Divide and Conquer: An Incremental Sparsity Promoting Compressive Sampling Approach for Polynomial Chaos Expansions

Abstract

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional expansions for a sparser recovery, and shows success when removal of uninfluential parameters that results in a lower coherence for measurement matrix, allows for a higher order and/or sparser expansion to be recovered. The incremental algorithm effectively searches for the sparsest PC approximation, and not only can it decrease the prediction error, it can also reduce the dimensionality of PCE model. Four numerical examples are provided to demonstrate the validity of the proposed approach. The results from these examples show that the incremental algorithm substantially outperforms conventional compressive sampling approaches for PCE, in terms of both solution sparsity and prediction error.

References in corpus (3)

• Sparsity and Incoherence in Compressive Sampling
• Supervised Dictionary Learning
• Compressive Sampling of Polynomial Chaos Expansions: Convergence Analysis and Sampling Strategies

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• Multivariate sensitivity-adaptive polynomial chaos expansion for high-dimensional surrogate modeling and uncertainty quantification
• Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization
• A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness
• A general framework of rotational sparse approximation in uncertainty quantification