To celebrate one of the most prolific mathematicians, I give you today’s Google doodle:
Also, a recent paper in SIREV provides perspective on the scale of computations we can do today:
From Euler, Ritz, and Galerkin to Modern Computing
Thanks to Peter Bradshaw for reminding me about Euler’s birthday!
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
SIAM Releases First Issue of JUQ
SIAM just released the first issue of its new journal — joint with ASA — on uncertainty quantification. Some great papers in the first issue!
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.
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.
These figures will be part of my talk at our minisymposium “Is MapReduce good for science and simulation data?” at SIAM CSE next week. Special thanks goes Trent Lukaczyk, Francisco Palacios, and Prof. Juan Alonso in Stanford’s Aerospace Design Laboratory for the data for the computations, and to Austin Benson for his TS-SVD codes.
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!