AMath seminars on Monday and Tuesday

[Randall J LeVeque]

There will be two seminars on Monday morning July 16, by Raymond Chan from Hong Kong and Tan Bui from UT-Austin.

Also on Tuesday morning there will be a brief talk by Donsub Rim.

All are welcome, please see below for more details and let me know if you'd like to meet with any of these visitors or join us for lunch one day.

 - Randy

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Time: 9:30am on Monday, July 16, 2018

Room: Wan Conference Room, Lewis 208

Speaker: Raymond H. Chan, The Chinese University of Hong Kong

Title: Flexible methodology for image segmentation

In this talk, we introduce a SaT (Smoothing and Thresholding) method for multiphase segmentation of images corrupted with different degradations: noise, information loss and blur. At the first stage, a convex variant of the Mumford-Shah model is applied to obtain a smooth image. We show that the model has unique solution under different degradations. In the second stage, we apply clustering and thresholding techniques to find the segmentation. The number of phases is only required in the last stage, so users can modify it without the need of repeating the first stage again. The methodology can be applied to various kind of segmentation problems, including color image segmentation, hyper-spectral image classification, and point cloud segmentation. Experiments demonstrate that our SaT method gives excellent results in terms of segmentation quality and CPU time in comparison with other state-of-the-art methods.

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Time: 10:30am on Monday, July 16, 2018

Room: Wan Conference Room, Lewis 208

Speaker: Tan Bui, University of Texas at Austin

Title: Scalable strategies for large-scale data-driven PDE-constrained Bayesian inverse problems

Abstract: 

Inverse problems and uncertainty quantification (UQ) are pervasive in engineering and science, especially in scientific discovery and decision-making for complex, natural, engineered, and societal systems.  Though the past decades have seen tremendous advances in both theories and computational algorithms for inverse problems, quantifying the uncertainty in their solution remains challenging. In this talk, we present several approaches tackling three main challenges in Bayesian inverse problems: 1) large-scale forward problems, 2) high-dimensional parameter spaces, and 3) big-data issues.

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Time: 11:00 - 11:30am on Tuesday, July 17, 2018

Room: Wan Conference Room, Lewis 208

Speaker: Donsub Rim, Columbia University

Title: Model reduction of Burgers’ equation

Abstract: We present a new numerical technique for reduction of parametrized, time-dependent nonlinear hyperbolic conservation laws in one spatial dimension. It aims to augment existing projection-based model reduction methods, by generating basis functions that are local in time and in parameter. The technique builds on a simple displacement interpolation scheme based on monotone rearrangement, a scheme that arises naturally from the Monge-Kantorovich problem in optimal transport. We will demonstrate that the interpolation scheme is able to generate time-and-parameter-dependent local basis suitable for a benchmark model reduction problem involving the Burgers equation. The local basis captures the behavior of the sharply localized shock-wave, as well as the globally supported source term. A closely related theoretical result will be discussed.