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From low-rank retractions to dynamical low-rank approximation and back

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Springer2024

Aggregating Spatial and Photometric Context for Photometric Stereo

David Honzátko

Photometric stereo, a computer vision technique for estimating the 3D shape of objects through images captured under varying illumination conditions, has been a topic of research for nearly four decades. In its general formulation, photometric stereo is an ...

EPFL2024

Fast and Future: Towards Efficient Forecasting in Video Semantic Segmentation

Evann Pierre Guy Courdier

Deep learning has revolutionized the field of computer vision, a success largely attributable to the growing size of models, datasets, and computational power. Simultaneously, a critical pain point arises as several computer vision applications are deploye ...

EPFL2024

Modular segmentation, spatial analysis and visualization of volume electron microscopy datasets

Martin Weigert

Volume electron microscopy is the method of choice for the in situ interrogation of cellular ultrastructure at the nanometer scale, and with the increase in large raw image datasets generated, improving computational strategies for image segmentation and s ...

Nature Portfolio2024

Incorporating Projective Geometry into Deep Learning

Michal Jan Tyszkiewicz

In this thesis we explore the applications of projective geometry, a mathematical theory of the relation between 3D scenes and their 2D images, in modern learning-based computer vision systems. This is an interesting research question which contradicts the ...

EPFL2024

Into the ice: Exploration and data capturing in glacial moulins by a tethered robot

Josephine Anna Eleanor Hughes, Max Mirko Polzin

Glacial moulins (cylindrical meltwater drainage shafts) provide valuable insights into glacier dynamics, but are inaccessible and hazardous environments for humans to study. Exploring them using passive sensor probes has revealed their complex geometry, wh ...

Wiley2024

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Nature Portfolio2024

Hausdorff dimension of fermions on a random lattice

Mattia Guerino Varrone

Geometric properties of lattice quantum gravity in two dimensions are studied numerically via Monte Carlo on Euclidean Dynamical Triangulations. A new computational method is proposed to simulate gravity coupled with fermions, which allows the study of int ...

Elsevier2024

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Jan Sickmann Hesthaven, Federico Pichi

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

Academic Press Inc Elsevier Science2024

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

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