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The F-snapshot Problem [article]

Gal Amram
2015 arXiv   pre-print
F-snapshot problem.  ...  The problem is interesting when the domain of F is infinite and the range of F is finite.  ...  Furthermore, the F -snapshot problem generalizes the signaling problem which provides a solution to the mailbox problem.  ... 
arXiv:1510.02211v1 fatcat:aheqq2mndvasrjhawpytcxhzj4

Best Friends Forever (BFF): Finding Lasting Dense Subgraphs [article]

Konstantinos Semertzidis, Evaggelia Pitoura, Evimaria Terzi, Panayiotis Tsaparas
2017 arXiv   pre-print
We then look at the On-Off BFF (O^2BFF) problem that relaxes the requirement of nodes being connected in all snapshots, and asks for the densest set of nodes in at least k of a given set of graph snapshots  ...  In this paper, we study the following problem: given a set of graph snapshots, which may correspond to the state of an evolving graph at different time instances, identify the set of nodes that are the  ...  These snapshots are then used for solving the corresponding BFF problem on input C 0 k and produce S 0 = FINDBFF(C 0 k , f ).  ... 
arXiv:1612.05440v3 fatcat:sxo5qy2r75ax5daqezrms2ho24

On the time complexity of minimum and maximum global snapshot problems

Loon-Been Chen, I-Chen Wu
1998 Information Processing Letters  
This problem is referred to as the minimum or maximum global snapshot problem [6] . Groselj [6] recently proposed an interesting method to derive the minimum global snapshot.  ...  In this paper we show in a reverse way that the MCNF problem is also linear-time reducible to these global snapshot problems.  ...  Acknowledgments The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC-86-2213-E-009-32.  ... 
doi:10.1016/s0020-0190(98)00100-8 fatcat:yio7s4e7zvcyznn4vh5yx5ubgy

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations [article]

Liu Yang, Dongkun Zhang, George Em Karniadakis
2018 arXiv   pre-print
Here, we have demonstrated the accuracy and effectiveness of PI-GANs in solving SDEs for up to 30 dimensions, but in principle, PI-GANs could tackle very high dimensional problems given more sensor data  ...  We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limited number of scattered  ...  Acknowledgement We would like to acknowledge support from the Army Research Office (ARO) W911NF-18-1-0301, and from the Department of Energy (DOE) DE-SC0019434 and DE-SC0019453.  ... 
arXiv:1811.02033v1 fatcat:iiwswunc5rbz7jbsdyp77veevy

Enabling interactive mobile simulations through distributed reduced models

Christoph Dibak, Bernard Haasdonk, Andreas Schmidt, Frank Dürr, Kurt Rothermel
2018 Pervasive and Mobile Computing  
Therefore, we propose a framework to support mobile simulations by distributing the computation between the mobile device and a remote server based on the reduced basis method.  ...  Interactive simulations have high demands on resources, which the mobile device alone is unable to satisfy.  ...  Furthermore, the authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/2) at the University  ... 
doi:10.1016/j.pmcj.2018.02.002 fatcat:opcm3zoxkngethyyurxxy5gei4

Model reduction of a coupled numerical model using proper orthogonal decomposition

Xinya Li, Xiao Chen, Bill X. Hu, I. Michael Navon
2013 Journal of Hydrology  
functions that span the snapshot collection.  ...  The developed 35 GFEM-POD model was applied to solve two classic VDFST cases, the Henry problem and the 36 Elder problem, in order to investigate the accuracy and efficiency of the POD model reduction  ...  } 1 2 1 2 , , ..., , 1,2,..., , , ..., , 1,2,..., ns k NN f f f f ns k NN h h h h R k ns c c c c R k ns ∈ = ∈ = (9) 209 wherens is the number of snapshots  ... 
doi:10.1016/j.jhydrol.2013.09.011 fatcat:uheaxwnsunajzdaezpkdsrhy5u

Sparse Generalized Multiscale Finite Element Methods and their applications [article]

Eric Chung, Yalchin Efendiev, Wing Tat Leung, Guanglian Li
2015 arXiv   pre-print
., those discussed in the paper), one may have a sparsity in the snapshot space for an appropriate choice of a snapshot space.  ...  In these approaches, multiscale basis functions are constructed using local snapshot spaces, where a snapshot space is a large space that represents the solution behavior in a coarse block.  ...  The general basis pursuit problem is as follows A τ,on (µ)z τ,on k = λ τ,on k S τ,on (µ)z τ,on k , (11) min x∈R n x 1 + ν Cx − f (x) , (12) where f ∈ R m , C ∈ R m×n , and m < < n.  ... 
arXiv:1506.08509v2 fatcat:smcnzvp5jbadpkzkykroiu63fu

High-SNR snapshot multiplex spectrometer with sub-Hadamard-S matrix coding [article]

