Publications associées à Distance-Based Discretization of Parametric Signal Manifolds

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

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

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

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

Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

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

Floyd's manifold is a conjugation space

Jérôme Scherer

E. E. Floyd showed in 1973 that there exist only two nontrivial cobor-dism classes that contain manifolds with three cells, and that they lie in dimen-sions 10 and 5. We prove that there is an action of the cyclic group C2 on the 10-dimensional Floyd manif ...

Scuola Normale Superiore2023

A structured prediction approach for robot imitation learning

Aude Billard, Iason Batzianoulis, Anqing Duan

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

Sage Publications Ltd2023

Critical Schrodinger Cat Qubit

Vincenzo Savona, Luca Gravina, Fabrizio Minganti

Encoding quantum information onto bosonic systems is a promising route to quantum error correc-tion. In a cat code, this encoding relies on the confinement of the dynamics of the system onto the two-dimensional manifold spanned by Schrodinger cats of oppos ...

AMER PHYSICAL SOC2023

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Berfin Simsek

Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans. The success in practice stems from the ability to successfully train massive neural ...

EPFL2023

Continuous-variable neural network quantum states and the quantum rotor model

Giuseppe Carleo

We initiate the study of neural network quantum state algorithms for analyzing continuous-variable quantum systems in which the quantum degrees of freedom correspond to coordinates on a smooth manifold. A simple family of continuous-variable trial wavefunc ...

SPRINGERNATURE2023

Persistence and the Sheaf-Function Correspondence

Nicolas Michel Berkouk

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold M with the Grothendieck group of constructible sheaves on M. When M is a finite dimensional real vector space, Kashiwara-Schapira have recently in ...

Cambridge Univ Press2023

Stochastic adaptive resampling for the estimation of discrete choice models

Michel Bierlaire, Nicola Marco Ortelli, Matthieu Marie Cochon de Lapparent

In the field of choice modeling, the availability of ever-larger datasets has the potential to significantly expand our understanding of human behavior, but this prospect is limited by the poor scalability of discrete choice models (DCMs): as sample sizes ...

2023

A geometric optimal control approach for imitation and generalization of manipulation skills

Sylvain Calinon, Amirreza Razmjoo Fard, Jie Zhao

Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...

Elsevier2023

Learning and optimization of anticipatory feedback controllers for robot manipulation

Hakan Girgin

Programming intelligent robots requires robust controllers that can achieve desired tasks while adapting to the changes in the task and the environment. In this thesis, we address the challenges in designing such adaptive and anticipatory feedback controll ...

EPFL2023

Finding stationary points on bounded-rank matrices: a geometric hurdle and a smooth remedy

Nicolas Boumal

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...

SPRINGER HEIDELBERG2022

A b-symplectic slice theorem

Anna Kiesenhofer

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...

WILEY2022

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

HIERARCHICAL MARKOV CHAIN MONTE CARLO METHODS FOR BAYESIAN INVERSE PROBLEMS

Juan Pablo Madrigal Cianci

This thesis is devoted to the construction, analysis, and implementation of two types of hierarchical Markov Chain Monte Carlo (MCMC) methods for the solution of large-scale Bayesian Inverse Problems (BIP). The first hierarchical method we present is base ...

EPFL2022