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A 2D Staggered Multi-Material ALE Code Using MOF Interface Reconstruction

Numerical mathematics(Theory,Methods and Applications) 2021年第1期14卷 219-241页

作者： Yibing Chen Junxia Cheng Liang Pan Haihua Yang Heng Yong Xin Yu Institute of Applied Physics and Computational Mathematics BeijingChina School of Mathematical Science Beijing Normal UniversityBeijingChina

Hydrocodes are necessary numerical tools in the fields of implosion and high-velocity impact,which often involve large deformations with changing-topology *** is very difficult for Lagrangian or Simplified Arbitrary Lagrangian-Eulerian(SALE)codes to tackle these kinds of large-deformation problems,so a stag-gered Multi-Material ALE(MMALE)code is developed in this paper,which is the explicit time-marching Lagrange plus remap *** use the Moment Of Fluid(MOF)method to reconstruct the interfaces of multi-material cells and present an adaptive bisection method to search for the global minimum value of the nonlinear objective *** keep the Lagrangian computations as long as possible,we develop a ro-bust rezoning method named as Combined Rezoning Method(CRM)to generate the convex,smooth grids for the large-deformation *** the staggered remap phase,we use two methods to remap the variables of Lagrangian mesh to the rezoned *** is the first-order intersection-based remapping method that doesn’t limit the distances between the rezoned and Lagrangian meshes,so it can be used in the applications of wide *** other one is the conservative second-order flux-based remapping method developed by Kucharika and Shashkov[22]that requires the rezoned element to locate in its adjacent old *** results of triple point problem show that the result of first-order remapping method using ALE computations is gradually convergent to that of second-order remapping method using Eulerian computations with the decrease of rezoning,thereby telling us that MMALE computations should be performed as few as possible to reduce the errors of the interface reconstruction and the *** results provide a clear evidence of the robustness and the accuracy of this MMALE scheme,and that our MMALE code is powerful for the large-deformation problems.

关键词： Staggered Lagrangian scheme multi-material ALE MOF interface reconstruction large-deformation problems

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Highly excited quantum state-selective capture dynamics in slow Ar8+−H2 collisions

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Physical Review A 2024年第3期109卷 032819-032819页

作者： Md Abul Kalam Azad Siddiki G. P. Zhao L. Liu Deepankar Misra Department of Nuclear and Atomic Physics Tata Institute of Fundamental Research Homi Bhabha Road Colaba Mumbai 400005 India College of Data Science Jiaxing University Jiaxing 314001 China Data Center for High Energy Density Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We report on the combined experimental and theoretical studies of the single-electron capture collisions of Ar8+ projectiles with the H2 molecules at 1, 2, and 4 keV/u collision energies. The nondissociative recoil H2+ molecular ions are measured in coincidence with the charge-changing Ar7+ projectiles. The relative cross sections of the different state-selective capture channels are obtained from the experimentally measured Q-value spectra. The 1s electron transfers to the highly excited 4d+4f, 5s, 5p, 5d+5f+5g, 6s+6p, and 6d+6f+6g+6h states are resolved experimentally. The differential scattering angle distributions for the dominant 1s to 5s, 5p, and 5d+5f+5g transitions are compared with the two-center atomic orbital close-coupling methods. A collision energy-dependent dynamical coupling effect is also observed for the 1s→5p0 and 1s→5p±1 transitions. The dominant oscillatory structures in the scattering-angle distributions are attributed to Stueckelberg-type oscillations. In contrast, the less visible undulations in the smaller scattering angles imprint the signature of the quantum matter-wave scattering of the projectiles. The quantum nature of the oscillations in the angular distributions is further validated by classical calculations. Our study thus illustrates the highly excited quantum state-selective electron capture process and sheds light on the scattering-angle-range-dependent collision dynamics for highly charged ion-molecule collisions in the highly perturbative regime.

关键词： Atomic & molecular collisions Scattering of atoms, molecules, clusters & ions Scattering theory

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The liberation set in the inverse eigenvalue problem of a graph

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arXiv 2023年第1期675卷 1-28页

作者： Lin, Jephian C.-H. Oblak, Polona Šmigoc, Helena Department of Applied Mathematics National Sun Yat-sen University Kaohsiung80424 Taiwan Faculty of Computer and Information Science University of Ljubljana Večna pot 113 LjubljanaSI-1000 Slovenia Faculty of Mathematics and Physics University of Ljubljana Institute of Mathematics Physics and Mechanics Jadranska ulica 19 Ljubljana1000 Slovenia School of Mathematics and Statistics University College Dublin BelfieldDublin 4 Ireland

The inverse eigenvalue problem of a graph G is the problem of characterizing all lists of eigenvalues of real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of G. The strong spectral property is a powerful tool in this problem, which identifies matrices whose entries can be perturbed while controlling the pattern and preserving the eigenvalues. The Matrix Liberation Lemma introduced by Barrett et al. in 2020 advances the notion to a more general setting. In this paper we revisit the Matrix Liberation Lemma and prove an equivalent statement, that reduces some of the technical difficulties in applying the result. We test our method on matrices of the form M = AB and show how this new approach supplements the results that can be obtained from the strong spectral property only. While extending this notion to the direct sums of graphs, we discover a surprising connection with the zero forcing game on Cartesian products of graphs. Throughout the paper we apply our results to resolve a selection of open cases for the inverse eigenvalue problem of a graph on six *** Codes 05C50, 15A18, 15B57, 65F18 © 2023, CC BY-SA.

