Python Active-subspaces Utility Library

Constantine, Paul G.; Howard, Ryan; Glaws, Andrew; Grey, Zachary; Diaz, Paul; Fletcher, L. R.

doi:10.21105/joss.00079

Cited by 19 publications

(13 citation statements)

References 2 publications

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“…(18), we use a Monte Carlo method as shown in Eq. (19), employing the software in [10]. Since we have only pairs of input/output data we need to approximate the gradients of the total wave resistance with respect to the parameters, that is ∇ µ f .…”

Section: Numerical Resultsmentioning

confidence: 99%

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

Tezzele

Salmoiraghi

Mola

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties. Given the high number of geometric and physical parameters which might affect the total ship drag, the main idea of this work is to employ the active subspaces properties to identify possible lower dimensional structures in the parameter space. Thus, a fully automated procedure has been implemented to produce several small shape perturbations of an original hull CAD geometry, in order to exploit the resulting shapes and to run high fidelity flow simulations with different structural and physical parameters as well, and then collect data for the active subspaces analysis. The free form deformation procedure used to morph the hull shapes, the high fidelity solver based on potential flow theory with fully nonlinear free surface treatment, and the active subspaces analysis tool employed in this work have all been developed and integrated within SISSA mathLab as open source tools. The contribution will also discuss several details of the implementation of such tools, as well as the results of their application to the selected target engineering problem.

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Section: Numerical Resultsmentioning

confidence: 99%

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

Tezzele

Salmoiraghi

Mola

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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“…Here we briefly introduce the active subspaces property for functions not depending on time, for the details and estimates regarding the method we refer to [10]. For the actual computations to find AS we used the open source Python package ATHENA-Advanced Techniques for High dimensional parameter spaces to Enhance Numerical Analysis [2], derived in part from the Python Active subspaces Utility Library [14].…”

Section: Global Sensitivity Analysis Through Active Subspacesmentioning

confidence: 99%

Enhancing CFD predictions in shape design problems by model and parameter space reduction

Tezzele

Demo

Stabile

et al. 2020

Adv. Model. and Simul. in Eng. Sci.

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In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.

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“…The inactive subspace V permits identification of designs which are invariant with regards to the quantity of interest. The task is to find input vectors x with a fixed w but different v, whilst obeying the constraint −1 ≤ x ≤ 1, for which we use a hit-and-run algorithm similar to that implemented in [52]. In Figure 10, this is done for the ridge approximations at the locations labelled a) and b) in Figure 6.…”

Section: Design Space Explorationmentioning

confidence: 99%

Polynomial Ridge Flowfield Estimation

Scillitoe,

Seshadri,

Wong

et al. 2021

Preprint

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Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods, in order to exploit the large volume of data generated by such computations. This paper introduces the idea of using spatially correlated polynomial ridge functions for rapid flowfield estimation. Dimension reducing ridge functions are obtained for numerous points within training flowfields. The functions can then be used to predict flow variables for new, previously unseen, flowfields. Their dimension reducing nature alleviates the problems associated with visualising high dimensional datasets, enabling improved understanding of design spaces and potentially providing valuable physical insights. The proposed framework is computationally efficient; consisting of either readily parallelisable tasks, or linear algebra operations. To further reduce the computational cost, ridge functions need only be computed at only a small number of subsampled locations. The flow physics encoded within covariance matrices obtained from the training flowfields can then be used to predict flow quantities, conditional upon those predicted by the ridge functions at the sampled points. To demonstrate the efficacy of the framework, the incompressible flow around an ensemble of aerofoils is used as a test case. On unseen aerofoils the ridge functions' predictive accuracy is found to be reasonably competitive with a state-of-the-art convolutional neural network (CNN). The local ridge functions can also be reused to obtain surrogate models for integral quantities such a loss coefficient, which is advantageous in situations where long-term storage of the CFD data is problematic. Finally, use of the ridge framework with varying boundary conditions is demonstrated on a three dimensional transonic wing flow.

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Python Active-subspaces Utility Library

Cited by 19 publications

References 2 publications

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems

Enhancing CFD predictions in shape design problems by model and parameter space reduction

Polynomial Ridge Flowfield Estimation

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