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arXiv 2023年

作者： Dai, Xiaoying Zhou, Aihui Zhou, Yuzhi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phys. 384, 99 (2019)], following extensions take place: (1) an tensor-producted basis set, which adopts PWs in the incommensurate dimensions, and localized basis in the interlayer dimension, (2) a practical application of a novel cutoff techniques we have recently developed, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2) now the dimensions of Hamiltonian matrix are reduced by about 2 orders of magnitude compared with the original framework. And (3) enables us to better organize the calculations and understand the results. For numerical examples, we study the electronic structures of the linear bilayer graphene lattice system with the magic twisted angle (∼ 1.05◦). The famous flat bands have been reproduced with their features in quantitative agreement with those from experiments and other theoretical calculations. Moreover, the extended framework has much less computational cost compared to the commensurate cell approximations, and is more extendable compared to the traditional model hamiltonians and tight binding models. Finally this framework can readily accommodate nonlinear models thus will laid the foundations for more effective yet accurate Density Functional Theory (DFT) calculations. © 2023, CC BY.

关键词： Electronic structure

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Localization in the Incommensurate systems: A Plane Wave Study via Effective Potentials

arXiv

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arXiv 2023年

作者： Wang, Ting Zhou, Yuzhi Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100094 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for the effective potentials of the incommensurate systems and utilize that, the localization of the electron density can be inferred from the effective potentials. Moreover, we show that the spectrum distribution can also be obtained from the effective potential version of Weyl’s law. We perform some numerical experiments on some typical incommensurate systems, showing that the effective potential provides an alternative tool for investigating the localization and spectrum distribution of the systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Elastic waves

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Canonical convolutional neural networks

arXiv

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arXiv 2022年

作者： Veeramacheneni, Lokesh Wolter, Moritz Klein, Reinhard Garcke, Jochen Department of Computer Science Hochschule Bonn-Rhein-Sieg Fraunhofer Center for Machine Learning SCAI Germany High Performance Computing and Analytics Lab University of Bonn Fraunhofer Center for Machine Learning SCAI Germany Department of Computer Science University of Bonn Germany Fraunhofer Center for Machine Learning SCAI Institute for Numerical Simulation University of Bonn Germany

We introduce canonical weight normalization for convolutional neural networks. Inspired by the canonical tensor decomposition, we express the weight tensors in so-called canonical networks as scaled sums of outer vector products. In particular, we train network weights in the decomposed form, where scale weights are optimized separately for each mode. Additionally, similarly to weight normalization, we include a global scaling parameter. We study the initialization of the canonical form by running the power method and by drawing randomly from Gaussian or uniform distributions. Our results indicate that we can replace the power method with cheaper initializations drawn from standard distributions. The canonical re-parametrization leads to competitive normalization performance on the MNIST, CIFAR10, and SVHN data sets. Moreover, the formulation simplifies network compression. Once training has converged, the canonical form allows convenient model-compression by truncating the parameter sums. © 2022, CC BY-NC-SA.

关键词： Convolutional neural networks

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On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics

arXiv

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arXiv 2022年

作者： Ranocha, Hendrik Winters, Andrew R. Castro, Hugo Guillermo Dalcin, Lisandro Schlottke-Lakemper, Michael Gassner, Gregor J. Parsani, Matteo Applied Mathematics University of Hamburg Germany Department of Mathematics Applied Mathematics Linköping University Sweden Thuwal23955-6900 Saudi Arabia Applied and Computational Mathematics RWTH Aachen University Germany High-Performance Computing Center Stuttgart University of Stuttgart Germany Department of Mathematics and Computer Science University of Cologne Germany Center for Data and Simulation Science University of Cologne Germany

We study temporal step size control of explicit Runge-Kutta methods for compressible computational fluid dynamics (CFD), including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler equations. We demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy (CFL) number. Our numerical examples show that error-based step size control is easy to use, robust, and efficient, e.g., for (initial) transient periods, complex geometries, nonlinear shock capturing approaches, and schemes that use nonlinear entropy projections. We demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases, the open source Julia packages *** with *** and the C/Fortran code SSDC based on *** Codes 65L06, 65M20, 65M70, 76M10, 76M22, 76N99, 35L50 Copyright © 2022, The Authors. All rights reserved.

关键词： Errors

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Abstract: MITK-modelfit: Generic open-source framework for model fitting

Abstract: MITK-modelfit: Generic open-source framework for m...

