scholarly journals Efficient Greedy Algorithms for High-Dimensional Parameter Spaces with Applications to Empirical Interpolation and Reduced Basis Methods

2011 ◽  
Author(s):  
Jan S. Hesthaven ◽  
Benjamin Stamm ◽  
Shun Zhang
Keyword(s):  
Greedy Algorithms ◽  
High Dimensional ◽  
Reduced Basis ◽  
Dimensional Parameter ◽  
Parameter Spaces ◽  
Reduced Basis Methods

scholarly journals ATHENA: Advanced Techniques for High Dimensional Parameter Spaces to Enhance Numerical Analysis

2021 ◽  
pp. 100133
Author(s):  
Francesco Romor ◽  
Marco Tezzele ◽  
Gianluigi Rozza
Keyword(s):  
Numerical Analysis ◽  
High Dimensional ◽  
Dimensional Parameter ◽  
Parameter Spaces

scholarly journals Convergence Rates for Greedy Algorithms in Reduced Basis Methods

2011 ◽  
Vol 43 (3) ◽  
pp. 1457-1472 ◽  
Author(s):  
Peter Binev ◽  
Albert Cohen ◽  
Wolfgang Dahmen ◽  
Ronald DeVore ◽  
Guergana Petrova ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Greedy Algorithms ◽  
Reduced Basis ◽  
Reduced Basis Methods

scholarly journals Efficient sampling of constrained high-dimensional theoretical spaces with machine learning

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Jacob Hollingsworth ◽  
Michael Ratz ◽  
Philip Tanedo ◽  
Daniel Whiteson
Keyword(s):  
Dimensional Space ◽  
Generative Models ◽  
Boson Mass ◽  
High Dimensional ◽  
Beyond The Standard Model ◽  
Dimensional Parameter ◽  
Parameter Spaces ◽  
Alternative Approach ◽  
The Standard Model ◽  
Standard Models

AbstractModels of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental results project onto a subspace of parameters that are consistent with those observations, but mapping these constraints to the underlying parameters is also typically intractable. Instead, physicists often resort to scanning small subsets of the full parameter space and testing for experimental consistency. We propose an alternative approach that uses generative models to significantly improve the computational efficiency of sampling high-dimensional parameter spaces. To demonstrate this, we sample the constrained and phenomenological Minimal Supersymmetric Standard Models subject to the requirement that the sampled points are consistent with the measured Higgs boson mass. Our method achieves orders of magnitude improvements in sampling efficiency compared to a brute force search.

Pattern selection in high-dimensional parameter spaces

2012 ◽  
Author(s):  
Georg Viehoever ◽  
Brian Ward ◽  
Hans-Juergen Stock
Keyword(s):  
High Dimensional ◽  
Pattern Selection ◽  
Dimensional Parameter ◽  
Parameter Spaces

scholarly journals Efficient characterization of high-dimensional parameter spaces for systems biology

2011 ◽  
Vol 5 (1) ◽  
pp. 142 ◽  
Author(s):  
Elías Zamora-Sillero ◽  
Marc Hafner ◽  
Ariane Ibig ◽  
Joerg Stelling ◽  
Andreas Wagner
Keyword(s):  
Systems Biology ◽  
High Dimensional ◽  
Dimensional Parameter ◽  
Parameter Spaces

scholarly journals Double greedy algorithms: Reduced basis methods for transport dominated problems

2014 ◽  
Vol 48 (3) ◽  
pp. 623-663 ◽  
Author(s):  
Wolfgang Dahmen ◽  
Christian Plesken ◽  
Gerrit Welper
Keyword(s):  
Greedy Algorithms ◽  
Reduced Basis ◽  
Reduced Basis Methods

Preset Based Interaction with High Dimensional Parameter Spaces

2003 ◽  
pp. 391-406 ◽  
Author(s):  
Jarke J. Wijk ◽  
Cornelius W. A. M. Overveld
Keyword(s):  
High Dimensional ◽  
Dimensional Parameter ◽  
Parameter Spaces

scholarly journals Constraining the parameters of high-dimensional models with active learning

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Sascha Caron ◽  
Tom Heskes ◽  
Sydney Otten ◽  
Bob Stienen
Keyword(s):  
Active Learning ◽  
Particle Physics ◽  
High Energy Physics ◽  
High Energy ◽  
Physical Models ◽  
High Dimensional ◽  
Physical Parameters ◽  
Model Parameters ◽  
Dimensional Parameter ◽  
Parameter Spaces

AbstractConstraining the parameters of physical models with $$>5-10$$>5-10 parameters is a widespread problem in fields like particle physics and astronomy. The generation of data to explore this parameter space often requires large amounts of computational resources. The commonly used solution of reducing the number of relevant physical parameters hampers the generality of the results. In this paper we show that this problem can be alleviated by the use of active learning. We illustrate this with examples from high energy physics, a field where simulations are often expensive and parameter spaces are high-dimensional. We show that the active learning techniques query-by-committee and query-by-dropout-committee allow for the identification of model points in interesting regions of high-dimensional parameter spaces (e.g. around decision boundaries). This makes it possible to constrain model parameters more efficiently than is currently done with the most common sampling algorithms and to train better performing machine learning models on the same amount of data. Code implementing the experiments in this paper can be found on GitHub "Image missing"

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