Week 2 - American Museums, Trump Hotels and Reservoirs

Now that my third week here in the Maryland is almost over, I ought really to be embarrassed about the lateness of posting about my second week, but instead, I will be shamelessly unapologetic. I am going to be following up with another blogpost soon about my third week here. I was set back by accidentally deleting all my previous work, which led in part to this post to being delayed.

My workweek wasn't to eventful, although I would like to note that I have discovered the beautiful pool here. At the recreation center they have both a 25m and 50m pool. The 50m pool is not only enormous in length, but also so deep, that I am worried of being gobbled up by a shark from the depths, sharing the fate of a poor seal in one of David Attenborough's documentaries.

Visit to DC
Saturday was my 20th Birthday. During the day I went in to Washington DC to visit the museum of American history. I was impressed by their exhibition on the internment of Japanese-Americans in camps in the western USA during the Second World War. Basically, all Japanese in the West, including citizens, were put into prison camps, because they were mistrusted, in total disregard of their rights!

Flowers from the exhibition

On the way back we stumbled on a familiar and nowadays quite notable hotel... Looking at it you could really see that the owner must be an educated man with a refined taste..!

My Alaskan flatmates John and Josh

We also passed the National Gallery sculpture garden, with a cooling fountain and interesting sculptures.

My all time favourite sculpture which tricked you to think it was a 3D house from all angles!

A different take on Rodin's The Thinker

Upon arriving back home I found a package awaiting me. It was the kind of package that every person in the world dreams of getting when they arrive home, and I was the lucky man that day. It contained a birthday cake from Timea! Which leads me straight onto the topic of my birthday.

The mysterious package

Birthday
That evening we celebrated my birthday with people from the TREND program and my flatmates. It was good fun. Being my third 20th birthday party in a third country I thought it was a fitting end to the festivities. On top of this, I have received many lovely cards. I now have a stunning collection plastering my desk!

Moments before digging into the cake

I got two 60th birthday cards!

Reservoir Computing
Up until now I had been working on a thing called reservoir computing. I have now changed my topic to Dynamical Systems, more on that later. I want to try to explain this technology anyway. It is really amazing. One of the postgraduate students here, Jaideep Pathak, someone who I have worked with, has written a very interesting and readable paper on the subject.

From Lu, Pathak et al. (2017)

Let me give an example of a problem that it can solve and how a reservoir computer solves this. The double pendulum is a very chaotic, unpredictable, crazy system. Say I were to give you the angle at every moment in time of this system and asked 'can you give me the positions of every part of this pendulum at every time, using just this one value?'. This is possible with a good dosis of Maths and Physics knowledge, plus a computer.

A reservoir however can solve this problem without knowing anything about the system. The 'nodes' in the reservoir have values and at each time step they receive a new input from our input value and simultaneously affect each others values in a randomly preset way. So far this network is just a jumble of values, continuously shifting around, and it is not useful in anyway. The magic comes in the output layer: over a certain amount of time we measure the values that we want our network to predict. We then determine the optimal way of adding together the values of the nodes at each moment in time, to approximate the output as closely as possible. We can then continue to apply this trick for times where we do not know the output. It turns out that this works very well. Look at the image below, where a reservoir can predict the y and z values of a chaotic Lorenz system using just the x value.

From Lu, Pathak et al. (2017)

This is quite amazing and the reservoirs perform very well. The question is if they can now be applied to other deterministic, yet hard to predict systems, such as the weather. Both the weather and the Lorenz system display the so-called 'butterfly effect', where a small initial difference can totally change the future. That is why there is the hope that this can be applied to such tricky to solve systems!