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A Reduced-Order Model for Nonlinear Radiative Transfer Problems Based on Moment Equations and POD-Petrov-Galerkin Projection of the Normalized Boltzmann Transport Equation

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arXiv 2023年

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective grey low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM’s effectiveness in the simulation of radiation wave phenomena. The ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions. © 2023, CC BY.

关键词： Tensors

Concurrent learning scheme for crystal structure prediction

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Physical Review B 2024年第9期109卷 094117-094117页

作者： Zhenyu Wang Xiaoyang Wang Xiaoshan Luo Pengyue Gao Ying Sun Jian Lv Han Wang Yanchao Wang Yanming Ma Key Laboratory of Material Simulation Methods and Software of Ministry of Education College of Physics Jilin University Changchun 130012 People's Republic of China International Center of Future Science Jilin University Changchun 130012 People's Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing 100094 People's Republic of China HEDPS CAPT College of Engineering Peking University Beijing 100871 People's Republic of China

Crystal structure prediction (CSP) and machine learning potential (MLP) are two fundamental methods for modern computational material discovery. While the former aims at efficient sampling of the potential energy surface (PES) for discovering new materials, the latter focuses on reproducing the PES to accelerate various atomic simulation tasks. In this work, we combine the two methods within a concurrent learning framework in an effort to generate efficient MLP models for accelerating CSP. The proposed scheme explores the PES through the swarm-intelligence calypso method, labels the most representative structures with quantum mechanical calculations, and learns the PES through a deep potential (DP) model. The process proceeds in an iterative, computationally efficient, and automated manner, leading to the collection of a most compact reference training set from which the resulting DP model is proven particularly suitable for accelerating calypso structure prediction. The scheme has been systematically benchmarked on binary magnesium-aluminium (Mg-Al) alloys and ternary lithium-lanthanum-hydrogen (Li-La-H) superhydrides, demonstrating its efficiency and reliability in DP model construction and calypso structure prediction. The proposed scheme represents a promising routine to perform the structure prediction of large or multicomponent systems.

关键词： Crystal structure Potential energy surfaces Machine learning

DPA-2:a large atomic model as a multitask learner

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npj computational Materials 2024年第1期10卷 185-199页

作者： Duo Zhang Xinzijian Liu Xiangyu Zhang Chengqian Zhang Chun Cai Hangrui Bi Yiming Du Xuejian Qin Anyang Peng Jiameng Huang Bowen Li Yifan Shan Jinzhe Zeng Yuzhi Zhang Siyuan Liu Yifan Li Junhan Chang Xinyan Wang Shuo Zhou Jianchuan Liu Xiaoshan Luo Zhenyu Wang Wanrun Jiang Jing Wu Yudi Yang Jiyuan Yang Manyi Yang Fu-Qiang Gong Linshuang Zhang Mengchao Shi Fu-Zhi Dai Darrin M.York Shi Liu Tong Zhu Zhicheng Zhong Jian Lv Jun Cheng Weile Jia Mohan Chen Guolin Ke Weinan E Linfeng Zhang Han Wang AI for Science Institute BeijingP.R.China DP Technology BeijingP.R.China Academy for Advanced Interdisciplinary Studies Peking UniversityBeijingP.R.China State Key Lab of Processors Institute of Computing TechnologyChinese Academy of SciencesBeijingP.R.China University of Chinese Academy of Sciences BeijingP.R.China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingP.R.China Ningbo Institute of Materials Technology and Engineering Chinese Academy of SciencesNingboP.R.China CAS Key Laboratory of Magnetic Materials and Devices and Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology Chinese Academy of SciencesNingboP.R.China School of Electronics Engineering and Computer Science Peking UniversityBeijingP.R.China Shanghai Engineering Research Center of Molecular Therapeutics&New Drug Development School of Chemistry and Molecular EngineeringEast China Normal UniversityShanghaiP.R.China Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine and Department of Chemistry and Chemical BiologyRutgers UniversityPiscatawayNJUSA Department of Chemistry Princeton UniversityPrincetonNJUSA College of Chemistry and Molecular Engineering Peking UniversityBeijingP.R.China Yuanpei College Peking UniversityBeijingP.R.China School of Electrical Engineering and Electronic Information Xihua UniversityChengduP.R.China State Key Laboratory of Superhard Materials College of PhysicsJilin UniversityChangchunP.R.China Key Laboratory of Material Simulation Methods&Software of Ministry of Education College of PhysicsJilin UniversityChangchunP.R.China International Center of Future Science Jilin UniversityChangchunP.R.China Key Laboratory for Quantum Materialsof Zhejiang Province Department of PhysicsSchool of ScienceWestlake UniversityHangzhouP.R.China Atomistic Simulations Italian Institute of TechnologyGenovaItaly State Key Laboratory of Physical Chemistry of Solid Surface iChEMCollege of Chemistry and Chemical EngineeringXiame

