Publications related to Introduction to optimization on smooth manifolds: first order methods

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

Mesh-based topology, shape and sizing optimization of ribbed plates

In this paper, we present a new parameterization and optimization procedure for minimizing the weight of ribbed plates. The primary goal is to reduce embodied CO2 in concrete floors as part of the effort to diminish the carbon footprint of the construction ...

Springer2024

On the boundedness of n-folds with κ(X) = n - 1

Stefano Filipazzi

In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...

European Mathematical Soc-Ems2024

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Matthieu Wyart, Carolina Brito Carvalho dos Santos

We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in ...

Amer Physical Soc2024

Efficient and insightful descriptors for representing molecular and material space

Alexander Jan Goscinski

Data-driven approaches have been applied to reduce the cost of accurate computational studies on materials, by using only a small number of expensive reference electronic structure calculations for a representative subset of the materials space, and using ...

EPFL2024

Biobased surfactant

Jeremy Luterbacher, Songlan Sun, Stefania Bertella, Anastasiia Komarova

The present invention relates to a compound of the general formula (I), (II) and (III), more specifically of formula (Ia), (Ib), (Ic)wherein R11 and R12 or R21 and R22 or R31 and R32 are both hydrogen or form together with CHR50 a cyclic moiety or one of R ...

2024

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 ...

San Diego2024

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Nicolas Boumal

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Siam Publications2024

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Fabio Zoccolan, Gianluigi Rozza

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

Experimental observation of topological transition in linear and nonlinear parametric oscillators

Romain Christophe Rémy Fleury, Benjamin Apffel

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuo ...

2024

Introduction to optimization on smooth manifolds: first order methods

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Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Mesh-based topology, shape and sizing optimization of ribbed plates

On the boundedness of n-folds with κ(X) = n - 1

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Efficient and insightful descriptors for representing molecular and material space

Biobased surfactant

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

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Experimental observation of topological transition in linear and nonlinear parametric oscillators

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

On the boundedness of n-folds with κ(X) = n - 1

Experimental observation of topological transition in linear and nonlinear parametric oscillators

Mesh-based topology, shape and sizing optimization of ribbed plates

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

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Efficient and insightful descriptors for representing molecular and material space

Biobased surfactant