关键词： Matrix algebra

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Balanced Training for Sparse GANs 37

Balanced Training for Sparse GANs

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37th Conference on Neural Information Processing Systems, NeurIPS 2023

作者： Wang, Yite Wu, Jing Hovakimyan, Naira Sun, Ruoyu University of Illinois Urbana-Champaign United States School of Data Science The Chinese University of Hong Kong Shenzhen China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China

ISBN: (纸本)9781713899921

Over the past few years, there has been growing interest in developing larger and deeper neural networks, including deep generative models like generative adversarial networks (GANs). However, GANs typically come with high computational complexity, leading researchers to explore methods for reducing the training and inference costs. One such approach gaining popularity in supervised learning is dynamic sparse training (DST), which maintains good performance while enjoying excellent training efficiency. Despite its potential benefits, applying DST to GANs presents challenges due to the adversarial nature of the training process. In this paper, we propose a novel metric called the balance ratio (BR) to study the balance between the sparse generator and discriminator. We also introduce a new method called balanced dynamic sparse training (ADAPT), which seeks to control the BR during GAN training to achieve a good trade-off between performance and computational cost. Our proposed method shows promising results on multiple datasets, demonstrating its effectiveness. Our code is available at https://***/YiteWang/ADAPT. © 2023 Neural information processing systems foundation. All rights reserved.

关键词： Generative adversarial networks

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Alignment at Pre-training! Towards Native Alignment for Arabic LLMs 38

Alignment at Pre-training! Towards Native Alignment for Arab...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Liang, Juhao Cai, Zhenyang Zhu, Jianqing Huang, Huang Zong, Kewei An, Bang Alharthi, Abdulmohsen He, Juncai Zhang, Lian Li, Haizhou Wang, Benyou Xu, Jinchao Shenzhen Research Institue of Big Data Shenzhen China The Chinese University of Hong Kong Shenzhen China King Abdullah University of Science and Technology Thuwal Saudi Arabia Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China

The alignment of large language models (LLMs) is critical for developing effective and safe language models. Traditional approaches focus on aligning models during the instruction tuning or reinforcement learning stages, referred to in this paper as 'post alignment'. We argue that alignment during the pre-training phase, which we term 'native alignment', warrants investigation. Native alignment aims to prevent unaligned content from the beginning, rather than relying on posthoc processing. This approach leverages extensively aligned pre-training data to enhance the effectiveness and usability of pre-trained models. Our study specifically explores the application of native alignment in the context of Arabic LLMs. We conduct comprehensive experiments and ablation studies to evaluate the impact of native alignment on model performance and alignment stability. Additionally, we release open-source Arabic LLMs that demonstrate state-of-the-art performance on various benchmarks, providing significant benefits to the Arabic LLM community. © 2024 Neural information processing systems foundation. All rights reserved.

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PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming 41

PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Li...

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41st International Conference on Machine Learning, ICML 2024

作者： Li, Bingheng Yang, Linxin Chen, Yupeng Wang, Senmiao Mao, Haitao Chen, Qian Ma, Yao Wang, Akang Ding, Tian Tang, Jiliang Sun, Ruoyu Michigan State University United States School of Data Science The Chinese University of Hong Kong Shenzhen China Shenzhen International Center For Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Rensselaer Polytechnic Institute United States

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance, and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs);(ii) Learning to optimize (L2O). In this work, we propose a FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques borrowed from graph neural networks. We prove that the proposed PDHG-Net can recover PDHG algorithm, thus can approximate optimal solutions of LP instances with a polynomial number of neurons. We propose a two-stage inference approach: first use PDHG-Net to generate an approximate solution, and then apply the PDHG algorithm to further improve the solution. Experiments show that our approach can significantly accelerate LP solving, achieving up to a 3× speedup compared to FOMs for large-scale LP problems. Copyright 2024 by the author(s)

关键词： Graph neural networks

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Electron kinetic effects in back-stimulated Raman scattering bursts driven by broadband laser pulses

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Matter and Radiation at Extremes 2024年第4期9卷 54-67页

作者： Q.K.Liu L.Deng Q.Wang X.Zhang F.Q.Meng Y.P.Wang Y.Q.Gao H.B.Cai S.P.Zhu Graduate School China Academy of Engineering PhysicsBeijing 100088China Institute of Applied Physics and Computational Mathematics Beijing 100094China School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026China Shanghai Institute of Laser Plasma Shanghai 201800China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100871China School of Physics Zhejiang UniversityHangzhou 310027China

We examine electron kinetic effects in broadband-laser-driven back-stimulated Raman scattering(BSRS)bursts using particle-in-cell *** bursts occur during the nonlinear stage,causing reflectivity spikes and generating large numbers of hot ***-duration simulations are performed to observe burst events,and a simplified model is developed to eliminate the interference of the broadband laser’s random intensity *** the simplified model,we isolate and characterize the spectrum of electron plasma *** spectrum changes from a sideband structure to a turbulence-like structure during the burst.A significant asymmetry in the spectrum is *** asymmetry is amplified and transferred to electron phase space by high-intensity broadband laser pulses,leading to violent vortex-merging and generation of hot *** proportion of hot electrons increases from 6.76%to 14.7%during a single violent burst *** demonstrate that kinetic effects profoundly influence the BSRS evolution driven by broadband lasers.

