Concept

Fonction génératrice des moments

Publications associées (32)

On the number of regions of piecewise linear neural networks

Michaël Unser, Alexis Marie Frederic Goujon

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

2024

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, Cheuk Yin Lee, David Jean-Michel Candil

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

New York2023

DATED: GUIDELINES FOR CREATING SYNTHETIC DATASETS FOR ENGINEERING DESIGN APPLICATIONS

Jürg Alexander Schiffmann, Cyril Picard, Faez Ahmed

Exploiting the recent advancements in artificial intelligence, showcased by ChatGPT and DALL-E, in real-world applications necessitates vast, domain-specific, and publicly accessible datasets. Unfortunately, the scarcity of such datasets poses a significan ...

Amer Soc Mechanical Engineers2023

Surface roughness and shear resistance in cracked concrete

Guillaume Anciaux, Mohit Pundir

In concrete structures, opened cracks contribute significantly to the transfer of shear and normal stresses through the contact forces acting on fractured surfaces. Such contact forces are due to protruding asperities, engaged by interlocking and friction ...

2022

Dual Approach for Two-Stage Robust Nonlinear Optimization

Jianzhe Zhen

Adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables are generally difficult to solve. In this paper, we reformulate the original adjustable robust nonlinear problem with a polyhedral ...

INFORMS2022

CFD Simulation of Particle-Laden Flow in a 3D Differentially Heated Cavity Using Coarse Large Eddy Simulation

Konstantin Mikityuk, Abdelouahab Dehbi

Particulate flow in closed space is involved in many engineering applications. In this paper, the prediction of particle removal is investigated in a thermally driven 3D cavity at turbulent Rayleigh number Ra = 1E9 using Coarse Large Eddy Simulation (CLES) ...

2022

Scattering Map for the Vlasov–Poisson System

Klaus Martin Widmayer

We construct (modified) scattering operators for the Vlasov–Poisson system in three dimensions, mapping small asymptotic dynamics as t→−∞ to asymptotic dynamics as t→+∞. The main novelty is the construction of modified wave operators, but we also obtain a ...

2021

Distributionally Robust Mechanism Design

Daniel Kuhn, Cagil Kocyigit, Wolfram Wiesemann

We study a mechanism design problem where an indivisible good is auctioned to multiple bidders, for each of whom it has a private value that is unknown to the seller and the other bidders. The agents perceive the ensemble of all bidder values as a random v ...

2020

Distributional Robustness in Mechanism Design

Cagil Kocyigit

Mechanism design theory examines the design of allocation mechanisms or incentive systems involving multiple rational but self-interested agents and plays a central role in many societally important problems in economics. In mechanism design problems, agen ...

EPFL2020

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

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