Solving Partial Differential Equations using Physics-Informed Neural Networks

In an attempt to find alternatives for solving partial differential equations (PDEs)<br/>with traditional numerical methods, a new field has emerged which incorporates<br/>the residual of a PDE into the loss function of an Artificial Neural Network. This<br/>method is called Physics-Informed Neural Network (PINN). In this thesis, we study dense...

Quantitative characteristics of brain lesions: a data visualization tool

One of the principal signs of disease progression in brain tumor patients is an increase in tumor size between time-separated medical image acquisitions. The current diagnosis of tumor progression is based on visual appraisal or manual measurement of largest diameters, neither of which is a fully quantitative measure. The RANO criteria dictate...

PINN inspired Freeform Design: Using Fraunhofer Diffraction to find Freeforms described by B-spline Surfaces

This project aims to recreate intensity patterns using Fraunhofer diffraction as a means of simulation. These intensity patterns are created by phase shifting specific parts of an incoming field of light. These phase shifts are determined by a B-spline surface, which is in turn controlled by so-called control points. Only a handful of control...

Evaluating the Robustness of the Recurrent Inference Machine Based on MRI Lesion Data from Multiple Sclerosis Patients

The Recurrent Inference Machine (RIM) has been developed as an alternative to the clinically used Compressed Sensing (CS) algorithm, using Deep Learning (DL). A common issue with DL networks is the generalization of the network to features that have not been trained for. In this study we evaluate the robustness of the RIM to white matter lesions...