Week 3

This week went by fast, and our group has been making steady progress. On Monday, we started working on revising our code to solve the multifidelity inverse problem with the Sea Surface Temperature (SST) dataset. We ran the code and plotted the results with cheap sensors and expensive sensors. The reconstruction plot of the posterior mean wasn't too bad with a relative error of about 11%. However, the standard deviation plot was a little off because we expected lower uncertainty near the expensive sensors since they collected better information with less noisy measurements, but the plot didn't reflect this. So, this coming week we will explore this further and start to work more with the multifidelty. We also had to submit an introduction that could go into a paper for one of our seminar workshops on Wednesday. So of course we wrote it the day before. It was a little hard writing a cohesive paper with three different people, but I think we did pretty well for our first draft. I'm also learning to write more in latex since most of the writing we do is math. On Wednesday, we had to read the other group's introductions and give feedback. It was a good exercise, and now we have to write a methods section for next week. This week we also spent a good chunk of our time writing proofs. I have only taken an introductory proofs class, so I will admit, I did not know how to start these proofs, but as my group explained it and we worked it out together, I felt better. This REU is definitely pushing my limits on what I know, but I've always loved a challenge - and I'm quickly learning that is what research is all about. Some of the proofs we did involved proving that the log-determinant of the posterior covariance is greater than or equal to 0, deriving the D-optimality function for the single and multifidelity cases, and proving an objective function does not decrease when an additional column to the selection matrix (i.e. adding an additional sensor) is added. There is a lot of notation involved and I'm also learning what these symbols are called, but I've been learning a lot of new things these first few weeks. On the left here, I've included one of the proofs we wrote.

One of the proofs we did on the board!

On Friday, we had to give another presentation about our progress, so we also worked on creating a slideshow the whole week. We presented our results and plots with the SST data and the new dataset that I mentioned last week (Cylinder Flow With Von Karman Vortex Street Data). I presented the slides on this new dataset, and I think we did pretty well. The presentations from the other groups were also good and we're all making good progress! Presentations this week, however, took a little longer (I think we all went over the 15 minute limit), so Mette (who is the program director) told all of us to cut it down for next time. After presentations, we had our weekly coffee/tea time and then we headed to the Howling Cow Ice Cream Center! This week, it was my group's turn to pick the Friday social activity, so we went with ice cream. There were cows, an optional 1 mile hike, and ice cream, but we didn't do the hike because it started raining in the afternoon. I got the famous Wolf Tracks ice cream flavor, and it was delicious. Unfortunately, I did not take any pictures, but we did see lots of cows. After that, we all went back to our apartments and then met up again for movie night. This week we decided to watch Friday the 13th since it was indeed Friday the 13th. I've actually never watched the movie before, but I enjoyed it. Since it's an older movie, the animations or special effects are always fun to watch. On Saturday, two of my group mates and I decided to hit the bookstore to buy some NC State merch. After that, we went for some Mediterranean food for lunch and picked up some groceries from Food Lion on the way back. At night, we all gathered to celebrate two birthdays, and we had a cake and music and it was a fun time. That's it for this week, I'll see you next time!

Gaby