is defined on a spatiotemporal domain, our methodology utilizes finite element basis functions in the time direction where the space-dependent coefficients are defined as the output of a neural network. We then apply the Galerkin or collocation projection in the time direction to obtain a system of PDEs for the space-dependent coefficients which is approximated in the framework of PINN. The advantages of such a hybrid formulation are twofold: statistical errors are avoided for the integral in the time direction, and the neural network’s output can be regarded as a set of reduced spatial basis functions. To further alleviate the difficulties from high dimensionality and low regularity, we have developed an adaptive sampling strategy that refines the training set. More specifically, we use an explicit density model to approximate the distribution induced by the PDE residual and then augment the training set with new time-dependent random samples given by the learned density model. The effectiveness and efficiency of our proposed method have been demonstrated through a series of numerical experiments. © 2024, CC BY.

关键词： Partial differential equations

Reformulating Task-Related Component Analysis for Reducing its computational Complexity

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TechRxiv

TechRxiv 2022年

作者： Chiang, Kuan-Jung Wong, Chi Man Wan, Feng Jung, Tzyy-Ping Nakanishi, Masaki Swartz Center for Computational Neuroscience Institute for Neural Computation University of California La Jolla San DiegoCA92093 United States Department of Electrical and Computer Engineering University of Macau Taipa China

The task-related component analysis (TRCA) is a data-driven method for extracting reproducible components across multiple data segments from multivariate data. TRCA has been proven effective in enhancing the signal-to-noise ratio of neuroimaging data in previous studies. However, it requires a computational cost of O(N2) to compute cross-covariance matrices, indicating that the computational time increases rapidly as the number of data segments N increases. This study proposed to reduce the computational complexity to O(N) theoretically by reformulating the covariance computations required in TRCA. Simulation study that compared the original and proposed TRCA against synthetic data with various sizes (e.g., data segments, dimensions, and lengths) validated the computation reduction. The proposed reformulation would be important in practice especially when applying the TRCA to large-scale computations. © 2022, CC BY.

关键词： computational complexity

Hamiltonian Quantum Generative Adversarial Networks

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arXiv 2022年

作者： Kim, Leeseok Lloyd, Seth Marvian, Milad Department of Electrical & Computer Engineering Center for Quantum Information and Control University of New Mexico AlbuquerqueNM87131 United States Department of Mechanical Engineering Massachusetts Institute of Technology CambridgeMA02139 United States

We propose Hamiltonian Quantum Generative Adversarial Networks (HQuGANs), to learn to generate unknown input quantum states using two competing quantum optimal controls. The game-theoretic framework of the algorithm is inspired by the success of classical generative adversarial networks in learning high-dimensional distributions. The quantum optimal control approach not only makes the algorithm naturally adaptable to the experimental constraints of near-term hardware, but also offers a more natural characterization of overparameterization compared to the circuit model. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states, using simple two-body Hamiltonians and under experimentally relevant constraints such as low-bandwidth controls. We analyze the computational cost of implementing HQuGANs on quantum computers and show how the framework can be extended to learn quantum dynamics. Furthermore, we introduce a new cost function that circumvents the problem of mode collapse that prevents convergence of HQuGANs and demonstrate how to accelerate the convergence of them when generating a pure state. Copyright © 2022, The Authors. All rights reserved.

关键词： Quantum computers

Topological edge states at singular points in non-Hermitian plasmonic systems

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Photonics Research 2022年第3期10卷 747-757页

作者： Yin Huang Yuecheng Shen Georgios Veronis Department of Optoelectrics Information Science and Engineering School of Physics and ElectronicsCentral South UniversityChangsha 410012China State Key Laboratory of Optoelectronic Materials and Technologies School of Electronics and Information TechnologySun Yat-sen UniversityGuangzhou 510275China School of Electrical Engineering and Computer Science Louisiana State UniversityBaton RougeLouisiana 70803USA Center for Computation and Technology Louisiana State UniversityBaton RougeLouisiana 70803USA

We introduce non-Hermitian plasmonic waveguide-cavity systems with topological edge states(TESs)at singular *** compound unit cells of the structures consist of metal-dielectric-metal(MDM)stub resonators side-coupled to an MDM *** show that we can realize both a TES and an exceptional point at the same frequency when a proper amount of loss is introduced into a finite three-unit-cell *** also show that the finite structure can exhibit both a TES and a spectral singularity when a proper amount of gain is introduced into the *** addition,we show that we can simultaneously realize a unidirectional spectral singularity and a TES when proper amounts of loss and gain are introduced into the *** finally show that this singularity leads to extremely high sensitivity of the reflected light intensity to variations of the refractive index of the active materials in the *** at singular points could potentially contribute to the development of singularity-based plasmonic devices with enhanced performance.

