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IEEE Education Engineering (EDUCON)

作者： Yue Zhang Pascal Reusch Department of Mathematics and Physics Hainan Bielefeld University of Applied Sciences Lingshui China Department of Engineering and Mathematics Center for Applied Data Science (CfADS) Bielefeld University of Applied Sciences and Arts (HSBI) Gütersloh Germany

ISBN: (数字)9798331539498

ISBN: (纸本)9798331539504

Generative AI has emerged as a transformative tool in the realm of higher education, offering a wealth of opportunities for personalized learning, automated feedback, and enhanced collaboration. However, its successful adoption within university environments is significantly dependent on the trust it earns from its users, particularly students. This study investigates the levels of trust and the adoption of Generative AI among students enrolled in both German and international study programs at Hochschule Bielefeld (HSBI) and its transnational partner, Hainan Bielefeld University of applied sciences (BiUH). Utilizing a comprehensive questionnaire, the research explores students' perceptions of the trustworthiness of Generative AI, their usage patterns, and their concerns regarding the ethical and academic implications of its use. Preliminary findings suggest that while students widely recognize the potential of Generative AI to improve learning outcomes and efficiency, the degree of trust in its reliability and fairness varies significantly. Key factors influencing this trust include the transparency of AI systems, the perceived accuracy of outputs, and concerns about bias and misuse. Students in international and cross-cultural programs face additional challenges, such as language barriers and cultural differences, which affect how AI is perceived and utilized. Ethical concerns, particularly regarding plagiarism and academic integrity, are prevalent across all groups, underscoring the need for clear institutional guidelines and policies. The findings highlight the importance of fostering AI literacy and providing support structures to build trust and encourage responsible use. Recommendations include the implementation of transparent AI tools, tailored training programs, and the development of ethical guidelines to ensure that Generative AI enhances education while upholding academic standards. This research provides actionable insights for universities aiming to i

关键词： Training Ethics Generative AI Plagiarism Learning automata Reliability Artificial intelligence Engineering education Standards Guidelines

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Nonlocal Boundary-Value Problems with Local Boundary Conditions

SSRN

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SSRN 2023年

作者： Scott, James M. Du, Qiang Department of Applied Physics and Applied Mathematics the Data Science Institute Co-lumbia University New YorkNY10027 United States

We study nonlocal integro-differential equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. Through estimates of boundary localized convolutions, we establish a nonlocal Green's identity, which leads to the well-posedness of these nonlocal problems with various types of classical local boundary conditions. We investigate the regularity properties of the nonlocal problems with rough data and prove the convergence of solutions of these nonlocal boundary-value problems with their classical local counterparts in the local limit. The Poisson data for the local boundary-value problem is permitted to be quite irregular, belonging to the dual of the classical Sobolev space. Heterogeneously mollifying such Poisson data for the local problem on the same length scale as the range of nonlocal interactions, we show that the solutions to the nonlocal problem with the mollified Poisson data converge to the variational solution of the classical Poisson problem with original data. © 2023, The Authors. All rights reserved.

关键词： Boundary value problems

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On the Power of Small-size Graph Neural Networks for Linear Programming 38

On the Power of Small-size Graph Neural Networks for Linear ...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Li, Qian Ding, Tian Yang, Linxin Ouyang, Minghui Shi, Qingjiang Sun, Ruoyu Shenzhen International Center for Industrial and Applied Mathematics Shenzhen China Shenzhen Research Institute of Big Data Shenzhen China School of Data Science The Chinese University of Hong Kong Shenzhen China Peking University Beijing China Tongji University Shanghai China

Graph neural networks (GNNs) have recently emerged as powerful tools for addressing complex optimization problems. It has been theoretically demonstrated that GNNs can universally approximate the solution mapping functions of linear programming (LP) problems. However, these theoretical results typically require GNNs to have large parameter sizes. Conversely, empirical experiments have shown that relatively small GNNs can solve LPs effectively, revealing a significant discrepancy between theoretical predictions and practical observations. In this work, we aim to bridge this gap by providing a theoretical foundation for the effectiveness of smaller GNNs. We prove that polylogarithmic-depth, constant-width GNNs are sufficient to solve packing and covering LPs, two widely used classes of LPs. Our proof leverages the capability of GNNs to simulate a variant of the gradient descent algorithm on a carefully selected potential function. Additionally, we introduce a new GNN architecture, termed GD-Net. Experimental results demonstrate that GD-Net significantly outperforms conventional GNN structures while using fewer parameters. © 2024 Neural information processing systems foundation. All rights reserved.