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International workshop on Algorithmen - systeme - Anwendungen, 2020

作者： Kompan, Ina Debus, Charlotte Ingrisch, Michael Maier-Hein, Klaus Abdollahi, Amir Nolden, Marco Floca, Ralf Division of Medical Image Computing German Cancer Research Center DKFZ Heidelberg Germany Simulation and Software Technology Department of High-Performance Computing German Aerospace Center Cologne Germany Department of Radiology University Hospital Munich Ludwig-Maximilians-University Munich Munich Germany Translational Radiation Oncology German Cancer Research Center DKFZ Heidelberg Germany

ISBN: (纸本)9783658292669

Model fitting is employed in numerous medical imaging applications for quantitative parameter estimation. Prominent examples include pharmacokinetic modelling of dynamic contrast-enhanced (DCE) MRI data and apparent diffusion coefficient calculations. There are many fitting tools available, however most of them are limited to a special purpose and do not allow for own development and extension. © Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature 2020.

关键词： Dynamic contrast enhanced MRI

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Uncertainty-based cardiac image registration using variational autoencoder with nonuniformly spaced control points

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Computer Methods and Programs in Biomedicine 2025年 269卷

作者： Yong Hua Haosheng Su Xuan Yang College of Computer Science and Software Engineering Shenzhen University Shenzhen 518060 Guangdong China Guangdong Province Key Laboratory of Popular High Performance Computers Shenzhen 518060 Guangdong China Guangdong Province Engineering Center of China-made High Performance Data Computing System Shenzhen 518060 Guangdong China

Background and Objective: The Variational Bayesian (VB) image registration model has garnered recent attention for its ability to offer uncertainty, particularly in the context of cardiac motion estimation. Nonetheless, several challenges have plagued VB image registration. Firstly, the Convolutional Neural Networks (CNNs) in VB excel with grid-based image features make it challenging to extract features from non-uniformly located points located at tissue boundaries. Secondly, the underutilization of VB-provided uncertainty and the misfocus of the regions of interest (ROIs) lead to misleading generative likelihoods. Lastly, existing VB prior distributions struggle to balance the posterior-prior gap and reconstruction accuracy. Methods: To address these concerns, we extend the VB image registration model by incorporating non-uniformly spaced control points that specifically target displacements at object boundaries. We develop a network capable of concurrently extracting image and spatial features from non-uniformly spaced control points. The uncertainty of the Displacement Vector Field (DVF) is integrated to prioritize matching ROIs in two images and enhance generative likelihood. Additionally, Our VB model employs a factorized prior to regularize the posterior distribution. Theoretical analysis shows that the factorized prior reduces the KL divergence between the posterior and the prior. Results: Results on four public datasets demonstrate that our network outperforms state-of-the-art registration networks while providing valuable uncertainty information on registration outcomes. Conclusions: Experiments confirm that our VB image registration utilizing non-uniformly spaced control points effectively extracts features from boundary, and the uncertainty-based generative likelihood guides the DVF to match ROIs accurately across images. The factorized prior significantly improves reconstruction accuracy compared to existing priors.

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A force-based gradient descent method for ab initio atomic structure relaxation

arXiv

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arXiv 2022年

作者： Hu, Yukuan Gao, Xingyu Zhao, Yafan Liu, Xin Song, Haifeng State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China

Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial stepsize capturing the local curvature of the energy surface. The exit is controlled by an unrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only two parameters are present without tuning. © 2022, CC BY.

关键词： Conjugate gradient method

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Wavelet-Packets for Deepfake Image Analysis and Detection

arXiv

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arXiv 2021年

作者： Wolter, Moritz Blanke, Felix Heese, Raoul Garcke, Jochen High Performance Computing & Analytics Lab Universität Bonn Germany Fraunhofer SCAI University of Bonn Germany Fraunhofer Center for Machine Learning Fraunhofer ITWM Germany Institute for Numerical Simulation University of Bonn Germany Fraunhofer Center for Machine Learning Fraunhofer SCAI Germany

As neural networks become able to generate realistic artificial images, they have the potential to improve movies, music, video games and make the internet an even more creative and inspiring place. Yet, the latest technology potentially enables new digital ways to lie. In response, the need for a diverse and reliable method toolbox arises to identify artificial images and other content. Previous work primarily relies on pixel-space convolutional neural networks or the Fourier transform. Synthesized fake image analysis and detection methods based on a multi-scale wavelet representation, localized in both space and frequency, have been absent thus far. The wavelet transform conserves spatial information to a degree, allowing us to present a new analysis. Comparing the wavelet coefficients of real and fake images significant differences are identified, where this representation also allows further interpretations. Additionally, this paper proposes to learn a model for the detection of synthetic images based on the wavelet-packet representation of natural and generative adversarial neural network (GAN)-generated images. Our forensic classifiers exhibit competitive or improved performance at small network sizes, as we demonstrate on the Flickr Faces high Quality (FFHQ), Large-scale Celeb Faces Attributes (CelebA) and Large-scale Scene UNderstanding (LSUN) source identification problems. Furthermore, we study the binary Face Forensics++ (ff++) fake-detection problem. © 2021, CC BY-NC-SA.

