The Snowbird meeting finishes today. I think it has been highly successful with over 800 participants. Last night, I was on the “forward looking panel” moderated by Alan Champneys and one of the questions asked was what defines nonlinear dynamics and this meeting. I gave a rather flip answer about how we are now in the age of machine learning and statistics and this meeting is everything in applied math that is not that. Of course that is not true given that data assimilation was a major part of this meeting and Sara Solla gave a brilliant talk on applying the generalized linear model to neural data to estimate functional connectivity in the underlying cortical circuit.
Given some time to reflect on that question, I think the common theme of Snowbird is the concept of taking a complicated system and reducing it to something simpler that can be analyzed. What we do is to create nontrivial models that can be accessed mathematically. This is distinctly different from other branches of applied math like optimization and numerical methods. However, one difference between previous meetings and now is that before the main tools to analyze these reduced systems were methods of dynamical systems such as geometric singular perturbation theory (e.g. see here) and bifurcation theory. Today, a much wider range of methods are being utilized.
Another question posed was whether there was too much biology at this meeting. I said yes because I thought there were too many parallel sessions. Although, I said it partially with tongue in cheek, I think there are both good and bad things about biology being overly represented. It is good that biology is doing well and attracting lots of people but it would be a bad thing if the meeting becomes so large that it devolves into multiple concurrent meetings where people only go to the talks that are directly related to what they already know. In a meeting with fewer parallel sessions one has more chance to learn something new and see something unexpected. I really have no idea what should be done about this if anything at all.
Finally, a question about how data will be relevant to our field was posed from the audience. My answer was that the big trend right now was in massive data mining but I thought that it had overpromised and would eventually fail to deliver. Eventually, dynamical systems methods will be required to help reduce and analyze the data. However, I do want to add that data will play a bigger and bigger role in dynamical systems research. In the past, we mostly strived to just qualitatively match experiments but now the data has improved to the point that we can try to quantitatively match it. This will require using statistics. Readers of this blog will know that I have been an advocate of using Bayesian methods. I really believe that the marriage of dynamical systems and statistics will have great impact. Statistics is about fitting models to data but the models used are rather simple and generally not motivated by mechanisms. Our field is about producing models based on the underlying mechanisms. It will be a perfect fit.