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Graph neural networks : operators and architectures

Grattarola, Daniele ; Alippi, Cesare (Dir.) ; Livi, Lorenzo (Codir.)

Thèse de doctorat : Università della Svizzera italiana, 2021 ; 2021INFO014.

This thesis explores the field of graph neural networks, a class of deep learning models designed to learn representations of graphs. We organise the work into two parts. In the first part, we focus on the essential building blocks of graph neural networks. We present three novel operators for learning graph representations: one graph convolutional layer and two methods for pooling. We put...

Multigrid methods for fractional diffusion equations

Trotti, Ken ; Krause, Rolf (Dir.) ; Donatelli, Marco (Codir.)

Thèse de doctorat : Università della Svizzera italiana, 2021 ; 2021INFO013.

Recent years have seen the rapid growth in interest towards fractional calculus. Fractional calculus plays an important role in modelling anomalous diffusion phenomena, however closed-form analytical solutions of such equations are rarely available, hence numerical estimates are needed. In this thesis we consider various fractional diffusion equations (FDEs), where different fractional ...

Residual-based a posteriori error estimation for contact problems approximated by Nitsche's method

Chouly, Franz ; Fabre, Mathieu ; Hild, Patrick ; Pousin, Jérôme ; Renard, Yves

In: IMA Journal of Numerical Analysis, 2018, vol. 38, no. 2, p. 921-954

Balanced Partitions of Trees and Applications

Feldmann, Andreas ; Foschini, Luca

In: Algorithmica, 2015, vol. 71, no. 2, p. 354-376

Escape of mass and entropy for diagonal flows in real rank one situations

Einsiedler, M. ; Kadyrov, S. ; Pohl, A.

In: Israel Journal of Mathematics, 2015, vol. 210, no. 1, p. 245-295

Dimensional estimates for singular sets in geometric variational problems with free boundaries

De Philippis, Guido ; Maggi, Francesco

In: Journal für die reine und angewandte Mathematik (Crelles Journal), 2017, vol. 2017, no. 725, p. 217-234

Isogeometric rotation-free analysis of planar extensible-elastica for static and dynamic applications

Maurin, Florian ; Dedè, Luca ; Spadoni, Alessandro

In: Nonlinear Dynamics, 2015, vol. 81, no. 1-2, p. 77-96

Finite Higher Spin Transformations from Exponentiation

Monnier, Samuel

In: Communications in Mathematical Physics, 2015, vol. 336, no. 1, p. 1-26

Transfer current and pattern fields in spanning trees

Kassel, Adrien ; Wu, Wei

In: Probability Theory and Related Fields, 2015, vol. 163, no. 1-2, p. 89-121

Orthotropic rotation-free thin shell elements

Munglani, Gautam ; Vetter, Roman ; Wittel, Falk ; Herrmann, Hans

In: Computational Mechanics, 2015, vol. 56, no. 5, p. 785-793