About Paul Constantine

Assistant Professor of Applied Mathematics and Statistics at Colorado School of Mines.

Where’s the love?

Our simulation informatics blog hasn’t received much attention recently. I (Paul) have been getting settled in my new position at Colorado School of Mines—learning how to be a professor. David has been busy with his gig at Purdue and his other blog. We’re also both in talks with the folks at SIAM about writing for their upcoming blog; stay tuned for that.

You can stay up-to-date with our latest musings on computational math by following us on Twitter: @DrPaulynomial and @dgleich, respectively.

Model Reduction with MapReduce-enabled Tall and Skinny Singular Value Decomposition

David and I recently submitted a paper on some work we’ve be churning on for a long long time. I’m pretty excited it’s finally submitted. Here’s a link to the preprint on arXiv:

Model Reduction with MapReduce-enabled Tall and Skinny Singular Value Decomposition

Stay tuned for a “Behind the Research” perspective…

Active subspace methods in theory and practice

Qiqi Wang, Eric Dow, and I just submitted our recent work on active subspace methods including a theoretical framework and connections to kriging response surfaces. 

I’m giving talks at the national labs this week telling people about the work. Here’s the link to the arXiv paper:

Active subspace methods in theory and practice: Applications to kriging surfaces

‘Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example’ by Allmaras, et al

This paper appears in the most recent in issue of SIAM Review, and it is simply fantastic. It is well written and clear, and it judiciously limits the scope to fundamental concepts in statistical inverse problems. I recommend this to anyone interested in such ideas — both students and experienced researchers. In fact, I’m giving a lecture this evening to the UQ class on inverse problems, and I plan to both borrow heavily from its presentation and make it required reading for the class.

Here’s the link.

‘A Taxonomy of Global Optimization Methods Based on Response Surfaces’ by Donald Jones

This paper ‘A Taxonomy of Global Optimization Methods Based on Response Surfaces’ by Donald Jones does a fantastic job of explaining the wide variety of options for response surfaces. It’s written with optimization in mind, but his explanation of the methods is much more general. It’s written clearly, and I strongly recommend it for anyone working with response surfaces.

Here’s a link to the paper.

Stay tuned for some updates from SIAM CSE13 — the conference that quadrupled my TODO list.

Paul’s (oversimplified and biased) response surface decision tree

I just gave a lecture to our UQ class on response surfaces, and I went over the attached slide containing a “decision tree” for choosing a response surface. The purpose for the class was to get the students asking questions about their “uncertain quantity of interest” before blindly applying a method — since I don’t expect them to know the details of all the methods, yet.

I might develop this further with more branches and hyperlinks to relevant research papers. Feel free to leave any comments!

rs-decision-tree