[Amath-seminars] AMath seminars on Monday and Tuesday

Randall J LeVeque rjl at uw.edu
Fri Jul 13 17:48:16 PDT 2018

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


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.


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

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.


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
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