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

Romor, Francesco; Tezzele, Marco; Rozza, Gianluigi

doi:10.48550/arxiv.2105.06713

Cited by 1 publication

(2 citation statements)

References 3 publications

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“…All the computations regarding AS are done with the open source Python package 1 called ATHENA [28], for the classification algorithms we use the scikit-learn package [5] and for the Gaussian process regression GPy [13].…”

Section: Numerical Resultsmentioning

confidence: 99%

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A local approach to parameter space reduction for regression and classification tasks

Romor¹,

Tezzele²,

Rozza³

2021

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Frequently, the parameter space, chosen for shape design or other applications that involve the definition of a surrogate model, present subdomains where the objective function of interest is highly regular or well behaved. So, it could be approximated more accurately if restricted to those subdomains and studied separately. The drawback of this approach is the possible scarsity of data in some applications, but in those, where a quantity of data, moderately abundant considering the parameter space dimension and the complexity of the objective function, is available, partitioned or local studies are beneficial. In this work we propose a new method called local active subspaces (LAS), which explores the synergies of active subspaces with supervised clustering techniques in order to perform a more efficient dimension reduction in the parameter space for the design of accurate response surfaces. We also developed a procedure to exploit the local active subspace information for classification tasks. Using this technique as a preprocessing step onto the parameter space, or output space in case of vectorial outputs, brings remarkable results for the purpose of surrogate modelling.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Figure 4: R 2 scores comparison between local versions varying the number of clusters for the quartic function in equation(28). Global AS has a score equal to 0.78.…”

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confidence: 99%