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On the density of the supremum of the solution to the linear stochastic heat equation

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On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Yannis Dirk Voet

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

ELSEVIER SCIENCE INC2023

Euclid preparation: XXVIII. Forecasts for ten different higher-order weak lensing statistics

Maurizio Martinelli, Frédéric Courbin, Gianluca Castignani, Austin Chandler Peel

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale ...

EDP SCIENCES S A2023

On the symmetries in the dynamics of wide two-layer neural networks

Lénaïc Chizat

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of s ...

AMER INST MATHEMATICAL SCIENCES-AIMS2023

Polynomial-time universality and limitations of deep learning

Emmanuel Abbé

The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...

WILEY2023

Engineering random spin models with atoms in a high-finesse cavity

Jean-Philippe Brantut, Nick Jacob Sauerwein, Tigrane Arthur Cantat Moltrecht, Francesca Orsi

Random spin models play a key role in our understanding of disorder and complex many-body systems. Two all-to-all interacting, disordered models have now been realized using a cavity quantum electrodynamics platform. ...

NATURE PORTFOLIO2023

Removing Algorithmic Discrimination (With Minimal Individual Error)

Rachid Guerraoui, El Mahdi El Mhamdi, Alexandre David Olivier Maurer, Le Nguyen Hoang

We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...

2022

Preconditioners for robust optimal control problems under uncertainty

Fabio Nobile, Tommaso Vanzan

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

2023

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

Siam Publications2023

On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

Daniel Kuhn, Wolfram Wiesemann

Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affec ...

2023

Distributional Regression and Autoregression via Optimal Transport

Laya Ghodrati

We present a framework for performing regression when both covariate and response are probability distributions on a compact and convex subset of

\R^d

. Our regression model is based on the theory of optimal transport and links the conditional Fr'echet m ...

EPFL2023

Detecting whether a stochastic process is finitely expressed in a basis

Victor Panaretos, Neda Mohammadi Jouzdani

Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning

Jean-Philippe Thiran, Roser Vinals Terres

Ultrafast ultrasound imaging, characterized by high frame rates, generates low-quality images. Convolutional neural networks (CNNs) have demonstrated great potential to enhance image quality without compromising the frame rate. However, CNNs have been most ...

2023

Minimax rate for optimal transport regression between distributions

Victor Panaretos, Laya Ghodrati

Distribution-on-distribution regression considers the problem of formulating and es-timating a regression relationship where both covariate and response are probability distributions. The optimal transport distributional regression model postulates that th ...

ELSEVIER2022

The elliptical Ornstein-Uhlenbeck process

Sofia Charlotta Olhede

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are obse ...

INT PRESS BOSTON, INC2023

Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method

Fabio Nobile, Sundar Subramaniam Ganesh

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method ...

2023

Assessment of the Lightning Performance of overhead distribution lines based on Lightning Location Systems data

Farhad Rachidi-Haeri

This article presents the Lightning Performance (LP) assessment of a realistic portion of the Italian distribution network with the use of probability distributions for lightning parameters inferred from local data recorded by a Lightning Location System ( ...

2022

A multigrid method for PDE-constrained optimization with uncertain inputs

Fabio Nobile, Tommaso Vanzan

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...

Springer Science and Business Media LLC2024