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Sparse approximation of data-driven polynomial chaos expansions: An induced sampling approach

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arXiv 2020年

作者： Guo, Ling Narayan, Akil Liu, Yongle Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States Department of Mathematics Southern University of Science and Technology Shenzhen China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

One of the open problems in the field of forward uncertainty quantification (UQ) is the ability to form accurate assessments of uncertainty having only incomplete information about the distribution of random inputs. Another challenge is to efficiently make use of limited training data for UQ predictions of complex engineering problems, particularly with high dimensional random parameters. We address these challenges by combining data-driven polynomial chaos expansions with a recently developed preconditioned sparse approximation approach for UQ problems. The first task in this two-step process is to employ the procedure developed in (Ahlfeld et al. 2016, [1]) to construct an "arbitrary" polynomial chaos expansion basis using a finite number of statistical moments of the random inputs. The second step is a novel procedure to effect sparse approximation via 1 minimization in order to quantify the forward uncertainty. To enhance the performance of the preconditioned 1 minimization problem, we sample from the so-called induced distribution, instead of using Monte Carlo (MC) sampling from the original, unknown probability measure. We demonstrate on test problems that induced sampling is a competitive and often better choice compared with sampling from asymptotically optimal measures (such as the equilibrium measure) when we have incomplete information about the distribution. We demonstrate the capacity of the proposed induced sampling algorithm via sparse representation with limited data on test functions, and on a Kirchoff plating bending problem with random Young’s modulus. Copyright © 2020, The Authors. All rights reserved.

关键词： Probability distributions

LINEARIZATION IN MAGNETOELASTICITY

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arXiv 2024年

作者： Almi, Stefano Kružík, Martin Molchanova, Anastasia University of Naples Federico II Department of Mathematics and Applications Renato Caccioppoli via Cintia Monte S. Angelo Naples80126 Italy Czech Academy of Sciences Institute of Information Theory and Automation Pod vodárenskou věží 4 Prague 8182 00 Czech Republic Faculty of Civil Engineering Czech Technical University Thákurova 7 Prague 6166 29 Czech Republic University of Vienna Faculty of Mathematics Oskar-Morgenstern-Platz 1 Vienna1090 Austria TU Wien Institute of Analysis and Scientific Computing Wiedner Hauptstraße 8–10 Wien1040 Austria

Starting from a model of nonlinear magnetoelasticity where magnetization is defined in the Eulerian configuration while elastic deformation is in the Lagrangian one, we rigorously derive a linearized model that coincides with the standard one that already appeared in the literature, see, e.g., [19] and where the zero-stress strain is quadratic in the magnetization. The relation of the nonlinear and linear model is stated in terms of the Γ-convergence and convergence of minimizers. © 2024, CC BY.

关键词： Elastic deformation

Complexity Analysis and Algorithm Design of Pooling Problem

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Journal of the Operations Research Society of China 2018年第2期6卷 249-266页

作者： Yu-Hong Dai Rui Diao Kai Fu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The pooling problem,also called the blending problem,is fundamental in production planning of *** can be formulated as an optimization problem similar with the minimum-cost flow ***,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general *** also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of *** this paper,we prove that the pooling problem is still strongly NP-hard even with only one *** means the quality is an essential difference between minimum-cost flow problem and the pooling *** solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming *** convergence of the algorithm is *** numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local *** results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.

关键词： Pooling problem Complexity analysis Successive linear programming Non-monotone

A Fast Rankability Method Based on Fuzzy Entropy

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SSRN

SSRN 2024年

作者： Kong, Lingping Velasquez, Juan D. Pant, Millie Pan, Jeng-Shyang Snášel, Václav Department of Computer Science VSB-Technical University of Ostrava Listpodu 17 Czech Republic Department of Industrial Engineering University of Chile O’Higgins 1058 Santiago Chile Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Uttarakhand Roorkee247667 India College of Computer Science and Engineering Shandong University of Science and Technology China School of Artificial Intelligence Nanjing University of Information Science and Technology 219 Ningliu Road China Instituto Sistemas Complejos de Ingeniería Santiago Chile Mehta Family School of Data Science and Artificial Intelligence Indian Institute of Technology Uttarakhand Roorkee247667 India