Zhuang Zhao and Lianfa Bai and Jing Han and Jiang Yue
2019 arXiv   pre-print
Simulations and experiments show that the proposed method could obtain comparable SNR improvement with the traditional HTS, maintaining snapshot.  ...  We present a robust high signal-to-noise ratio (SNR) snapshot multiplex spectrometer with sub-Hadamard-S matrix coding.  ...  Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 61727802, 61601225). We thank Enlai Guo, Zhaoxin Wang for technical supports.  ... 
arXiv:1905.07543v1 fatcat:fspvqso2lbcujgrrciypqz3dhu

Reduced-Order Model Accounting for High-Frequency Effects in Power Electronic Components

Yannick Paquay, Christophe Geuzaine, Rokibul Hasan, Ruth V. Sabariego
2016 IEEE transactions on magnetics  
Particular attention is paid to the choice of the most suitable snapshots by means of three different greedy algorithms, the performance of which is compared.  ...  Starting from a full-wave finite-element model and several snapshots/frequencies, the reduced-order (RO) model is constructed.  ...  Herein the full problem (4) is solved in the frequency domain for a set of M frequencies (snapshots).  ... 
doi:10.1109/tmag.2015.2472559 fatcat:akuwt3xpuvbqrb62v4zsyto4l4

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

D. Xiao, P. Yang, F. Fang, J. Xiang, C.C. Pain, I.M. Navon, M. Chen
2017 Journal of Computational Physics  
In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper.  ...  It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots.  ...  N} and j ∈ {1, 2, . . . m}; endfor from the snapshots and used to construct the NIROM for coupling of fluid and solid problems.  ... 
doi:10.1016/ fatcat:ioj2ogxqdfe4lakhwejp7js3ey

Parallel Factor-Based Model for Two-Dimensional Direction Estimation

Nizar Tayem, Khaqan Majeed, Ahmed A. Hussain
2017 International Journal of Antennas and Propagation  
Most of the existing schemes have drawbacks in estimating 2D DOA for multiple narrowband incident sources as follows: use of large number of snapshots, estimation failure problem for elevation and azimuth  ...  (2) it reduces the estimation complexity by constructing Toeplitz data matrices, which are based on a single or few snapshots; (3) it derives parallel factor (PARAFAC) model to avoid pair-matching problems  ...  The TWA G is constructed such that the snapshots of the Toeplitz matrices defined earlier are concatenated together as shown in the following: G = [F (1) F (2) ⋅ ⋅ ⋅ F ( )] = [ [ [ [ [ [ R 푥 (1) R 푥 (2  ... 
doi:10.1155/2017/1813497 fatcat:3hpcqw657vezlbwwy34rx2lwf4

A POD reduced-order model for eigenvalue problems with application to reactor physics

A. G. Buchan, C. C. Pain, F. Fang, I. M. Navon
2013 International Journal for Numerical Methods in Engineering  
Part of the novelty of this work is in how this snapshot data is generated, and this is through the recasting of eigenvalue problem, which is time-independent, into a time dependent form.  ...  Instances of time dependent eigenfunction solutions are therefore used to construct the snapshot matrix.  ...  The remaining problems are however different from those used in building the snapshots. Problem R2 resembles the reactor with both control rods inserted.  ... 
doi:10.1002/nme.4533 fatcat:54cezzrowfgvdjblniurhrlzyi

Overcoming slowly decaying Kolmogorov n-width by transport maps: application to model order reduction of fluid dynamics and fluid–structure interaction problems [article]

Monica Nonino and Francesco Ballarin and Gianluigi Rozza and Yvon Maday
2019 arXiv   pre-print
Such preprocessing is based on the composition of the snapshots with a transport map, that is a family of smooth and invertible mappings that map the physical domain of the problem into itself.  ...  In this work we focus on reduced order modelling for problems for which the resulting reduced basis spaces show a slow decay of the Kolmogorov n-width, or, in practical calculations, its computational  ...  The computations in this work have been performed with multiphenics [2] , which is a library that aims at providing tools in FEniCS [34] for an easy prototyping of multiphysics problems on conforming  ... 
arXiv:1911.06598v1 fatcat:oifpl373qvcgxosyoqyiaalvhm

Randomized Oversampling for Generalized Multiscale Finite Element Methods

Victor M. Calo, Yalchin Efendiev, Juan Galvis, Guanglian Li
2016 Multiscale Modeling & simulation  
In particular, we propose solving local problems with random boundary conditions and perform the local spectral decomposition in the space of these snapshots.  ...  However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces.  ...  Yalchin Efendiev would like to thank the partial support from the U.S.  ... 
doi:10.1137/140988826 fatcat:fw6bix7wpbf5leo4zcvp5gk6xq

Hierarchical multiscale modeling for flows in fractured media using Generalized Multiscale Finite Element Method [article]

Yalchin Efendiev, Seong Lee, Guanglian Li, Jun Yao, Na Zhang
2015 arXiv   pre-print
We also discuss the use of randomized snapshots (randomized2014) which reduces the offline computational cost.  ...  These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM.  ...  We denote the linear system corresponding to the discrete form of the problem above is       A m B 1 mf · · · B N f mf B 1 f m B 1 . . . 0 . . . . . . . . . . . . B N f f m 0 . . .  ... 
arXiv:1502.03828v1 fatcat:g5ca4a6x4zecfh5vmacrlxismq
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