Applied/ACMS: Difference between revisions

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|[https://knewhall.web.unc.edu Katie Newhall] (UNC Chapel Hill)
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|Energy landscapes, metastability, and transition paths
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I will provide a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more about this area. The talk will exploit many elementary examples, which are understandable to graduate students and senior undergraduates, to present the ideas of UQ. Topics include characterizing uncertainties using information theory, UQ in linear and nonlinear dynamical systems, UQ via data assimilation, the role of uncertainty in diagnostics, and UQ in advancing efficient modeling. The surprisingly simple examples in each topic explain why and how UQ is essential. Both Matlab and Python codes have been made available for these simple examples.
I will provide a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more about this area. The talk will exploit many elementary examples, which are understandable to graduate students and senior undergraduates, to present the ideas of UQ. Topics include characterizing uncertainties using information theory, UQ in linear and nonlinear dynamical systems, UQ via data assimilation, the role of uncertainty in diagnostics, and UQ in advancing efficient modeling. The surprisingly simple examples in each topic explain why and how UQ is essential. Both Matlab and Python codes have been made available for these simple examples.
'''Katie Newhall (UNC Chapel Hill)'''
Title: Energy landscapes, metastability, and transition paths
The concept of an energy landscape emerged in the 1930’s as a way to calculate chemical reaction rate constants via Henry Eyring’s transition state theory. Its use has expanded since then, remaining central to quantifying metastability (infrequent jumps between deterministically-stable, energy minimizing, states) that arises in noisy systems when the thermal energy is small relative to the energy barrier separating two states. In this talk, I will present extensions of this theory that I have developed and applied to physical and biological systems. The first is an infinite dimensional system for which I prove metastability is present in the absence of an energy barrier; I extend transition state theory to compute mean transition times. In the second, I derive a model for a spatially-extended magnetic system with spatially-correlated noise designed to sample the Gibbs distribution relative to a defined energy functional. In the third, I show a quasi-potential can be found and used to describe metastable transitions between stable clusters in a bead-spring polymer model of chromosome dynamics with additional stochastic binding pushing the system out of equilibrium.


==== Anil Damle (Cornell)====
==== Anil Damle (Cornell)====

Revision as of 14:29, 12 September 2024


Applied and Computational Mathematics Seminar


Fall 2024

Date Speaker Title Host(s)
Sep 13 Nan Chen (UW) Intro. to Uncertainty Quantification (UQ) (tutorial) Spagnolie
Sep 20 Katie Newhall (UNC Chapel Hill) Energy landscapes, metastability, and transition paths Rycroft
Sep 27 Indresan Govender (Mintek / Univ. of KwaZulu-Natal, South Africa) Rycroft
Oct 4* Hongfei Chen (Tulane) Jean-Luc
Oct 11 Colloquium in B239 at 4:00pm Mikaela Iacobelli (ETH/IAS) TBA Li
Oct 18 Colloquium in B239 at 4:00pm Guillaume Bal (U Chicago) TBA Li, Stechmann
Oct 25 Anil Damle (Cornell) Fine-grained Theory and Hybrid Algorithms for Randomized Numerical Linear Algebra Li
Nov 1 Michael Sprague (NREL) TBA Spagnolie
Nov 8 Miranda Holmes-Cerfon (UBC) Stechmann
Nov 15* Yue Sun (UW–Madison) Rycroft
Nov 22 Ondrej Maxian (U Chicago) TBA Ohm & Spagnolie
Nov 29* Thanksgiving
Dec 6 Ido Lavi (Flatiron) TBA Spagnolie

Dates marked with an asterisk correspond to home football games of the UW–Madison Badgers. On these dates it can be difficult to get a hotel room close to campus at short notice.

Abstracts

Nan Chen (UW–Madison)

Title: Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners

I will provide a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more about this area. The talk will exploit many elementary examples, which are understandable to graduate students and senior undergraduates, to present the ideas of UQ. Topics include characterizing uncertainties using information theory, UQ in linear and nonlinear dynamical systems, UQ via data assimilation, the role of uncertainty in diagnostics, and UQ in advancing efficient modeling. The surprisingly simple examples in each topic explain why and how UQ is essential. Both Matlab and Python codes have been made available for these simple examples.

Katie Newhall (UNC Chapel Hill)

Title: Energy landscapes, metastability, and transition paths

The concept of an energy landscape emerged in the 1930’s as a way to calculate chemical reaction rate constants via Henry Eyring’s transition state theory. Its use has expanded since then, remaining central to quantifying metastability (infrequent jumps between deterministically-stable, energy minimizing, states) that arises in noisy systems when the thermal energy is small relative to the energy barrier separating two states. In this talk, I will present extensions of this theory that I have developed and applied to physical and biological systems. The first is an infinite dimensional system for which I prove metastability is present in the absence of an energy barrier; I extend transition state theory to compute mean transition times. In the second, I derive a model for a spatially-extended magnetic system with spatially-correlated noise designed to sample the Gibbs distribution relative to a defined energy functional. In the third, I show a quasi-potential can be found and used to describe metastable transitions between stable clusters in a bead-spring polymer model of chromosome dynamics with additional stochastic binding pushing the system out of equilibrium.

Anil Damle (Cornell)

Title: Fine-grained Theory and Hybrid Algorithms for Randomized Numerical Linear Algebra

Randomized algorithms have gained increased prominence within numerical linear algebra and they play a key role in an ever-expanding range of problems driven by a breadth of scientific applications. In this talk we will explore two aspects of randomized algorithms by (1) providing experiments and accompanying theoretical analysis that demonstrate how their performance depends on matrix structures beyond singular values (such as coherence of singular subspaces), and (2) showing how to leverage those insights to build hybrid algorithms that blend favorable aspects of deterministic and randomized methods. A focus of this talk will be on methods that approximate matrices using subsets of columns. Relevant motivating applications will be discussed and numerical experiments will illuminate directions for further research.

Future semesters

Archived semesters


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