关键词： scattering kinetic simplified

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NTK-SAP: IMPROVING NEURAL NETWORK PRUNING BY ALIGNING TRAINING DYNAMICS 11

NTK-SAP: IMPROVING NEURAL NETWORK PRUNING BY ALIGNING TRAINI...

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11th International Conference on Learning Representations, ICLR 2023

作者： Wang, Yite Li, Dawei Sun, Ruoyu University of Illinois Urbana-Champaign United States Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China School of Data Science The Chinese University of Hong Kong Shenzhen China

Pruning neural networks before training has received increasing interest due to its potential to reduce training time and memory. One popular method is to prune the connections based on a certain metric, but it is not entirely clear what metric is the best choice. Recent advances in neural tangent kernel (NTK) theory suggest that the training dynamics of large enough neural networks is closely related to the spectrum of the NTK. Motivated by this finding, we propose to prune the connections that have the least influence on the spectrum of the NTK. This method can help maintain the NTK spectrum, which may help align the training dynamics to that of its dense counterpart. However, one possible issue is that the fixed-weight-NTK corresponding to a given initial point can be very different from the NTK corresponding to later iterates during the training phase. We further propose to sample multiple realizations of random weights to estimate the NTK spectrum. Note that our approach is weight-agnostic, which is different from most existing methods that are weight-dependent. In addition, we use random inputs to compute the fixed-weight-NTK, making our method data-agnostic as well. We name our foresight pruning algorithm Neural Tangent Kernel Spectrum-Aware Pruning (NTK-SAP). Empirically, our method achieves better performance than all baselines on multiple datasets. Our code is available at https://***/YiteWang/NTK-SAP. © 2023 11th International Conference on Learning Representations, ICLR 2023. All rights reserved.

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Augmented Lagrangian Methods for Convex Matrix Optimization Problems

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Journal of the Operations Research Society of China 2022年第2期10卷 305-342页

作者： Ying Cui Chao Ding Xu-Dong Li Xin-Yuan Zhao Department of Industrial and Systems Engineering University of MinnesotaMinneapolis 55411USA Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Data Science Fudan UniversityShanghai 200433China Shanghai Center for Mathematical Sciences Fudan UniversityShanghai 200433China College of Applied Sciences Beijing University of TechnologyBeijing 100124China

In this paper,we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems(cMOP).Specifically,we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral *** a mild quadratic growth condition on the dual of cMOP,we further discussed the R-superlinear convergence of the Karush-Kuhn-Tucker(KKT)residuals of the sequence generated by the augmented Lagrangian methods(ALM)for solving convex matrix optimization *** details of the ALM for solving core convex matrix optimization problems are also provided.

关键词： Matrix optimization Spectral functions Quadratic growth conditions Metric subregularity Augmented Lagrangian methods Fast convergence rates Semismooth Newton methods

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Mechanism of magnetic phase transition in correlated magnetic metal: insight into itinerant ferromagnet Fe3−δGeTe2

arXiv

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arXiv 2024年

作者： Xu, Yuanji Wang, Yue-Chao Jin, Xintao Liu, Haifeng Liu, Yu Song, Haifeng Tian, Fuyang Institute for Applied Physics University of Science and Technology Beijing Beijing100083 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

Developing a comprehensive magnetic theory for correlated itinerant magnets poses challenges due to the difficulty in reconciling both local moments and itinerant electrons. In this work, we investigate the microscopic process of magnetic phase transition in ferromagnetic metal Fe3−δGeTe2. We find that Hund’s coupling is crucial for establishing ferromagnetic order. During the ferromagnetic transition, we observe the formation of quasiparticle flat bands and an opposing tendency in spectral weight transfer, primarily between the lower and upper Hubbard bands, across the two spin channels. Moreover, our results indicate that one of the inequivalent Fe sites exhibits Mott physics, while the other Fe site exhibits Hund’s physics, attributable to their distinct atomic environments. We suggest that ferromagnetic order reduces spin fluctuations and makes flat bands near the Fermi level more distinct. The hybridization between the distinctly flat bands and other itinerant bands offers a possible way to form heavy fermion behavior in ferromagnets. The complex interactions of competing orders drive correlated magnetic metals to a new frontier for discovering outstanding quantum states. © 2024, CC BY.

关键词： Ferromagnetism

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