The rapid advancements in artificial intelligence(AI)are catalyzing transformative changes in atomic modeling,simulation,and ***-driven potential energy models havedemonstrated the capability to conduct large-scale,long-duration simulations with the accuracy of ab initio electronic structure ***,the model generation process remains a bottleneck for large-scale *** propose a shift towards a model-centric ecosystem,wherein a large atomic model(LAM),pretrained across multiple disciplines,can be efficiently fine-tuned and distilled for various downstream tasks,thereby establishing a new framework for molecular *** this study,we introduce the DPA-2 architecture as a prototype for ***-trained on a diverse array of chemical and materials systemsusing a multi-task approach,DPA-2demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning *** approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research.

关键词： DPA establishing thereby

Interactive and Markerless Visual Recognition of Brazilian Sign Language Alphabet

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Interactive and Markerless Visual Recognition of Brazilian S...

IEEE Instrumentation and Measurement Technology Conference

作者： Silas Luiz Furtado Jauvane C. De Oliveira Shervin Shirmohammadi Computer Engineering Department Military Institute of Engineering Rio de Janeiro Brazil Mathematical and Computational Methods Department National Laboratory for Scientific Computing Petrópolis Brazil Discover Lab School of EECS University of Ottawa Ottawa Canada

The automatic recognition of sign languages will increase the inclusion of non-verbal persons in society by allowing them to communicate with people who are not familiar with sign language. To this end, recently some systems have been proposed to automatically recognize sign language. Among them, those with external aids such as gloves, markers, clothing/background control, or radars usually have high accuracy, but are not practical in daily life situations. On the other hand, those that use only a camera, such as prevalent smartphone cameras, are practical but have lower accuracy. In this work, we present a system that can recognize the alphabet in the Brazilian sign language, Língua Brasileira de Sinais (LIBRAS), using only a camera yet achieving high accuracy. Like most existing works, our system captures and processes the image of hand gesture and uses a classifier to recognize the sign. However, unlike existing works, the classifier is the Inception-v3 neural network trained with transfer learning on our custom-collected LIBRAS alphabet dataset. Performance evaluations show the system recognizes LIBRAS alphabet with 97% accuracy. We also developed an interactive app, demonstrating that it can run in real time.

关键词：

Full trajectory optimizing operator inference for reduced-order modeling using differentiable programming

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arXiv 2023年

作者： Chakrabarti, Surya Gaitonde, Datta V. Mohan, Arvind T. Livescu, Daniel The Ohio State University Mechanical and Aerospace Engineering Department ColumbusOH43210 United States Los Alamos National Laboratory Los AlamosNM87545 United States Computational Physics and Methods Group United States