关键词： structure singularity singular

A Unifying Passivity-Based Framework for Pressure and Volume Flow Rate control in District Heating Networks

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arXiv 2023年

作者： Strehle, Felix Machado, Juan E. Cucuzzella, Michele Malan, Albertus J. Scherpen, Jacquelien M.A. Hohmann, Sören Karlsruhe76131 Germany The Jan C. Willems Center for Systems and Control ENTEG Faculty of Science and Engineering University of Groningen Nijenborgh 4 Groningen9747 AG Netherlands The Department of Electrical Computer and Biomedical Engineering University of Pavia via Ferrata 5 Pavia27100 Italy

A fundamental precondition for the secure and efficient operation of district heating networks (DHNs) is a stable hydraulic behavior. However, the ongoing transition towards a sustainable heat supply, especially the rising integration of distributed heat sources and the increasingly meshed topologies, introduce complex and potentially destabilizing hydraulic dynamics. In this work, we propose a unifying, passivity-based framework which guarantees asymptotic stability of any forced hydraulic DHN equilibrium while allowing for meshed, time-varying topologies and different, dynamically interacting distributed heat sources. To establish the desired hydraulic equilibria, we propose decentralized, passivity-based pressure and volume flow rate controllers for the pumps and valves in the actuated DHN subsystems. In particular, we leverage the equilibrium-independent passivity (EIP) properties of the DHN subsystems, the skew-symmetric nature of their interconnections, and LaSalle's Invariance principle to assess asymptotic stability in a modular manner. The obtained results hold for the state-of-the-art as well as future DHN generations featuring, for example, multiple distributed heat sources, asymmetric pipe networks, and multiple temperature layers. We verify our findings by means of simulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Asymptotic stability

Estimating distinguishability measures on quantum computers

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Physical Review A 2023年第1期108卷 012409-012409页

作者： Soorya Rethinasamy Rochisha Agarwal Kunal Sharma Mark M. Wilde Hearne Institute for Theoretical Physics Department of Physics and Astronomy and Center for Computation and Technology Louisiana State University Baton Rouge Louisiana 70803 USA School of Applied and Engineering Physics Cornell University Ithaca New York 14850 USA Department of Physics Indian Institute of Technology Roorkee Roorkee Uttarakhand 247667 India School of Electrical and Computer Engineering Cornell University Ithaca New York 14850 USA Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA IBM Quantum IBM T. J. Watson Research Center Yorktown Heights New York 10598 USA

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as “quantum combs”). The fidelity-based algorithms offer physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate many of these algorithms by using a variational approach with parameterized quantum circuits. We find that the simulations converge well in both the noiseless and noisy scenarios for all examples considered. Furthermore, the noisy simulations exhibit a parameter noise resilience. Finally, we establish a strong relationship between various quantum computational complexity classes and distance estimation problems.

关键词： Machine learning Quantum algorithms Quantum channels Quantum computation Quantum information theory

Defining, measuring, and modeling passenger's in-vehicle experience and acceptance of automated vehicles

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arXiv 2023年

作者： Bhide, Neeraja Hashimoto, Nanami Dokurno, Kazimierz Van der Hoorn, Chris Hoogendoorn-Lanser, Sascha Nordhoff, Sina Delft Center for Systems and Control Delft University of Technology Netherlands Department of Cognitive Robotics Delft University of Technology Netherlands Faculty of Electrical Engineering Mathematics and Computer Science University of Twente Netherlands Department Transport & Planning Delft University of Technology Netherlands

