Publications related to Compact convergence

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

Residual-based attention in physics-informed neural networks

Nikolaos Stergiopoulos, Sokratis Anagnostopoulos

Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Lausanne2024

Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment-based approach and advanced collision operators

Paolo Ricci, Baptiste Jimmy Frei, Antoine Cyril David Hoffmann

The first nonlinear gyrokinetic simulations obtained using a moment approach based on the Hermite-Laguerre decomposition of the distribution function are presented, implementing advanced models for the collision operator. Turbulence in a two-dimensional Z- ...

CAMBRIDGE UNIV PRESS2023

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Maria Carola Colombo, Silja Noëmi Aline Haffter

We consider the SQG equation with dissipation given by a fractional Laplacian of order α

2021

A combinatorial proof of a sumset conjecture of Furstenberg

Florian Karl Richter

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Data-Driven Convergence Prediction of Astrobots Swarms

Denis Gillet, Jean-Paul Richard Kneib, Matin Macktoobian, Francesco Basciani

Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination\footnote{\z{A coordination sa ...

2021

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Volkan Cevher, Ali Kavis, Shaul Nadav Hallak

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...

2020

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020

MATHICSE Technical Report : Generalized Parallel Tempering on Bayesian Inverse Problems

Fabio Nobile, Juan Pablo Madrigal Cianci

In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be understood as th ...

MATHICSE2020

Compact convergence

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Generalization of Scaled Deep ResNets in the Mean-Field Regime

Residual-based attention in physics-informed neural networks

Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment-based approach and advanced collision operators

Localization errors of the stochastic heat equation

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

A combinatorial proof of a sumset conjecture of Furstenberg

Data-Driven Convergence Prediction of Astrobots Swarms

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

On the asymptotic behavior of the solutions to parabolic variational inequalities

MATHICSE Technical Report : Generalized Parallel Tempering on Bayesian Inverse Problems

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

A combinatorial proof of a sumset conjecture of Furstenberg

On the asymptotic behavior of the solutions to parabolic variational inequalities

Residual-based attention in physics-informed neural networks

Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment-based approach and advanced collision operators

Data-Driven Convergence Prediction of Astrobots Swarms

On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems

Localization errors of the stochastic heat equation

MATHICSE Technical Report : Generalized Parallel Tempering on Bayesian Inverse Problems