Accurate and computationally inexpensive Reduced Order Models (ROMs) capable of forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control strategies in engineering problems. Galerkin projection based Reduced Order Models (GP-ROMs), derived by projecting the Navier-Stokes equations on a truncated Proper Orthogonal Decomposition (POD) basis, are popular because of their low computational costs and theoretical foundations in the governing fluid flow equations. However, the accuracy of traditional GP-ROMs degrades over long time prediction horizons. While calibration can somewhat mitigate this issue, the procedure is cumbersome and requires insight into the full order solver. To address these issues, we extend the recently proposed Neural Galerkin Projection (NeuralGP) data driven framework to compressibility-dominated transonic flow, considering a prototypical problem of a buffeting NACA0012 airfoil governed by the full Navier-Stokes equations. The algorithm maintains the form of the ROM-ODE obtained from the Galerkin projection;however coefficients are learned directly from the data using gradient descent facilitated by differentiable programming. This effectively blends the strengths of the physics driven GP-ROM and purely data driven neural network-based techniques, resulting in a computationally cheaper model that is easier to interpret. While both NeuralGP and traditional GP-ROMs yield accurate forecasts over short time prediction horizons, the former accurately tracks the reference POD coefficients over longer prediction horizons, in time ranges where the calibrated GP-ROM displays the tendency to diverge in amplitude and frequency. We show that the distinct long-term behavior of the blended NeuralGP method minimizes a more rigorous full trajectory error norm compared to a linearized error definition optimized by the calibration procedure. We also find that while both procedures stabilize the ROM by displaci

关键词： Navier Stokes equations

Physics-constrained coupled neural differential equations for one dimensional blood flow modeling

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arXiv 2024年

作者： Csala, Hunor Mohan, Arvind Livescu, Daniel Arzani, Amirhossein Department of Mechanical Engineering University of Utah Salt Lake CityUT United States Scientific Computing and Imaging Institute University of Utah Salt Lake CityUT United States Computational Physics and Methods Los Alamos National Laboratory Los AlamosNM United States

Background: computational cardiovascular flow modeling plays a crucial role in understanding blood flow dynamics. While 3D models provide acute details, they are computationally expensive, especially with fluid-structure interaction (FSI) simulations. 1D models offer a computationally efficient alternative, by simplifying the 3D Navier-Stokes equations through axisymmetric flow assumption and cross-sectional averaging. However, traditional 1D models based on finite element methods (FEM) often lack accuracy compared to 3D averaged solutions. methods: This study introduces a novel physics-constrained machine learning technique that enhances the accuracy of 1D cardiovascular flow models while maintaining computational efficiency. Our approach, utilizing a physics-constrained coupled neural differential equation (PCNDE) framework, demonstrates superior performance compared to conventional FEM-based 1D models across a wide range of inlet boundary condition waveforms and stenosis blockage ratios. A key innovation lies in the spatial formulation of the momentum conservation equation, departing from the traditional temporal approach and capitalizing on the inherent temporal periodicity of blood flow. Results: This spatial neural differential equation formulation switches space and time and overcomes issues related to coupling stability and smoothness, while simplifying boundary condition implementation. The model accurately captures flow rate, area, and pressure variations for unseen waveforms and geometries, having 3-5 times smaller error than 1D FEM, and less than 1.2% relative error compared to 3D averaged training data. We evaluate the model’s robustness to input noise and explore the loss landscapes associated with the inclusion of different physics terms. Conclusion: This advanced 1D modeling technique offers promising potential for rapid cardiovascular simulations, achieving computational efficiency and accuracy. By combining the strengths of physics-based and data-d

关键词： Navier Stokes equations

Asymptotic Relaxation of Moment Equations for a Multi-species, Homogeneous BGK Model

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arXiv 2023年

作者： Habbershaw, Evan Glasby, Ryan S. Haack, Jeffrey R. Hauck, Cory D. Wise, Steven M. Department of Mathematics The University of Tennessee KnoxvilleTN37996 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Physics and Methods Group Los Alamos National Laboratory Los AlamosNM87545 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States

Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially non-trivial velocity distributions. In this paper, moment equations for the bulk velocities, energies, and temperatures of a spatially homogeneous multi-species BGK model are examined. A key challenge in analyzing these equations is the fact that the collision frequencies are allowed to depend on the species temperatures, which allows for more realistic simulations of dilute gas flow. Therefore, a positive lower bound is established for the species temperatures. With this lower bound, a global existence and uniqueness of solutions to the coupled velocity-energy ODE system is established. The lower bound also enables a proof of exponential decay to a unique steady-state solution. Numerical results are presented to demonstrate how the bulk velocities and temperatures relax for large *** Codes 37A60, 34A12, 82C40 © 2023, CC BY.

