Publications related to A Continuized View on Nesterov Acceleration

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

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

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In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Philadelphia2024

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Volkan Cevher, Grigorios Chrysos, Fanghui Liu

Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

2024

Anomalous dissipation and other non-smooth phenomena in fluids

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The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

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We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

New York2024

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

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Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

EPFL2024

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Stefano Alberti, Jean-Philippe Hogge, Joaquim Loizu Cisquella, Jérémy Genoud, Francesco Romano

This paper presents the new 2D electrostatic particle-in-cell code FENNECS de- veloped to study the formation of magnetized non-neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gy- rotron electron gun des ...

2024

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

Lausanne2024

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

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that allows u ...

2024

A Continuized View on Nesterov Acceleration

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

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

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Anomalous dissipation and other non-smooth phenomena in fluids

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

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

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

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

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

Anomalous dissipation and other non-smooth phenomena in fluids

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks