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Speaker:   Youzuo Lin
Los Alamos National Laboratories
Title: Large-Scale Inverse Model Analyses Employing Randomization-based Data Reduction and Krylov Subspace Recycling Techniques
Time / Date: 4-5 PM Monday, November 28
Location: Blocker 220
Abstract: Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a couple of new computational techniques for solving inverse modeling problems with large number of observations and highly parameterized model space. To solve the problem of high computational cost because of large number of observations, we employ a randomized numerical linear algebra technique to effectively reduce the dimension of the observations without losing the information needed for the inverse analysis. To further tackle the issue of computational cost because of the highly parameterized model space, we develop a novel Levenberg-Marquardt method using Krylov subspace recycling technique. The Levenberg-Marquardt method requires the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear system down to a Krylov subspace, such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply our new inverse modeling methods to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework. By comparing with Levenberg-Marquardt method using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10^1 to ~10^2 in a multi-core computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.
Location: Blocker 506A
Time / Date: 1-4 PM, November 26th
firstname.lastname@example.org. The deadline for applications is Feb. 1, 2016.