Rankability is a fundamental concept that evaluates a dataset's inherent capacity to establish a meaningful ranking of its elements, with widespread applications in web search, data mining, cybersecurity, and machine *** its significance, relatively little focus has been on evaluating datasets for ranking suitability. Several rankability measures have emerged, such as comparing graphs representing datasets with complete dominance graphs using combinatorial and linear algebraic techniques. However, these approaches typically involve solving eigenvalue problems for large matrices or training regression models on extensive datasets. In this paper, we propose to adopt efficient and straightforward statistical metrics, entropy, and variance to develop a novel rankability method. Our method is designed to be fast and efficient, addressing the challenges posed by existing techniques. We conducted experiments using three football tournament datasets, and the results demonstrate a strong correlation scores (correlation coefficients) in terms of Spearman and Kendall's tau evaluations with Elo rating, a system developed by Arpad Elo in the 1950s and applied in many competitions. Specifically, the Spearman correlation between the proposed method and the Elo rating reached 0.9205 on Atlantic Coast data with a p-value of 0.0004, which is higher than the compared algorithm by 0.2424 in correlation score. © 2024, The Authors. All rights reserved.

关键词： Entropy

A Lightweight Feature Selection Method Based on Rankability

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SSRN

SSRN 2023年

作者： Kong, Lingping Silva, Juan Domingo Velasquez Perfilieva, Irina Pant, Millie Snášel, Václav Department of Computer Science VSB-Technical University of Ostrava Ostrava Czech Republic Department of Industrial Engineering University of Chile Santiago Chile Santiago Chile University Hospital Ostrava Czech Republic Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Uttarakhand Roorkee247667 India Instituto Sistemas Complejos de Ingeniería Santiago Chile Mehta Family School of Data Science and Artificial Intelligence Indian Institute of Technology Uttarakhand Roorkee247667 India

Feature selection, as one of the essential dimensionality reduction techniques, hasbecome one popular yet challenging area in the field, such as data mining andmachine learning. Unlike feature extraction (such as principle component analysis andnon-negative matrix factorization), preserving the entire information but losing thefeature relevance. Data processing in feature selection will lose information, leading tothe need to develop lightweight, efficient, and practical methods that preserve the datainformation as much as possible while performing dimensional reduction. In this paper,we propose a rankability-based feature selection method. The rankability concept wasproposed in 2019, similar to the entropy concept, and has not been studied widely *** proposed method is lightweight in terms of complexity, which requires no iterativeoptimization or auxiliary estimator *** experimented with sixteen datasets and compared our results with four otheralgorithms. The results show that our rankability-based feature selection methodoutperforms the fuzzy entropy-based method on five datasets in eight, and the averageaccuracy increased by 0.1482, 0.1078, and 0.1157, respectively. Then, in the varieddimension-reducing experiments, the proposed method shows superiority on fourdatasets out of eight and is competitive with others on two datasets out of eight. © 2023, The Authors. All rights reserved.

关键词： Feature Selection

Phenomenology and origin of late-time tails in eccentric binary black hole mergers

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arXiv 2024年

作者： Islam, Tousif Faggioli, Guglielmo Khanna, Gaurav Field, Scott E. van de Meent, Maarten Buonanno, Alessandra Kavli Institute for Theoretical Physics University of California Santa Barbara Kohn Hall Lagoon Rd Santa BarbaraCA93106 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Max Planck Institute for Gravitational Physics Albert Einstein Institute Am M¨uhlenberg 1 Potsdam14476 Germany Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States Niels Bohr International Academy Niels Bohr Institute Blegdamsvej 17 Copenhagen2100 Denmark

We investigate the late-time tail behavior in gravitational waves from merging eccentric binary black holes (BBH) using black hole perturbation theory. For simplicity, we focus only on the dominant quadrupolar mode of the radiation. We demonstrate that such tails become more prominent as eccentricity increases. Exploring the phenomenology of the tails in both spinning and non-spinning eccentric binaries, with the spin magnitude varying from χ = −0.6 to χ = +0.6 and eccentricity as high as e = 0.98, we find that these tails can be well approximated by a slowly decaying power law. We study the power law for varying systems and find that the power law exponent lies close to the theoretically expected value −4. Finally, using both plunge geodesic and radiation-reaction-driven orbits, we perform a series of numerical experiments to understand the origin of the tails in BBH simulations. Our results suggest that the late-time tails are strongly excited in eccentric BBH systems when the smaller black hole is in the neighborhood of the apocenter, as opposed to any structure in the strong field of the larger black hole. Our analysis framework is publicly available through the gwtails Python package. Copyright © 2024, The Authors. All rights reserved.

