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

We present a distributed active subspace method for training surrogate models of complex physical processes with high-dimensional inputs and function valued outputs. Specifically, we represent the model output with a truncated Karhunen–Loève (KL) expansion, screen the structure of the input space wi...

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Bibliographic Details
Published in:Journal of scientific computing 2020-11, Vol.85 (2), p.36, Article 36
Main Authors: Guy, Hayley, Alexanderian, Alen, Yu, Meilin
Format: Article
Language:English
Subjects:
Algorithms
Computation
Computational Mathematics and Numerical Analysis
Error analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Parameter estimation
Partial differential equations
Permeability
Pressure distribution
Random variables
Subspace methods
Subspaces
Theoretical
Tissues
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Summary:We present a distributed active subspace method for training surrogate models of complex physical processes with high-dimensional inputs and function valued outputs. Specifically, we represent the model output with a truncated Karhunen–Loève (KL) expansion, screen the structure of the input space with respect to each KL mode via the active subspace method, and finally form an overall surrogate model of the output by combining surrogates of individual output KL modes. To ensure scalable computation of the gradients of the output KL modes, needed in active subspace discovery, we rely on adjoint-based gradient computation. The proposed method combines benefits of active subspace methods for input dimension reduction and KL expansions used for spectral representation of the output field. We provide a mathematical framework for the proposed method and conduct an error analysis of the mixed KL active subspace approach. Specifically, we provide an error estimate that quantifies errors due to active subspace projection and truncated KL expansion of the output. We demonstrate the numerical performance of the surrogate modeling approach with an application example from biotransport.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-020-01346-2