‘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

Stanford University Unstructured

I’ve been running some of the test cases with the Stanford University Unstructured (SU2, read “S-U-squared”) code to generate CFD data sets to play with. I also recently used SU2 to produce the function evaluation in a Monte Carlo demo I did recently for ME470: Uncertainty Quantification. It’s a very nice set of codes with good documentation. It’s easy to get running — both on your laptop and your cluster.

Also, it turns out that the Tecplot files produced by SU2 are surprisingly easy to work with in Hadoop. Stay tuned for some BIGDATA computations on CFD flow fields (which I hope to finish in time for SIAM CSE).

Least squares methods for Lorenz trajectories

I’ve been working with Qiqi Wang to implement a continuation method combined with a nonlinear least squares solver to approximate trajectories of the Lorenz equation at different parameter values. I used DOLFIN to build the solver, which interfaces with PETSc’s SNES. Here is a figure of the trajectories as a function of the R parameter. I started with a reference solution at R=30 and used the continuation method with the solver to take R down to 1.

lorenz

Click the figure for higher resolution. Here’s a link to the code. Check out Qiqi’s arXiv paper here.

You know, at some point we’ll update the pictures in the header of this blog. You’d think a blog called “simulation informatics” would have cool pictures.

Matt Knepley is my personal hero

Mathematicians are known to engage in hero worship, and I’m not really an exception.

Matt Knepley is a researcher at Argonne National Labs who works on the award-winning software package PETSc (Portable, Extensible Toolkit for Scientific Computation). It contains a suite of scalable tools for a host of scientific computing problems.

I’ve never met Matt in person, but I suspect that when I do I’ll be a little star struck.