University of Twente Student Theses


PDE Based Neural Networks for Arterial Hemodynamics Estimation

Werven, Jente van (2023) PDE Based Neural Networks for Arterial Hemodynamics Estimation.

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Abstract:Learning on manifolds is an important and difficult task within deep learning. In order to learn on a manifold, it is necessary to first discretize it. Many graph and mesh based techniques overfit to the particular discretization of the discrete representation of the manifold. DiffusionNet [35] shows multiple contemporary networks suffer from sensitivity to discretization, and proposes spatial diffusion to define feature communication on the manifold. This makes their network less sensitive to mesh discretization. However, diffusion acts as a spectral low-pass filter, removing detail from the signal. Additionally, diffusion encourages local feature sharing but does not offer support for long-distance feature sharing beyond diffusing the signal to a global mean. We investigate the use of the hyperbolic wave equation to replace the diffusion dynamics in DiffusionNet. We evaluate our method by learning biomedical signals dependent on local and global manifold structure. We utilize a spectral kernel to evolve our network layers via the wave equation, and show this kernel drops less high frequency coefficients from the signal than diffusion. Finally, we derive several network architectures based on DiffusionNet using the spectral wave kernel, and show they are outperformed by DiffusionNet.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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