Publications related to Prime manifold

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

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 ...

San Diego2024

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

OSLO: On-the-Sphere Learning for Omnidirectional Images and Its Application to 360-Degree Image Compression

Pascal Frossard, Thomas Maugey, Roberto Gerson De Albuquerque Azevedo

State-of-the-art 2D image compression schemes rely on the power of convolutional neural networks (CNNs). Although CNNs offer promising perspectives for 2D image compression, extending such models to omnidirectional images is not straightforward. First, omn ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

How Lagrangian States Evolve Into Random Waves

Alejandro Rivera

In this paper, we consider a compact connected manifold (X, g) of negative curvature, and a family of semi-classical Lagrangian states f(h)(x) = a(x)e(i phi(x)/h) on X. For a wide family of phases phi, we show that f(h), when evolved by the semi-classical ...

ECOLE POLYTECHNIQUE2022

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland

We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...

OXFORD UNIV PRESS2021

Dynamical Reduced Basis Methods for Hamiltonian Systems

Cecilia Pagliantini

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...

2019

Bayesian adaptation of chaos representations using variational inference and sampling on geodesics

Panagiotis Tsilifis

A novel approach is presented for constructing polynomial chaos representations of scalar quantities of interest (QoI) that extends previously developed methods for adaptation in Homogeneous Chaos spaces. In this work, we develop a Bayesian formulation of ...

ROYAL SOC2018

The connectivity at infinity of a manifold and Sobolev inequalities

Marc Troyanov

The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an L-q,L-p-Sobolev inequality (2

Elsevier2014

Learning Smooth Pattern Transformation Manifolds

Pascal Frossard, Elif Vural

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that are ob ...

Institute of Electrical and Electronics Engineers2013

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

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

OSLO: On-the-Sphere Learning for Omnidirectional Images and Its Application to 360-Degree Image Compression

How Lagrangian States Evolve Into Random Waves

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Dynamical Reduced Basis Methods for Hamiltonian Systems

Bayesian adaptation of chaos representations using variational inference and sampling on geodesics

The connectivity at infinity of a manifold and Sobolev inequalities

Learning Smooth Pattern Transformation Manifolds

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

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

Dynamical Reduced Basis Methods for Hamiltonian Systems

OSLO: On-the-Sphere Learning for Omnidirectional Images and Its Application to 360-Degree Image Compression

How Lagrangian States Evolve Into Random Waves

Bayesian adaptation of chaos representations using variational inference and sampling on geodesics

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

The connectivity at infinity of a manifold and Sobolev inequalities

Learning Smooth Pattern Transformation Manifolds