Leon Gerard studied mathematics at the Technical University of Berlin with the focus on probability theory and deep neural networks. In February 2022, he joined the research network Data Science as a PhD candidate. In particular, he is interested in solving high-dimensional partial differential equations with the use of deep neural networks. Currently, Leon is working on the Schrödinger equation from Quantum Mechanics by accelerating the performance of existing methodologies with the contribution of deep neural networks and a transfer learning approach.
Dissertation
Solving the electronic Schrödinger equation using Deep Neural Networks and Transfer Learning
In my thesis, we improved the efficiency and accuracy of a method called Deep Learning-based Variational Monte Carlo (DL-VMC). DL-VMC is a technique for solving the electronic Schrödinger equation, which is a partial differential equation. Having access to solutions of the Schrödinger equations allows, in general, the prediction of any quantum property of any kind of molecule.
What motivated you to pursue a PhD and how did you choose your field of research?
During my master's thesis, I worked on Deep Learning-based methods for topics in mathematics that I greatly enjoyed. Especially the connection between partial differential equations and how Deep Learning can be used to solve them was a topic I wanted to learn more about. Therefore, I decided to pursue a PhD in this direction.
To what extent was it beneficial for your research to be part of our research network Data Science?
My research topic is somehow interdisciplinary, connecting areas such as physics, mathematics, computer science, and chemistry. Having the opportunity to connect to people with different areas of expertise, especially in physics and chemistry, helped us a lot to define better the research questions we wanted to solve.
What was the most significant discovery of your research and how do you think it will impact your field and benefit our society?
Computing solutions to the Schrödinger equation, in principle, allows you to predict any kind of quantum property of any kind of molecule and, with that, the ability to accelerate material design. Unfortunately, solving the Schrödinger equation is computationally challenging. Therefore, we must rely on somewhat efficient but accurate computational methods to approximate the solutions. We improved the efficiency of a recently established method called Deep Learning-based Variational Monte Carlo to accelerate predictions of the so-called ground-state energy, a fundamental quantum property. I believe it is a promising direction, and I am curious how the field will evolve. However, I believe we are still at the beginning and require further improvements to the method to impact fields such as material design.
What were the biggest challenges and how did you maintain your motivation and focus during your studies?
Developing new research ideas that eventually proved successful was the most challenging aspect of my PhD studies. Particularly at the beginning of a project, it is often unclear whether it will work out and how successful it will be. Fortunately, being part of a team with motivated and curiosity-driven individuals made it much easier to stay motivated.
What are your future career plans and how do you see your PhD degree influencing your professional trajectory?
I would like to connect my knowledge in Deep Learning I gained during my PhD studies with topics in drug discovery. Therefore, for the next steps in my career, I want to start researching how AI can help accelerate the drug discovery process.
Please tell us why you stay affiliated to the research network.
I believe the opportunity to connect with experts from different fields is extremely valuable, and therefore, I hope to stay affiliated and closely connected to the research network.
