Programme: PhD Student in Machine Learning and Differential Equations, Year Three
Previous education: B.Sc. Mathematics with Computer Science from Technische Universität Darmstadt (Germany) | Exchange Year at Hong Kong University of Science and Technology (HKUST) | M.Sc. Interdisciplinary Mathematics TU Darmstadt
Previous employment: R&D at Dassault Systemes
Favourite places in London: Battersea Park
Imperial and Previous Experience
Why did you choose to study a PhD within the Department of Aeronautics at Imperial?
I completed my master’s thesis on physics-informed neural networks and wanted to pursue a PhD in the intersection of machine learning and differential equations. With a strong background in mathematics, I wanted to focus on engineering problems. I discovered my current position on my supervisor’s website and applied. Initially, a PhD at Imperial College London in Aeronautical Engineering seemed intimidating, but I knew it was an amazing opportunity.
Did you have any work experience prior to your PhD? If so, how did this prepare you for your PhD?
I took an exchange year during my bachelors and studies at the Hong Kong University of Science and Technology, which encouraged me to pursue a PhD in an international environment.
During my master’s program, I worked part-time in R&D at Dassault Systemes. I was tasked with implementing compressed sensing algorithms for electromagnetic simulations. This experience was particularly beneficial in preparing me for my PhD, as the daily work was really similar. In both roles, I was reading papers, implementing different algorithms, and testing various approaches.
Additionally, in my team at Dassault Systemes, everyone had a PhD and had a strong passion for developing innovative solutions. This work experience provided me with a solid understanding of what to expect in a research-focused career and encouraged me to pursue a PhD.
What has been the greatest opportunity you’ve had at Imperial?
Thanks to Imperial’s strong partnerships with the Technical University of Munich (TUM) and the Nanyang Technological University, Singapore (NTU Singapore), I am able to participate in the Global Fellows Programme.
For one week in June 2023, I will work with 40 other doctoral researchers on “Data for Sustainability” in Singapore and I look forward to this amazing opportunity for international collaboration and networking.
Study and Research
Are you able to tell us a little bit about your research?
My research aims to combine machine learning techniques with physical constraints to solve engineering problems based on differential equations. Machine learning is widely used in many applications, but in many engineering problems, there are underlying physics that govern the system. To address this challenge, we develop neural networks with physics constraints, allowing us to capture the underlying physical behaviour in the machine learning models.
Our specific focus is on chaotic systems, and as such turbulent flows. The chaotic nature of many flows makes it very difficult to make accurate predictions of the dynamics over time. To overcome this challenge, we explore temporal patterns using recurrent neural networks, which have been shown to be effective in capturing long-term dependencies in sequential data. Additionally, we seek to improve our understanding of the netowrk’s properties, which will aid in developing more accurate and efficient models that respect governing laws of physics. Ultimately, our goal is to develop models that can accurately reconstruct and predict the dynamics from sensor measurements of chaotic systems, which have important applications in fields such as fluid dynamics and weather forecasting.
What aspects of your PhD have been the most challenging so far?
PhD life is both challenging and rewarding for me. The most challenging part has been the level of independence required. You’re expected to do a lot of self-guided research, which can be tough when you get stuck or can’t figure things out. Sometimes a problem persists for months before you find a solution.
That being said, there’s nothing quite like the feeling of finally solving a tricky problem. When you do make progress, it’s an amazing feeling of accomplishment.
London
What is your favourite thing about studying in London?
London is a beautiful and exciting city with endless options for museums, theatre shows, and events, there’s always something new and interesting to explore. It is also amazing how easy it is to take trips to other cities in the UK such as Cambridge or Brighton. Whatever your interests are, you always have plenty of options.
Have you discovered any hidden campus gems while at Imperial?
In my opinion, Imperial College is located in the most beautiful neighbourhood of London. Whenever I need a break from my work, I like to take a walk to the Albert Memorial. Walking around the college is scenic all year round and immediately boosts my mood.
Words of wisdom
What advice do you have for prospective PhD students?
A PhD is a very individual experience and can vary depending on your research group. A lot of tasks are not straightforward, so make sure that you are in a good environment and passionate about your topic. Try to make friends in your office – it will keep you motivated to come and work even when your research appears tricky.