关键词： Black holes

General liquid-crystal theory for anisotropically shaped molecules: Symmetry, orientational order parameters, and system free energy

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Physical Review E 2020年第6期102卷 062701-062701页

作者： Jie Xu Jeff Z. Y. Chen LSEC & NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing (ICMSEC) Academy of Mathematics and Systems Science (AMSS) Chinese Academy of Sciences Beijing 100190 China Department of Physics and Astronomy University of Waterloo Ontario Canada N2L 3G1

A general theory of liquid crystals is presented, starting from the group-theory symmetry analysis of the constituting molecules. A particular attention is paid to the type of elastic free-energies and their relationships with the molecular symmetries. The orientational order-parameter tensors are identified for each molecular symmetry, in a consideration of consistently keeping the leading, characteristic elastic free energies in a model. The order parameters are expressed in terms of symmetric traceless tensors, some of high orders, for all major molecular symmetries, including seven groups of axial symmetries and seven groups of polyhedral symmetries. For spatially inhomogeneous liquid crystals, the couplings of these tensors in the elastic energies are derived by expanding the interaction energies between these molecules. The aim is to provide a general view of the molecular symmetries of individual molecules, orientational order parameters characterizing the orientational distribution functions, and the elastic free energies, all under one single group-theory approach.

关键词： Bent-core liquid crystals Liquid crystals Lyotropic liquid crystals Nematic liquid crystals

Circumferential crack modeling of thin cylindrical shells in modal deformation

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arXiv 2021年

作者： Alijani, Ali Barrera, Olga Bordas, Stéphane P.A. Department of Mechanical Engineering Bandar Anzali Branch Islamic Azad University Bandar Anzali Iran School of Engineering Computing and Mathematics Oxford Brookes University United Kingdom Institute of Computational Engineering Faculty of Sciences and Technology University of Luxembourg Luxembourg City Luxembourg

An innovative technique, called conversion, is introduced to model circumferential cracks in thin cylindrical shells. The semi-analytical finite element method is applied to investigate the modal deformation of the cylinder. An element including the crack is divided into three sub-elements with four nodes in which the stiffness matrix is enriched. The crack characteristics are included in the finite element method relations through conversion matrices and a rotational spring corresponding to the crack. Conversion matrices obtained by applying continuity conditions at the crack tip are used to transform displacements of the middle nodes to those of the main nodes. Moreover, another technique, called spring set, is represented based on a set of springs to model the crack as a separated element. Components of the stiffness matrix related to the separated element are incorporated while the geometric boundary conditions at the crack tip are satisfied. The effects of the circumferential mode number, the crack depth and the length of the cylinder on the critical buckling load are investigated. Experimental tests, ABAQUS modeling and results from literature are used to verify and validate the results and derived relations. In addition, the crack effect on the natural frequency is examined using the vibration analysis based on the conversion technique. Copyright © 2021, The Authors. All rights reserved.

关键词： Deformation

Extending the limit of molecular dynamics with ab initio accuracy to 10 billion atoms

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arXiv 2022年

作者： Guo, Zhuoqiang Lu, Denghui Yan, Yujin Hu, Siyu Liu, Rongrong Tan, Guangming Sun, Ninghui Jiang, Wanrun Liu, Lijun Chen, Yixiao Zhang, Linfeng Chen, Mohan Wang, Han Jia, Weile Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China State Key Laboratory of Computer Architecture ICT Chinese Academy of Sciences Beijing China HEDPS CAPT College of Engineering Peking University Beijing China AI for Science Institute Beijing China Osaka University Osaka Japan Princeton University Princeton United States DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

High-performance computing, together with a neural network model trained from data generated with first-principles methods, has greatly boosted applications of ab initio molecular dynamics in terms of spatial and temporal scales on modern supercomputers. Previous state-of-the-art can achieve 1 − 2 nanoseconds molecular dynamics simulation per day for 100-million atoms on the entire Summit supercomputer. In this paper, we have significantly reduced the memory footprint and computational time by a comprehensive approach with both algorithmic and system innovations. The neural network model is compressed by model tabulation, kernel fusion, and redundancy removal. Then optimizations such as acceleration of customized kernel, tabulation of activation function, MPI+OpenMP parallelization are implemented on GPU and ARM architectures. Testing results of the copper system show that the optimized code can scale up to the entire machine of both Fugaku and Summit, and the corresponding system size can be extended by a factor of 134 to an © 2022, CC BY-NC-SA.

关键词： Supercomputers