Summer Research Series: Karlo Pohjanen, BSc in Mathematical Sciences

Course: Mathematical Sciences
Supervisor: Kevin Moroney
Name of Research Project/Activity: Exploration of Physics-Informed Neural Networks for approximating solutions of differential equations

Q) Can you tell me a bit about yourself and why you decided to study the course you are taking at UL?

In secondary school I always enjoyed scientific subjects the most, and while maths was always my strongest subject it wasn’t something that I felt an overwhelming desire to specialise in. When I was applying for a course on the CAO, I was unsure of what to choose until I realised that studying mathematics would allow me to enter a wide variety of scientific fields through an interdisciplinary approach. I chose UL’s maths course because of its strong focus on applied math and its co-op system.

Q) What motivated you to apply for the Summer Bursary Programme?

I wanted to gain some insight into what doing research was like, to help clarify my goals for after my bachelor’s degree. It also seemed like a much more enjoyable and interesting way to spend the summer than doing menial work full-time.

Q) What are you doing as part of your research here at UL?

My project involves exploring the use of physics informed neural networks to predict the motion of a pendulum. A neural network is a machine learning algorithm loosely inspired by networks of biological networks in the brain. They have a wide variety of uses, including approximating solutions of differential equations. The drawback of these networks is how data dependent they are to achieve good results, and how poorly they can predict solutions outside the domain of the original solutions from the data. The “physics informed” concept helps mitigate this drawback if known differential equations are governing the process being modelled. 
Specifically, my project involved building and comparing models in MATLAB to find the best way to use neural networks to quickly and accurately predict a pendulums motion, given data of various quality and quantity. Initially these models were built assuming the complete differential equation was known, but eventually I moved on to “inverse problems” where at least one parameter of the differential equation was unknown, and had to be learned by combining the incomplete equation with known data. Currently, in the final stages of my project I am working on applying what I’ve learned in this problem to modelling a predator prey system, predicting how to populations of a predator and prey species vary based on the population of one another.

Q) what skills have you developed over the summer?

As my project is being entirely done in MATLAB, I built up my comfort using and knowledge of the software greatly, specifically with the use of machine learning related techniques. The most critical skill that I had to develop was parsing information and learning from dense research papers. The study of PINNs is fairly nascent, with the research paper introducing and formalising the concept being published in 2017. The amount of basic, user friendly information on them that is intended for students to learn from is far sparser than the mathematical concepts I’ve learned about for my course.

Q) What has this experience taught you and what would you recommend it to others?

I feel like my experience with the summer research has taught me a lot about the gist of doing largely independent research in the maths department. It’s the kind of experience that can’t be gained solely engaging with college in the semester, and even something generally not offered through other summer internship programs. 
I would definitely recommend it to any student considering research as a potential career path, or simply curious about matters outside the scope of their course.

Q) What are your future career plans, would you consider a career in research?

I am strongly considering a career in research and as such I appreciate the clarity which this experience provided as to what a career in research would entail day to day.
 

Find out more about the BSc in Mathematical Sciences: Mathematical Sciences - BSc | University of Limerick