Comparing RSVD and Krylov methods for linear inverse problems

Luiken, Nick; Leeuwen, Tristan van

doi:10.1016/j.cageo.2020.104427

Cited by 3 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This equation can be calculated more efficiently through the Krylov model reduction method introduced in (7). Using (34), we can redefine (29) as follows:…”

Section: A Regularization Parameter For Stabilitymentioning

confidence: 99%

“…In addition, measurement errors should be carefully controlled in VTS because small errors are dramatically am-plified through the inverse problem. To address this issue, many researchers have developed the stabilizers such as the sequential function specification method (SFSM) [9], regularization method (RM) [30], [31], iterative regularization (IR) [32], combined SFSM-RM [33], and randomized singular value decomposition [34]. These methods provide good stabilization performance, but those may require additional computational burden at every time step to reduce the ill-conditioning of the gain coefficient matrix.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Virtual Thermal Sensor for Real-Time Monitoring of Electronic Packages in a Totally Enclosed System

Ahn

Kim

et al. 2022

IEEE Access

View full text Add to dashboard Cite

A monitoring system is essential for controlling temperatures under safe levels of operation. It is often challenging to attach temperature sensors directly to drive chips owing to the operating environment or geometric challenges. Based on this motivation, we present a model-based virtual thermal sensing technique for the real-time temperature monitoring of the electronics package. A few real sensors located far from the target position are utilized in this virtual sensing system. These are then connected to a well-tuned finite element model for data augmentation utilizing an inverse heat conduction framework. Therefore, the virtual sensor allows us to estimate the temperature without the aid of a sensor installed inside. However, this technique has a stability issue because it is classified into an inverse problem (i.e., an ill-posed problem). We propose a Tikhonov regularization method to address this challenge, including an efficient ridge estimator. The ridge estimator is used to select an optimal regularization parameter so that we can obtain the stable and reliable inverse solution. Since conventional ridge estimators rely on total transient errors, they require a significant computation. The proposed estimator is based on the bias and variance errors, not the total errors, which allow us to efficiently find the optimal parameter. In this paper, the thermal model is modeled using the finite element method, and the Krylov subspace-based model order reduction is employed to reduce the computational burden. Finally, the proposed virtual thermal sensor was experimentally validated utilizing a sealed cylindrical structure in which the commercial servo drive operated.INDEX TERMS Electronic packages, finite element method, inverse heat conduction problem, ridge estimator, Tikhonov regularization, virtual thermal sensor.

show abstract

“…This equation can be calculated more efficiently through the Krylov model reduction method introduced in (7). Using (34), we can redefine (29) as follows:…”

Section: A Regularization Parameter For Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Virtual Thermal Sensor for Real-Time Monitoring of Electronic Packages in a Totally Enclosed System

Ahn

Kim

et al. 2022

IEEE Access

View full text Add to dashboard Cite

show abstract

“…Furthermore, in recent years, various methods have aimed to reduce computational costs, e.g. through trace estimation and other randomized linear algebra approaches [60]. However, for many large-scale problems, the burden of computing a suitable regularization parameter λ still remains.…”

Section: Standard Tikhonov Regularizationmentioning

confidence: 99%

Learning regularization parameters of inverse problems via deep neural networks

Afkham¹,

Chung²,

Chung³

2021

Inverse Problems

View full text Add to dashboard Cite

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the mapping from observation data to regularization parameters. Once the network is trained, regularization parameters for newly obtained data are computed by efficient forward propagation of the DNN. We show that a wide variety of regularization functionals, forward models, and noise models may be considered. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. We emphasize that the key advantage of using DNNs for learning regularization parameters, compared to previous works on learning via bilevel optimization or empirical Bayes risk minimization, is greater generalizability. That is, rather than computing one set of parameters that is optimal with respect to one particular design objective, DNN-computed regularization parameters are tailored to the specific features or properties of the newly observed data. Thus, our approach may better handle cases where the observation is not a close representation of the training set. Furthermore, we avoid the need for expensive and challenging bilevel optimization methods as utilized in other existing training approaches. Numerical results demonstrate that trained DNNs can predict regularization parameters faster and better than existing methods, hence resulting in more accurate solutions to inverse problems.

show abstract

A fast methodology for large-scale focusing inversion of gravity and magnetic data using the structured model matrix and the 2-D fast Fourier transform

Renaut

Hogue

Vatankhah

et al. 2020

Geophysical Journal International

View full text Add to dashboard Cite

Summary We discuss the focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid. For the uniform grid, the model sensitivity matrices have a block Toeplitz Toeplitz block structure for each block of columns related to a fixed depth layer of the subsurface. Then, all forward operations with the sensitivity matrix, or its transpose, are performed using the two dimensional fast Fourier transform. Simulations are provided to show that the implementation of the focusing inversion algorithm using the fast Fourier transform is efficient, and that the algorithm can be realized on standard desktop computers with sufficient memory for storage of volumes up to size n ≈ 106. The linear systems of equations arising in the focusing inversion algorithm are solved using either Golub-Kahan bidiagonalization or randomized singular value decomposition algorithms. These two algorithms are contrasted for their efficiency when used to solve large-scale problems with respect to the sizes of the projected subspaces adopted for the solutions of the linear systems. The results confirm earlier studies that the randomized algorithms are to be preferred for the inversion of gravity data, and for data sets of size m it is sufficient to use projected spaces of size approximately m/8. For the inversion of magnetic data sets, we show that it is more efficient to use the Golub-Kahan bidiagonalization, and that it is again sufficient to use projected spaces of size approximately m/8. Simulations support the presented conclusions and are verified for the inversion of a magnetic data set obtained over the Wuskwatim Lake region in Manitoba, Canada.

show abstract

Comparing RSVD and Krylov methods for linear inverse problems

Cited by 3 publications

References 39 publications

Virtual Thermal Sensor for Real-Time Monitoring of Electronic Packages in a Totally Enclosed System

Virtual Thermal Sensor for Real-Time Monitoring of Electronic Packages in a Totally Enclosed System

Learning regularization parameters of inverse problems via deep neural networks

A fast methodology for large-scale focusing inversion of gravity and magnetic data using the structured model matrix and the 2-D fast Fourier transform

Contact Info

Product

Resources

About