Topics for master theses
DeepErwin: Solving the Schrödinger Equation
Finding accurate solutions to the Schrödinger equation is of utmost importance for chemistry and materials science, but is notoriously hard due to the high dimensionality and required accuracy.
We have recently developed and improved a method, which finds solutions to the Schrödinger equation using Deep Neural Networks and shown that for small molecules our approach yields more accurate solutions than any other existing method.
We look for motivated students who want to join our team and help improve this exciting new field. Potentials topics could include (but are not limited to):
- Development of new neural network architectures to better approximate solutions to the Schrödinger equation
- Development of novel optimization schemes
- Extension of our approach to other types of materials
- Benchmarking against other high-accuracy methods
Students should have experience with programming (ideally python). A basic understanding of neural networks and physics is helpful but not required.
Contacts (current PhD students):
michael.scherbela@univie.ac.at
leon.gerard@univie.ac.at
Solving high dimensional parabolic PDEs via random feature neural networks
The numerical solution of high dimensional parabolic PDEs is of crucial importance in computational finance and optimal control. Unfortunately, most current algorithms suffer from the curse of dimension, meaning that their computational runtime scales exponentially in the input dimension, rendering them useless in the high dimensional regime. Methods inspired by deep learning have been shown to constitute a promising alternative. We would like to explore the use of random feature neural networks and particularly prove (both mathematically and empirically) that they can break the curse of dimension.
Students should be familiar with stochastic analysis and programming (ideally in python).
Contact: philipp.grohs@univie.ac.at
References:
arxiv.org/abs/2011.04602
arxiv.org/abs/2106.08900