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A Monte Carlo Approach to Sparse Approximate Inverse Matrix Computations

J. Straßburg, V.N. Alexandrov
2013 Procedia Computer Science  
The advantage of this approach is that we use sparse Monte Carlo matrix inversion whose complexity is linear to the size of the matrix.  ...  Monte Carlo methods quantify the uncertainties by enabling us to estimate the non-zero elements of the inverse matrix with a given precision and certain probability.  ...  Therefore, we concentrate on Monte Carlo methods for matrix inversion (MI) that only require O(NL) steps to find a single element or a row of the inverse matrix.  ... 
doi:10.1016/j.procs.2013.05.402 fatcat:yg2t7ui765eetkmhbajmcim5au

Enhancing Monte Carlo Preconditioning Methods for Matrix Computations

Janko Straßburg, Vassil Alexandrov
2014 Procedia Computer Science  
The advantage of this approach is that we use sparse Monte Carlo matrix inversion whose computational complexity is linear of the size of the matrix.  ...  Thus we present a Monte Carlo preconditioner that relies on the use of Markov Chain Monte Carlo (MCMC) methods to compute a rough matrix inverse first, which is further optimized by an iterative filter  ...  Acknowledgements This research work was partially supported by High Performance Computing VI project, number TIN2012-34557, of the Spanish Ministry of Economics and Competitiveness .  ... 
doi:10.1016/j.procs.2014.05.143 fatcat:5luky3xb3fex5ojs4hykuuncwy

Monte Carlo scalable algorithms for Computational Finance

V.N. Alexandrov, Christian González Martel, J. Straßburg
2011 Procedia Computer Science  
We will briefly present our approach to Monte Carlo scalable algorithms for Linear Algebra and explain how these approaches are extended to the field of Computational Finance.  ...  In this paper, examples of various approaches of designing scalable algorithms for such advanced architectures will be given.  ...  Carlo method for Matrix Inversion (MI) is described: Step1.  ... 
doi:10.1016/j.procs.2011.04.185 fatcat:t5hkc6ubefh6pgtbgxgxpfwtaa

2D Deconvolution Using Adaptive Kernel

Dirk Nille, Udo von Toussaint
2019 Proceedings (MDPI)  
An alternative to searching for the MAP solution is to integrate using Marcov Chain Monte Carlo without the need to determine the determinant of the Hessian.  ...  An analysis tool using Adaptive Kernel to solve an ill-posed inverse problem for a 2D model space is introduced.  ...  Stochastic Trace Estimation as alternative way to deal with large matrices is investigated and together with the SVD compared against results obtained by Marcov Chain Monte Carlo.  ... 
doi:10.3390/proceedings2019033006 fatcat:qeu2blkcqfdjxhh5cc6x6as53q

Can Agents Model Hydrocarbon Migration for Petroleum System Analysis? A Fast Screening Tool to De-Risk Hydrocarbon Prospects

Bastian Steffens, Quentin Corlay, Nathan Suurmeyer, Jessica Noglows, Dan Arnold, Vasily Demyanov
2022 Energies  
This work investigates how intelligent agent models can mimic these complex natural subsurface processes and account for geological uncertainty.  ...  It is fast and is therefore suitable for uncertainty quantification, before using petroleum system modelling software for a more accurate evaluation of migration scenarios.  ...  We would also like to thank the Natural Environmental Research Council (NERC) Centre for Doctoral Training (CDT) in Oil and Gas of which both PhD studies are part.  ... 
doi:10.3390/en15030902 fatcat:nkb3upvq3jcqrcwg27ck3iu4aq

Supplementary material from Influencing dynamics on social networks without knowledge of network microstructure

Matthew Garrod, Nick S. Jones
2021 figshare.com  
Supplementary material containing in depth descriptions of the algorithms described in the main text, a table of symbols, additional analysis and details of the data pre-processing steps carried out.  ...  R Tburn Burn-in time for Monte Carlo simulations (see Section 2 C). Z+ T Post burn-in run time for Monte Carlo simulations.  ...  The true magnetisation of each block M B i (1) is estimated from the average of 10 Monte Carlo simulations. We also show the behaviour of the average deviation across all blocks δM (black line).  ... 
doi:10.6084/m9.figshare.15111852.v1 fatcat:scfaoflytbdk5ai3kmgcbxxy4a

Structural Health and Load Monitoring with Material-embedded Sensor Networks and Self-organizing Multi-agent Systems

Stefan Bosse, Armin Lechleiter
2014 Procedia Technology - Elsevier  
An issue of this inverse method that might sometimes be critical for its application in a sensor network is the inversion of a dense linear system.  ...  Simulation results obtained from different network situation using Monte-Carlo simulation are shown in Fig. 7 .  ...  noise level of the sensor signals or the modeling or discretization error of the matrix T.  ... 
doi:10.1016/j.protcy.2014.09.039 fatcat:egajpbftgrdvdaqznayanhsopy

Influencing dynamics on social networks without knowledge of network microstructure [article]

Matthew Garrod, Nick S. Jones
2021 arXiv   pre-print
We investigate strategies for influencing the system state in a statistical mechanics based model of opinion formation.  ...  Social network based information campaigns can be used for promoting beneficial health behaviours and mitigating polarisation (e.g. regarding climate change or vaccines).  ...  The first is used to compute the magnetisation of Ising systems on networks under the mean-field approximation and the second is used to carry out the Monte Carlo simulations in order to validate the algorithms  ... 
arXiv:2011.05774v2 fatcat:7v5526hoqzaariub55x7lpgyey

Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks [article]