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A fitting formula for electron–ion energy partition fraction of 3.54-MeV fusion alpha particles in hot dense deuterium–tritium plasmas

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Chinese physics B 2021年第1期30卷 345-349页

作者： Yan-Ning Zhang Zhi-Gang Wang Yong-Tao Zhao Bin He School of Science Xi’an Jiaotong UniversityXi’an 710049China Institute of Applied Physics and Computational Mathematics Beijing 100088China

Based on our previous work(*** 25 012704(2018)),a fitting formula is given for electron-ion energy partition fraction of 3.54-MeV fusion alpha particles in deuterium-tritium(DT) plasmas as a function of plasma mass density ρ,electron temperature T_(e),and ion temperature T_(i).The formula can be used in a huge range of the plasma state,where ρ varies between 1.0 g/cc~10.0^(3) g/cc and both T_(e) and T_(i) change from 0.1 keV to 100.0 *** effect for electrons is investigated including the effect of the projectile recoil in the plasmas at T_(e)≥ 50.0 *** partition fraction for T_(e)>T_(i) is found to be close to that for T_(e)=T_(i). The comparisons with other fitting results are made at some plasma densities when T_(e)=T_(i),and the difference is *** fitting result is very close to the calculated one in most cases,which is convenient for the simulation of alpha heating in hot dense DT plasmas for inertial confined fusion.

关键词： inertial confinement fusion deuterium–tritium plasma alpha heating energy loss

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PLOD: Point cloud level of detail for polygon mesh 32

PLOD: Point cloud level of detail for polygon mesh

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32nd International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, WSCG 2024

作者： Konks, Eric Shcherbakov, Alexandr Phystech School of Applied Mathematics and Computer Science Moscow Institute of Physics and Technology Institutskiy Pereulok 9 Dolgoprudny Oblast Moscow141701 Russia Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University Moscow119991 Russia

Rendering high-polygonal models from distant perspectives has certain performance issues related to high density of subpixel triangles, which can be solved by levels of detail, a classical optimization method. Since a mesh occupies a small area on the screen, an alternative representation of the geometry in the form of a point cloud can replace the original geometry with little or no change to the image, and allowing for significant performance improvements due to the smaller number of primitives rendered. This paper presents a method for automatically generating a point cloud from a polygonal mesh with nested levels of detail. It also considers a method for rendering cloud with dynamically varying cloud density in real time based on view frustum and distance. © 2024 University of West Bohemia. All rights reserved.

关键词： Mesh generation

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Local order metrics for many-particle systems across length scales

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Physical Review Research 2024年第3期6卷 033262页

作者： Charles Emmett Maher Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.

关键词： Classical statistical mechanics

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Formation mechanism of multiple spallation and its penetration induced by shear localization in NiTi alloy under implosion loading

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Matter and Radiation at Extremes 2025年第1期10卷 81-97页

作者： Xianye Wu Xiaoyang Pei Xiang Chen Hao Zhang Jin Wang Xin Yang Meizhen Xiang Shang Gao Fang Wang School of Materials and Energy Southwest UniversityChongqing 400715China Institute of Fluid Physics China Academy of Engineering PhysicsMianyang 621999China State Key Laboratory of Nuclear Physics and Technology Center for Applied Physics and TechnologyPeking UniversityBeijing 100871China School of Environment and Resource Southwest University of Science and TechnologyMianyang 621010China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China

This study uses nonequilibrium molecular dynamics simulations to explore the dynamic failures and deformation mechanisms of a cylindrical shell composed of nanocrystalline nickel-titanium alloy under implosion *** discover that some individual spall planes are sequentially generated in the material along the propagation of a radial stress wave,indicative of the formation of multiple *** larger grain sizes,void nucleation at the first spallation occurs in a coexisting intergranular/transgranular manner,whereas with decreasing grain size,voids tend to nucleate along the grain ***,the spall strength exhibits a transition from an inverse Hall-Petch to a Hall-Petch *** larger grain sizes,at the secondary spallation,localized shearing zones and grain boundaries provide potential void-nucleated ***,the formation of shear deformation bands promotes grain refinement,contributing to a reduction in the dislocation-induced strengthening ***,a lower spall strength is produced,in contrast to the first *** the grain size becomes smaller,voids nucleate mostly along grain boundaries,and plastic deformation is dominated by dense grain ***,the high temperature caused by shear localization leads to material weakening,and in turn there is a significant decrease in the spall strength for the secondary spallation,compared with the ***,significant penetration between two spall planes is observed for large grain size,which can be attributed to the nucleation of voids on linking grain boundaries,with temperatures exceeding the melting point of the material.