关键词： Velocity distribution

MOOSE ProbML: Parallelized Probabilistic Machine Learning and Uncertainty Quantification for computational Energy Applications

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arXiv 2025年

作者： Dhulipala, Somayajulu L.N. German, Peter Che, Yifeng Prince, Zachary M. Simon, Pierre-Clément A. Xie, Xianjian Labouré, Vincent M. Yan, Hao Computational Mechanics and Materials Department Idaho National Laboratory Idaho FallsID83415 United States Computational Frameworks Department Idaho National Laboratory Idaho FallsID83415 United States Woodruff School of Mechanical Engineering Georgia Institute of Technology AtlantaGA30332 United States School of Computing and Augmented Intelligence Arizona State University TempeAZ85287 United States Reactor Physics Methods and Analysis Department Idaho National Laboratory Idaho FallsID83415 United States Civil and Environmental Engineering Department Idaho State University PocatelloID83209 United States

This paper presents the development and demonstration of massively parallel probabilistic machine learning (ML) and uncertainty quantification (UQ) capabilities within the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source computational platform for parallel finite element and finite volume analyses. In addressing the computational expense and uncertainties inherent in complex multiphysics simulations, this paper integrates Gaussian process (GP) variants, active learning, Bayesian inverse UQ, adaptive forward UQ, Bayesian optimization, evolutionary optimization, and Markov chain Monte Carlo (MCMC) within MOOSE. It also elaborates on the interaction among key MOOSE systems—Sampler, MultiApp, Reporter, and Surrogate—in enabling these capabilities. The modularity offered by these systems enables development of a multitude of probabilistic ML and UQ algorithms in MOOSE. Example code demonstrations include parallel active learning and parallel Bayesian inference via active learning. The impact of these developments is illustrated through five applications relevant to computational energy applications: UQ of nuclear fuel fission product release, using parallel active learning Bayesian inference;very rare events analysis in nuclear microreactors using active learning;advanced manufacturing process modeling using multi-output GPs (MOGPs) and dimensionality reduction;fluid flow using deep GPs (DGPs);and tritium transport model parameter optimization for fusion energy, using batch Bayesian optimization. © 2025, CC BY-NC-SA.

关键词： Markov chains

Masked Thought: Simply Masking Partial Reasoning Steps Can Improve Mathematical Reasoning Learning of Language Models

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arXiv 2024年

作者： Chen, Changyu Wang, Xiting Lin, Ting-En Lv, Ang Wu, Yuchuan Gao, Xin Wen, Ji-Rong Yan, Rui Li, Yongbin Beijing Key Laboratory of Big Data Management and Analysis Methods Gaoling School of Artificial Intelligence Renmin University of China China Alibaba Group China Engineering Research Center of Next-Generation Intelligent Search and Recommendation Ministry of Education China Computational Bioscience Research Center KAUST Saudi Arabia

In reasoning tasks, even a minor error can cascade into inaccurate results, leading to suboptimal performance of large language models in such domains. Earlier fine-tuning approaches sought to mitigate this by leveraging more precise supervisory signals from human labeling, larger models, or self-sampling, although at a high cost. Conversely, we develop a method that avoids external resources, relying instead on introducing perturbations to the input. Our training approach randomly masks certain tokens within the chain of thought, a technique we found to be particularly effective for reasoning tasks. When applied to fine-tuning with GSM8K on Llama-2-7B, this method achieved a 5% improvement in GSM8K accuracy and a 10% improvement in GSM-IC accuracy over standard supervised fine-tuning with a few codes modified. Furthermore, it is complementary to existing methods. When integrated with related explicit data augmentation methods, it leads to improvements across five datasets of various augmentation methods, as well as two different base models. We further investigate the mechanisms behind this improvement through case studies and quantitative analysis, suggesting that our approach may provide superior support for the model in capturing long-distance dependencies, especially those related to questions. This enhancement could deepen understanding of the premises in questions and prior steps. Our code is available at Github. © 2024, CC BY.

关键词： Signal sampling