关键词： Fake detection

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Advancements in neural network techniques for electric and magnetic field reconstruction: Application to ion radiography

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AIP Advances 2024年第2期14卷 025037-025037页

作者： Jao, C.-S. Chen, Y.-C. Nikaido, F. Liu, Y.-L. Sakai, K. Minami, T. Isayama, S. Abe, Y. Kuramitsu, Y. Department of Physics National Cheng Kung University Tainan City70101 Taiwan National Center for High-Performance Computing National Applied Research Laboratories Tainan City711010 Taiwan Graduate School of Engineering Osaka University Osaka565-0871 Japan Institute of Space and Plasma Sciences National Cheng Kung University Tainan City70101 Taiwan National Institute for Fusion Science Gifu509-5202 Japan Department of Earth System Science and Technology Kyushu University Fukuoka816-8580 Japan Institute of Laser Engineering Osaka University Osaka565-0871 Japan

In the realm of high-energy-density laboratory plasma experiments, ion radiography is a vital tool for measuring electromagnetic fields. Leveraging the deflection of injected protons, ion imaging can reveal the intricate patterns of electromagnetic fields within the plasma. However, the complex task of reconstructing electromagnetic fields within the plasma system from ion images presents a formidable challenge. In response, we propose the application of neural network techniques to facilitate electromagnetic field reconstructions. For the training data, we generate corresponding particle data on ion radiography with diverse field profiles in the plasma system, drawing from analytical solutions of charged particle motions and test-particle simulations. With these training data, our expectation is that the developed neural network can assimilate information from ion radiography and accurately predict the corresponding field profiles. In this study, our primary emphasis is on developing these techniques within the context of the simplest setups, specifically uniform (single-layer) or two-layer systems. We begin by examining systems with only electric or magnetic fields and subsequently extend our exploration to systems with combined electromagnetic fields. Our findings demonstrate the viability of employing neural networks for electromagnetic field reconstructions. In all the presented scenarios, the correlation coefficients between the actual and neural network-predicted values consistently reach 0.99. We have also learned that physics concepts can help us understand the weaknesses in neural network performance and identify directions for improvement. © 2024 Author(s).

关键词： Electromagnetic fields

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Loophole-free test of macroscopic realism via high-order correlations of measurement

arXiv

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arXiv 2024年

作者： Wang, Ping Chen, Chong Liao, Hao Vorobyov, Vadim V. Wrachtrup, Jörg Liu, Ren-Bao College of Education for the Future Beijing Normal University Zhuhai519087 China Department of Physics The Chinese University of Hong Kong New Territories Shatin Hong Kong Centre for Quantum Coherence The Chinese University of Hong Kong New Territories Shatin Hong Kong The Hong Kong Institute of Quantum Information Science and Technology The Chinese University of Hong Kong New Territories Shatin Hong Kong National Engineering Laboratory on Big Data System Computing Technology Guangdong Province Engineering Center of China-made High Performance Data Computing System College of Computer Science and Software Engineering Shenzhen University Shenzhen518060 China 3rd Institute of Physics Research Center SCoPE and IQST University of Stuttgart Stuttgart70569 Germany New Cornerstone Science Laboratory The Chinese University of Hong Kong New Territories Shatin Hong Kong

Test of macroscopic realism (MR) is key to understanding the foundation of quantum mechanics. Due to the existence of the non-invasive measurability loophole and other interpretation loopholes, however, such test remains an open question. Here we propose a general inequality based on high-order correlations of measurements for a loophole-free test of MR at the weak signal limit. Importantly, the inequality is established using the statistics of raw data recorded by classical devices, without requiring a specific model for the measurement process, so its violation would falsify MR without the interpretation loophole. The non-invasive measurability loophole is also closed, since the weak signal limit can be verified solely by measurement data (using the relative scaling behaviors of different orders of correlations). We demonstrate that the inequality can be broken by a quantum spin model. The inequality proposed here provides an unambiguous test of the MR principle and is also useful to characterizing quantum coherence. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum theory

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