A near-optimal sampling strategy for sparse recovery of polynomial chaos expansions

Alemazkoor, Negin; Meidani, Hadi

doi:10.1016/j.jcp.2018.05.025

Cited by 24 publications

(27 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…ADM can also be integrated with other optimization methods to solve the compressive sensing problem, e.g., OMP [6], ℓ 1−2 minimization [59], etc. Further, it could be advantageous to integrate our method with sampling strategies (e.g., [3,4]), basis selection method (e.g., [23]), or Bayesian approach (e.g., [25]). The combination of these methods can be especially useful for problems where experiments or simulations are costly and where a good surrogate model of the QoI is needed, e.g., in inverse problems based on a Bayesian framework ( [40,57]).…”

Section: Discussionmentioning

confidence: 99%

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Yang

Tartakovsky

2018

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

Compressive-sensing-based uncertainty quantification methods have become a powerful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic quantity of interest. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensingbased uncertainty quantification method. We demonstrate that the initial guess from SIR is suitable for cases when the available data are limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with SIR. Then it constructs a Hermite polynomial expansion of the reduced model. This method affords the ability to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. The effectiveness of these two methods (Algorithms 4 and 5) are demonstrated using problems with up to 500 random dimensions.

show abstract

Section: Discussionmentioning

confidence: 99%

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Yang

Tartakovsky

2018

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

show abstract

“…Compressive sampling first appeared in the field of signal processing, with the objective of recovering a sparse signal with significantly smaller number of samples compared to that from the conventional Shannon-Nyquist sampling rate [19]. Compressive sampling has been extensively applied in various fields where small sampling rate is desirable [20]- [23]. In [17], motivated by the fact that discrete cosine transformation for connected vehicles data could be (approximately) sparse, compressive sampling was used to perform discrete cosine transformation with a small number of samples, thereby reducing the number of data transmissions.…”

Section: B Compressive Samplingmentioning

confidence: 99%

Efficient Collection of Connected Vehicles Data With Precision Guarantees

Alemazkoor

Meidani

2020

IEEE Trans. Intell. Transport. Syst.

Self Cite

View full text Add to dashboard Cite

Connected vehicles disseminate detailed data, including their position and speed, at a very high frequency. Such data can be used for accurate real-time analysis, prediction and control of transportation systems. The outstanding challenge for such analysis is how to continuously collect and process extremely large volumes of data. To address this challenge, efficient collection of data is critical to prevent overburdening the communication systems and overreaching computational and memory capacity. In this work, we propose an efficient data collection scheme that selects and transmits only a small subset of data to alleviate data transmission burden. As a demonstration, we have used the proposed approach to select data points to be transmitted from 10,000 connected vehicles trips available in the Safety Pilot Model Deployment dataset. The presented results show that collection ratio can be as small as 0.05 depending on the required precision. Moreover, a simulation study was performed to evaluate the travel time estimation accuracy using the proposed data collection approach. Results show that the proposed data collection approach can significantly improve travel time estimation accuracy.

show abstract

“…The coherence-optimal sampling strategy presented in Section 2.3 is known to produce at least as accurate as PC approximations compared to standard Monte Carlo sampling from f (ξ) for both LSA and ℓ 1 -minimization [21,44,53,80,79]. Further, constructing D-optimal designs from a large pool of candidate samples, regardless of how the candidate samples are generated, can improve least squares PC approximation accuracy compared to designs constructed randomly [60,53].…”

Section: Subspace Pursuit With D-coherence-optimal Samplingmentioning

confidence: 99%

Sparse polynomial chaos expansions via compressed sensing and D-optimal design

Diaz

Doostan

Hampton

2018

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this sparsity in order to reduce computational costs. A class of greedy compressed sensing algorithms use least squares minimization to approximate PC coefficients. This least squares problem lends itself to the theory of optimal design of experiments (ODE). Our work focuses on selecting an experimental design that improves the accuracy of sparse PC approximations for a fixed computational budget. We propose DSP, a novel sequential design, greedy algorithm for sparse PC approximation. The algorithm sequentially augments an experimental design according to a set of the basis polynomials deemed important by the magnitude of their coefficients, at each iteration. Our algorithm incorporates topics from ODE to estimate the PC coefficients. A variety of numerical simulations are performed on three physical models and manufactured sparse PC expansions to provide a comparative study between our proposed algorithm and other non-adaptive methods. Further, we examine the importance of sampling by comparing different strategies in terms of their ability to generate a candidate pool from which an optimal experimental design is chosen. It is demonstrated that the most accurate PC coefficient approximations, with the least variability, are produced with our design-adaptive greedy algorithm and the use of a studied importance sampling strategy. We provide theoretical and numerical results which show that using an optimal sampling strategy for the candidate pool is key, both in terms of accuracy in the approximation, but also in terms of constructing an optimal design.

show abstract

A near-optimal sampling strategy for sparse recovery of polynomial chaos expansions

Cited by 24 publications

References 49 publications

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Efficient Collection of Connected Vehicles Data With Precision Guarantees

Sparse polynomial chaos expansions via compressed sensing and D-optimal design

Contact Info

Product

Resources

About