关键词： grain alloy deformation

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αSetup-PCTL:An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations

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Communications in Computational physics 2022年第10期32卷 1287-1309页

作者： Silu Huang Xiaoqiang Yue Xiaowen Xu Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100088China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing and Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105China

The iterative solution of the sequence of linear systems arising from threetemperature(3-T)energy equations is an essential component in the numerical simulation of radiative hydrodynamic(RHD)***,due to the complicated application features of the RHD problems,solving 3-T linear systems with classical preconditioned iterative techniques is *** address this difficulty,a physicalvariable based coarsening two-level(PCTL)preconditioner has been proposed by dividing the fully coupled system into four individual easier-to-solve *** its nearly optimal complexity and robustness,the PCTL algorithm suffers from poor efficiency because of the overhead associatedwith the construction of setup phase and the solution of ***,the PCTL algorithm employs a fixed strategy for solving the sequence of 3-T linear systems,which completely ignores the dynamically and slowly changing features of these linear *** address these problems and to efficiently solve the sequence of 3-T linear systems,we propose an adaptive two-level preconditioner based on the PCTL algorithm,referred to as α*** adaptive strategies of the αSetup-PCTL algorithm are inspired by those of αSetup-AMG algorithm,which is an adaptive-setup-based AMG solver for sequence of sparse linear *** proposed αSetup-PCTL algorithm could adaptively employ the appropriate strategies for each linear system,and thus increase the overall *** results demonstrate that,for 36 linear systems,the αSetup-PCTL algorithm achieves an average speedup of 2.2,and a maximum speedup of 4.2 when compared to the PCTL algorithm.

关键词： Sequence of linear systems sparse linear solver preconditioning methods radiation hydrodynamics simulation

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Position: Is machine learning good or bad for the natural sciences? 41

Position: Is machine learning good or bad for the natural sc...

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41st International Conference on Machine Learning, ICML 2024

作者： Hogg, David W. Villar, Soledad Center for Cosmology and Particle Physics Department of Physics New York University United States Max-Planck-Institut für Astronomie Heidelberg Germany Flatiron Institute New York United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Mathematical Institute for Data Science Johns Hopkins University United States

Machine learning (ML) methods are having a huge impact across all of the sciences. However, ML has a strong ontology-in which only the data exist-and a strong epistemology-in which a model is considered good if it performs well on held-out training data. These philosophies are in strong conflict with both standard practices and key philosophies in the natural sciences. Here we identify some locations for ML in the natural sciences at which the ontology and epistemology are valuable. For example, when an expressive machine learning model is used in a causal inference to represent the effects of confounders, such as foregrounds, backgrounds, or instrument calibration parameters, the model capacity and loose philosophy of ML can make the results more trustworthy. We also show that there are contexts in which the introduction of ML introduces strong, unwanted statistical biases. For one, when ML models are used to emulate physical (or first-principles) simulations, they amplify confirmation biases. For another, when expressive regressions are used to label datasets, those labels cannot be used in downstream joint or ensemble analyses without taking on uncontrolled biases. The question in the title is being asked of all of the natural sciences;that is, we are calling on the scientific communities to take a step back and consider the role and value of ML in their fields;the (partial) answers we give here come from the particular perspective of physics. Copyright 2024 by the author(s)

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NONLOCAL BOUNDARY-VALUE PROBLEMS WITH LOCAL BOUNDARY CONDITIONS

arXiv

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arXiv 2023年

作者： Scott, James M. Du, Qiang Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Department of Applied Physics and Applied Mathematics The Data Science Institute Columbia University New YorkNY10027 United States

We describe and analyze nonlocal integro-differential equations with classical local boundary conditions. The interaction kernel of the nonlocal operator has horizon parameter dependent on position in the domain, and vanishes as the boundary of the domain is approached. This heterogeneous localization allows for boundary values to be captured in the trace sense. We state and prove a nonlocal Green’s identity for these nonlocal operators that involve local boundary terms. We use this identity to state and establish the well-posedness of variational formulations of the nonlocal problems with several types of classical boundary conditions. We show the consistency of these nonlocal boundary-value problems with their classical local counterparts in the vanishing horizon limit via the convergence of solutions. The Poisson data for the local boundary-value problem is permitted to be quite irregular, belonging to the dual of the classical Sobolev space. Heterogeneously mollifying this Poisson data for the local problem on the same length scale as the horizon and using the regularity of the interaction kernel, we show that the solutions to the nonlocal boundary-value problem with the mollified Poisson data actually belong to the classical Sobolev space, and converge weakly to the unique variational solution of the classical Poisson problem with original Poisson data. Copyright © 2023, The Authors. All rights reserved.

关键词： Sobolev spaces

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