A Study on Physics Informed Neural Networks, with Applications for Compartment Models

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.