Automated vehicle acceptance (AVA) has been measured mostly subjectively by questionnaires and interviews, with a main focus on drivers inside automated vehicles (AVs). To ensure that AVs are widely accepted by the public, ensuring the acceptance by both drivers and passengers is key. The in-vehicle experience of passengers will determine the extent to which AVs will be accepted by passengers. A comprehensive understanding of potential assessment methods to measure the passenger experience in AVs is needed to improve the in-vehicle experience of passengers and thereby the acceptance. The present work provides an overview of assessment methods that were used to measure a driver's behavior, and cognitive and emotional states during (automated) driving. The results of the review have shown that these assessment methods can be classified by type of data-collection method (e.g., questionnaires, interviews, direct input devices, sensors), object of their measurement (i.e., perception, behavior, state), time of measurement, and degree of objectivity of the data collected. A conceptual model synthesizes the results of the literature review, formulating relationships between the factors constituting the in-vehicle experience and AVA acceptance. It is theorized that the in-vehicle experience influences the intention to use, with intention to use serving as predictor of actual use. The model also formulates relationships between actual use and well-being. A combined approach of using both subjective and objective assessment methods is needed to provide more accurate estimates for AVA, and advance the uptake and use of AVs. © 2023, CC BY.

关键词： Vehicles

Stealthy Attacks on Sampled-Data control and Encryption-Based Countermeasures

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IEEE Transactions on Automatic control 2025年

作者： Shang, Jun Li, Yuzhe Chen, Tongwen Tongji University Department of Control Science and Engineering Shanghai Institute of Intelligent Science and Technology National Key Laboratory of Autonomous Intelligent Unmanned Systems Frontiers Science Center for Intelligent Autonomous Systems Shanghai200092 China Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang110004 China University of Alberta Department of Electrical and Computer Engineering EdmontonABT6G 1H9 Canada

This paper investigates stealthy attacks on sampled-data control systems, where a continuous process is sampled periodically, and the resultant discrete output and control signals are transmitted through dual channels in wireless communication networks. Acknowledging the vulnerability of these transmitted data to cyber threats, we analyze two types of stealthy attacks that compromise either one or both channels. We explicitly present the necessary and sufficient conditions for the existence of stealthy single-channel attacks. To mitigate these security risks, we implement encryption-based countermeasures, including linear time-invariant and periodic encryption methods. We detail sufficient conditions under which these encryption strategies effectively thwart single- and dual-channel stealthy attacks. The effectiveness of these approaches and the theoretical findings are demonstrated through numerical simulations. © 1963-2012 IEEE.

关键词： Cyber attacks

An Exoskeleton BCI System for Stroke Rehabilitation Using Multi-modality Training Mode

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An Exoskeleton BCI System for Stroke Rehabilitation Using Mu...

2023 International Automatic control Conference, CACS 2023

作者： Su, Kai-Hsiang Chen, Chiao-Hsin Chen, Chia-Hsin Zhang, Yong-Liang Ko, Li-Wei National Yang Ming Chiao Tung University Former National Chiao Tung University Institute of Biological Science and Technology Hsinchu30010 Taiwan National Yang Ming Chiao Tung University Former National Chiao Tung University Institute of Molecular Medicine and Bioengineering Hsinchu30010 Taiwan Medical University Chung-Ho Memorial Hospital Rehabilitation Department of Kaohsiung Taiwan College of Biological Science and Technology Hsinchu30010 Taiwan National Yang Ming Chiao Tung University Former National Chiao Tung University Institute of Electrical and Control Engineering Hsinchu30010 Taiwan Brain Research Center Department of Electrical and Computer Engineering Hsinchu30010 Taiwan

ISBN: (纸本)9798350306354

With the advent of the global aging era, the impact of stroke on humans is continuously increasing. Therefore, new therapeutic approaches to enhance patient recovery are receiving growing attention. Stroke is a severe neurological disorder that causes brain damage, requiring extended periods of rehabilitation for patients to return to normal life. Currently, common clinical methods largely rely on traditional passive limb rehabilitation, primarily targeting peripheral nerve training. Nowadays, an increasing number of people are recognizing the importance of post-stroke neuroplasticity. This study aims to activate patients' central nervous system and proposes a brain-machine interface (BCI) exoskeleton system based on human cognition. By designing three cognitive brainwave training models, including an attention-based standing-up model detecting θ-band power decrease, a relaxation-based sitting-down model detecting α-band power increase, and a walking model detecting MRCP, patients can actively control lower limb exoskeleton movement using *** study provides cross-validation accuracy through both normal subjects and stroke patients, with accuracies of 87.13±9.38 and 80.83±9.68, respectively. Envisioning a rehabilitation system guided by human cognition, our team has developed an intuitive BCI exoskeleton system. © 2023 IEEE.

关键词： Brain