Pablo graduated with an MSc from the University of Chile in 2020, where he studied the backward heat equation as a method to deblurring images obtained from a Light Sheet Fluorescence Microscope. Also, in the last year, he worked on an image registration problem for cardiovascular magnetic resonance images using Physics-Informed Neural Networks. His interests are inverse problems, PDE’s, deep learning, and applying these topics to medical imaging. Outside of maths, Pablo enjoys playing the piano and playing football.

Research project title:
Solving Dynamics Inverse Problems with Physics-Informed Neural Networks

Supervisor(s):
Matthias Ehrhardt, Lisa Kreusser

Project description:
In inverse problems, image reconstruction from noisy measurements is one of the classical tasks to be solved. Many imaging techniques take measurements throughout the time of some dynamic process and then a sequence of frames needs to be retrieved (such as a heart beating imaged with magnetic resonance). The underlying physical behaviour can be incorporated into the formulation as a regulariser that may endorse the reconstruction of images by modelling an additional variable (a velocity field for instance) satisfying some PDE. The goal of this PhD project is to solve this problem with the so-called Physics-Informed Neural Networks (PINN), a new paradigm introduced in 2019 where a neural network is trained while respecting physical constraints by taking advantage of automatic differentiation.