Computing Reduced Order Models via Inner-Outer Krylov Recycling in Diffuse Optical Tomography

@article{OConnell2017ComputingRO,
title={Computing Reduced Order Models via Inner-Outer Krylov Recycling in Diffuse Optical Tomography},
author={Meghan O'Connell and Misha Elena Kilmer and Eric de Sturler and Serkan Gugercin},
journal={SIAM J. Sci. Comput.},
year={2017},
volume={39}
}
In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of the optimization process. In the context of absorption imaging in diffuse optical tomography, one approach to addressing this bottleneck proposed recently (de Sturler, et al, 2015) reformulates the viewing of the forward problem as a differential algebraic…
Randomization for the Efficient Computation of Parametric Reduced Order Models for Inversion
• Computer Science, Mathematics
ArXiv
• 2020
This work focuses on diffuse optical tomography in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical (forward) model, and proposes to use randomization to approximate this basis with a drastically reduced number of large linear solves.
A multiscale method for model order reduction in PDE parameter estimation
• Computer Science, Mathematics
J. Comput. Appl. Math.
• 2019
This work presents a computationally tractable way of explicitly differentiating the MOR solution that acknowledges the change of basis and leads to computational savings for large-scale parameter estimation problems where iterative PDE solvers are necessary and offers potential for additional speed-ups through parallel implementation.
Robust Parameter Inversion using Adaptive Reduced Order Models
• Computer Science, Mathematics
ArXiv
• 2020
This paper proposes a method to update the model reduction basis that reduces the number of large linear solves required by 46%-98% compared with the fixed reduced-order model and demonstrates that this leads to a highly efficient and robust inversion method.
ℋ2-Optimal Model Reduction Using Projected Nonlinear Least Squares
• Computer Science, Mathematics
SIAM J. Sci. Comput.
• 2020
This application of projected nonlinear least squares to the $\mathcal{H}_2$-optimal model reduction problem suggests extensions of this approach related model reduction problems.
Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces
• Computer Science, Mathematics
Multiscale Model. Simul.
• 2018
The preconditioned RKS algorithm is proposed, which results in a reduction of the frequency sampling well below the Nyquist-Shannon rate, a weak dependence of the RKS size on the number of inputs and outputs for multiple-input/multiple-output (MIMO) problems, and a significant coarsening of the finite-difference grid used to generate the R KS.
Iterative methods for solving linear systems on massively parallel architectures
This thesis proposes a cheap procedure to adapt the initial guess that permits to reduce the overall number of iterations in such situations as well as investigating the usage of so-called recycling strategies in this context.
Finite element model updating for structural applications
• Computer Science, Mathematics
J. Comput. Appl. Math.
• 2020
It is shown that, by slightly modifying the projection scheme used to compute the eigenvalues at the lowest end of the spectrum one can obtain local parametric reduced order models that, embedded in a trust-region scheme, are the basis of a reliable and efficient specialized algorithm.
How to optimize preconditioners for the conjugate gradient method: a stochastic approach
• Mathematics
• 2018
The conjugate gradient method (CG) is usually used with a preconditioner which improves efficiency and robustness of the method. Many preconditioners include parameters and a proper choice of a

References

SHOWING 1-10 OF 48 REFERENCES
Recycling Subspace Information for Diffuse Optical Tomography
• Mathematics, Computer Science
SIAM J. Sci. Comput.
• 2006
This work derives strategies for recycling Krylov subspace information that exploit properties of the application and the nonlinear optimization algorithm to significantly reduce the total number of iterations over all linear systems.
Nonlinear Parametric Inversion Using Interpolatory Model Reduction
• Mathematics, Computer Science
SIAM J. Sci. Comput.
• 2015
This paper shows how interpolatory parametric model reduction can significantly reduce the cost of the inversion process in DOT by drastically reducing the computational cost of solving the forward problems.
A Regularized Gauss-Newton Trust Region Approach to Imaging in Diffuse Optical Tomography
• Mathematics, Computer Science
SIAM J. Sci. Comput.
• 2011
The algorithm aims to minimize the total number of function and Jacobian evaluations by analyzing which spectral components of the Gauss-Newton direction should be discarded or damped, and proves that the algorithm is globally convergent to a critical point.
Domain decomposition and balanced truncation model reduction for shape optimization of the Stokes system
• Mathematics, Computer Science
Optim. Methods Softw.
• 2011
This paper will be concerned with the optimal design of capillary barriers as part of a network of microchannels and reservoirs on microfluidic biochips that are used in clinical diagnostics, pharmacology, and forensics for high-throughput screening and hybridization in genomics and protein profiling in proteomics.
Fast Algorithms for Hyperspectral Diffuse Optical Tomography
• Mathematics, Computer Science
SIAM J. Sci. Comput.
• 2015
A novel recycling-based Krylov subspace approach that leverages certain system similarities across wavelengths and develops a fast algorithm for compressing the Born operator that locally compresses across wavelengths for a given source-detector set and then recursively combines the low-rank factors to provide a global low- rank approximation.
A Reduced Basis Landweber method for nonlinear inverse problems
• Mathematics
• 2015
We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative
Large-scale topology optimization using preconditioned Krylov subspace methods with recycling
• Mathematics
• 2007
SUMMARY The computational bottleneck of topology optimization is the solution of a large number of linear systems arising in the finite element analysis. We propose fast iterative solvers for large
Parametric model order reduction accelerated by subspace recycling
• Mathematics, Computer Science
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference
• 2009
A fast recycling algorithm is applied to solve the whole sequence of linear systems and is shown to be much more efficient than the standard iterative solver GMRES as well as the newly proposed recycling method MKR-GMRES from [10].
Recycling Krylov subspaces for efficient large-scale electrical impedance tomography
• Mathematics
• 2010
Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the
A Flexible Krylov Solver for Shifted Systems with Application to Oscillatory Hydraulic Tomography
• Mathematics, Computer Science
SIAM J. Sci. Comput.
• 2013
The reconstruction of hydrogeological parameters such as hydraulic conductivity and specific storage using limited discrete measurements of pressure (head) obtained from sequential oscillatory pumping tests, leads to a nonlinear inverse problem.