Simon Ohler and Daniel Brady and Winfried Lötzsch and Michael Fleischhauer and Johannes S. Otterbach
2022 arXiv   pre-print
The simulation of SOC dynamics is typically based on Monte-Carlo (MC) methods, which are however numerically expensive and do not scale beyond certain system sizes.  ...  We investigate the use of Graph Neural Networks (GNNs) as an effective surrogate model to learn the dynamics operator for a paradigmatic SOC system, inspired by an experimentally accessible physics example  ...  We make both the code for our experiments as well as the Monte Carlo code to create our datasets publicly available upon acceptance. Related Work GNNs have been used in a multitude of applications.  ... 
arXiv:2207.08927v1 fatcat:h7bx6mtuqnce5cdtgtskjwyqom

Whole-Genome Analyses of Lung Function, Height and Smoking

Luc Janss, Torben Sigsgaard, Daniel Sorensen
2014 Annals of Human Genetics  
This simplifies programming and results in excellent numerical behaviour. The approach can be readily extended for the joint analysis of an arbitrary number of traits.  ...  A first goal of the study was to incorporate dense genetic marker information in a random regression (Bayesian) model to quantify the relative contributions of genomic and environmental factors to the  ...  A histogram of the Monte Carlo estimate of the genomic heritability is shown in Figure 2 .  ... 
doi:10.1111/ahg.12078 pmid:25081033 pmcid:PMC4404199 fatcat:l2lp4e2lfjhtzmbmhpzjchhufi

Spectral Properties of Unimodular Lattice Triangulations

Benedikt Krüger, Ella M. Schmidt, Klaus Mecke
2016 Journal of statistical physics  
Here, we consider the spectra of the adja cency and the Laplacian matrix as well as the algebraic connectivity and the spectral radius.  ...  Using the ergodic Pachner flips that transform such triangulations into another and an energy functional that corresponds to the degree distribution variance, Markov chain Monte-Carlo simulations can be  ...  We measure the spectra of the adjacency and the Laplacian matrix of random triangulations, which is the ensemble of all triangulations with constant weights, using Metropolis Monte Carlo simulations, and  ... 
doi:10.1007/s10955-016-1493-0 fatcat:fdzlfluk5je6thhitdxyd4xepm

Exa-Dune—Flexible PDE Solvers, Numerical Methods and Applications [chapter]

Peter Bastian, Mirco Altenbernd, Nils-Arne Dreier, Christian Engwer, Jorrit Fahlke, René Fritze, Markus Geveler, Dominik Göddeke, Oleg Iliev, Olaf Ippisch, Jan Mohring, Steffen Müthing (+4 others)
2020 Lecture Notes in Computational Science and Engineering  
choice of the coarse/fine scale and the overlap region as well as the combination of local reduced basis multiscale methods and the multilevel Monte-Carlo algorithm.  ...  Continuous improvement of the underlying hardware-oriented numerical methods have included GPU-based sparse approximate inverses, matrix-free sum-factorisation for high-order discontinuous Galerkin discretisations  ...  Multilevel Monte Carlo (MLMC) algorithms attract great interest due to their superiority over the standard Monte Carlo approach.  ... 
doi:10.1007/978-3-030-47956-5_9 fatcat:iwfk3gsln5endcqe3uq42fzxwa

Ab initio path integral Monte Carlo simulation of the Uniform Electron Gas in the High Energy Density Regime [article]

Tobias Dornheim and Zhandos Moldabekov and Jan Vorberger and Simon Groth
2020 arXiv   pre-print
B 101, 045129 (2020)] conditions based on exact ab initio path integral Monte Carlo (PIMC) simulations.  ...  Recently, highly accurate results for the static density response function and the corresponding local field correction have been provided both for warm dense matter [J. Chem.  ...  TD acknowledges support by the Center for Advanced Systems Understanding (CASUS) which is financed by Germany's Federal Ministry of Education and Research  ... 
arXiv:2003.00858v1 fatcat:2idrnkvwnbbr7b4h67zgnq67su

Subcontinuum mass transport of condensed hydrocarbons in nanoporous media

Kerstin Falk, Benoit Coasne, Roland Pellenq, Franz-Josef Ulm, Lydéric Bocquet
2015 Nature Communications  
We rationalize this non-hydrodynamic behaviour using a molecular description capturing the scaling of permeance with alkane length and density.  ...  The non-Darcy behaviour arises from strong adsorption in kerogen and the breakdown of hydrodynamics at the nanoscale, which contradict the assumption of viscous flow.  ...  Acknowledgements This work has been carried out within the framework of the french 'Investissements d'Avenir' program (projects ICoME2 Labex, ANR-11-LABX-0053 and A*MIDEX projects ANR-11-IDEX-0001-02).  ... 
doi:10.1038/ncomms7949 pmid:25901931 pmcid:PMC4421809 fatcat:brzsyzmsn5dyff77vuxhrw3uya

Characteristics of the new phase in CDT

J. Ambjørn, J. Gizbert-Studnicki, A. Görlich, J. Jurkiewicz, N. Klitgaard, R. Loll
2017 European Physical Journal C: Particles and Fields  
The transition lines separating this phase from the "time-collapsed" B-phase and the de Sitter phase C_dS are of great interest when searching for physical scaling limits.  ...  We investigate the recently discovered bifurcation phase C_b and relate some of its characteristics to the presence of singular vertices of very high order.  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution  ... 
doi:10.1140/epjc/s10052-017-4710-3 pmid:28344506 pmcid:PMC5347531 fatcat:j6yhvs4navbqtkdkumvjdhsgli
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