A Distributed Active Subspace Method for Scalable Surrogate Modeling of Function Valued Outputs

Guy, Hayley; Alexanderian, Alen; Yu, Meilin

doi:10.1007/s10915-020-01346-2

J Sci Comput

2020

DOI: 10.1007/s10915-020-01346-2

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A Distributed Active Subspace Method for Scalable Surrogate Modeling of Function Valued Outputs

Hayley Guy

Alen Alexanderian

Meilin Yu

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Cited by 3 publications

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“…That said, recent work has shown that with some modification, the active-subspace method can be extended to vector-valued QoIs. These are based on minimizing an upper bound on the approximation error [39] or modeling the output with a truncated Karhunen--Lo\ève expansion [23]. The constrained ANN and DAS method can handle vector-valued QoI…”

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confidence: 99%

On the Deep Active-Subspace Method

Edeling

2023

SIAM/ASA J. Uncertainty Quantification

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The deep active-subspace method is a neural-network based tool for the propagation of uncertainty through computational models with high-dimensional input spaces. Unlike the original activesubspace method, it does not require access to the gradient of the model. It relies on an orthogonal projection matrix constructed with Gram--Schmidt orthogonalization to reduce the input dimensionality. This matrix is incorporated into a neural network as the weight matrix of the first hidden layer (acting as an orthogonal encoder), and optimized using back propagation to identify the active subspace of the input. We propose several theoretical extensions, starting with a new analytic relation for the derivatives of Gram--Schmidt vectors, which are required for back propagation. We also study the use of vector-valued model outputs, which is difficult in the case of the original active-subspace method. Additionally, we investigate an alternative neural network with an encoder without embedded orthonormality, which shows equally good performance compared to the deep active-subspace method. Two epidemiological models are considered as applications, where one requires supercomputer access to generate the training data.

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confidence: 99%

On the Deep Active-Subspace Method

Edeling

2023

SIAM/ASA J. Uncertainty Quantification

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Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media

2021

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We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-value outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Loéve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs.

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Benchmarking Active Subspace methods of global sensitivity analysis against variance-based Sobol' and Morris methods with established test functions

Sun¹,

Croke²,

Jakeman³

et al. 2022

Environmental Modelling & Software

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A Distributed Active Subspace Method for Scalable Surrogate Modeling of Function Valued Outputs

Cited by 3 publications

References 46 publications

On the Deep Active-Subspace Method

On the Deep Active-Subspace Method

Structure exploiting methods for fast uncertainty quantification in multiphase flow through heterogeneous media

Benchmarking Active Subspace methods of global sensitivity analysis against variance-based Sobol' and Morris methods with established test functions

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