Stochastic Models for Sparse and Piecewise-Smooth Signals

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We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

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 ...

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 ...

We describe a novel method to compute the components of dynamo tensors from direct magnetohydrodynamic (MHD) simulations. Our method relies upon an extension and generalization of the standard H & ouml;gbom CLEAN algorithm widely used in radio astronomy to ...

Decentralized learning is appealing as it enables the scalable usage of large amounts of distributed data and resources (without resorting to any central entity), while promoting privacy since every user minimizes the direct exposure of their data. Yet, wi ...

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 ...

Information theory has allowed us to determine the fundamental limit of various communication and algorithmic problems, e.g., the channel coding problem, the compression problem, and the hypothesis testing problem. In this work, we revisit the assumptions ...

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 ...

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

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 ...

We study the compact support property for solutions of the following stochastic partial differential equations: partial derivative tu=aijuxixj(t,x)+biuxi(t,x)+cu+h(t,x,u(t,x))F-center dot(t,x),(t,x)is an element of(0,infinity)xRd,where F-center dot is a sp ...

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations ...

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Stochastic Models for Sparse and Piecewise-Smooth Signals

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Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

Exploiting the Signal-Leak Bias in Diffusion Models

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Spectral Estimators for High-Dimensional Matrix Inference

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

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

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

Iterative removal of sources to model the turbulent electromotive force

The Privacy Power of Correlated Noise in Decentralized Learning

Generalization of Scaled Deep ResNets in the Mean-Field Regime

On Speed and Advantage : Results in Information Velocity and Monitoring Problems

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Transportation-based functional ANOVA and PCA for covariance operators

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

THE COMPACT SUPPORT PROPERTY FOR SOLUTIONS TO THE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH COLORED NOISE

Functional data analysis with rough sample paths?

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Distributionally Robust Linear Quadratic Control

Stochastic particle transport by deep-water irregular breaking waves