(Machine) Learning the Barrier from the Beam

Description

If you shoot particles at an unknown object and watch where they come out, can you reconstruct the object from how the particles were deflected? This inverse scattering problem appears in medical CT imaging, oil exploration, and quantum scattering experiments, and is notoriously messy to solve by classical methods.

In this project you will tackle various versions of this problem, both in the context of classical physics (where the particle probes obey Newton's laws) and in the context of quantum mechanics (with wavepackets obeying Schrödinger's equation). You will use a modern approach based on machine learning techniques (also known as “physics-informed neural networks”). The idea is simple: parameterise the unknown potential as a small neural network, simulate the physics, and let automatic differentiation tell you how to improve the network until the simulation matches the observed data.

Mode of Operation and Evidence of Learning

During the first few weeks you will mostly learn by reading review papers and articles, and present those insights to the rest of the group. We will then focus mostly on doing hands-on work. You will learn by writing or adapting code in Python, by producing visualisations, and by using these programs and images to study questions about what can be recovered from limited measurements and where the methods (sometimes quietly) fail.

Individual project

In the individual project you will have the opportunity to go into more depth of the mathematical and numerical background, and explore other specific physics problems. This may involve:

• Two-dimensional quantum scattering in a potential.
• Comparison with other, non-machine-learning techniques.
• Applications in fluid flow.
• Other differentiable-physics problems.

Mode of Operation and Evidence of Learning

In the individual project you will be explore and read literature on your chosen sub-topic, and you will write code (or extend code from the group project) to solve concrete problems. You will report on these in your written final report.

Co- and pre-requisites

Taking Quantum Mechanics III at the same time is strongly advised. And even though you will read a lot and will be provided with sample programs, you will mostly learn by doing. You therefore have to have good Python skills. Prior experience with machine learning is not required.

Some background material

• “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations”, M. Raissi, P. Perdikaris and G.E. Karniadaki, Journal of Computational Physics 278 (2019) 686-707.