| dc.description.abstract | The main goal of this thesis was to investigate the methodology of Physics Informed
Neural Networks (PiNN), as a computational tool leveraging differential equations
as a regularization for a learning task. PiNN is a new field of research and therefore
particular concern was given to the task of obtaining an understanding of the
method, gauging benefits, performance, and appropriateness in relation to established
methods. In order to develop this knowledge, the methodology was implemented
and applied through four case studies, three of which demonstrates achievements
already supported by the literature. In addition case three incorporates a thorough
testing scheme, scoping out PiNNs’ capabilities of parameter discovery and
regularization. From this a larger framework is developed. In case four, the framework
is utilized applying of the method of PiNN in a real world biomedical context,
realized as a model of the circulatory system. The implementations were realized in
a bottom up approach utilizing the neural network capabilities of PyTorch. Overall,
the findings of the thesis support the established findings of previous literature in
regards to performance and capabilities. Additionally, important details in regards
to implementation and solution validity is highlighted, addressing the conditions
necessary for the optimal use of PiNN as a methodology. | |
