On Preconditioning of Decentralized Gradient-Descent When Solving a System of Linear Equations

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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 ...

Here we provide the neural data, activation and predictions for the best models and result dataframes of our article "Task-driven neural network models predict neural dynamics of proprioception". It contains the behavioral and neural experimental data (cu ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

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 ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

This paper proposes a data-driven control design method for nonlinear systems that builds upon the Koopman operator framework. In particular, the Koopman operator is used to lift the nonlinear dynamics to a higher-dimensional space where the so-called obse ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

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 ...

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 ...

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

This work considers the low-rank approximation of a matrix (Formula presented.) depending on a parameter (Formula presented.) in a compact set (Formula presented.). Application areas that give rise to such problems include computational statistics and dyna ...

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

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 ...

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 ...

Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison. Managing their complexity and facilitating their design drove part of the co-evolution of mode ...

The nitrogen-vacancy (NV) center in diamond is a powerful and versatile quantum sensor for diverse quantities. In particular, relaxometry (or T1), can be used to detect magnetic noise at the nanoscale. For experiments with single NV centers the analysis of ...

Magnetic resonance spectroscopy is a powerful, non-invasive, quantitative imaging technique that allows for the measurement of brain metabolites that has demonstrated utility in diagnosing and characterizing a broad range of neurological diseases. Its impa ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

On Preconditioning of Decentralized Gradient-Descent When Solving a System of Linear Equations

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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

Task-driven neural network models predict neural dynamics of proprioception: Experimental data, activations and predictions of neural network models

Randomized flexible GMRES with deflated restarting

Random matrix methods for high-dimensional machine learning models

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

Reliable data-driven decision-making through optimal transport

Data-Driven Control Synthesis using Koopman Operator: A Robust Approach

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

The Privacy Power of Correlated Noise in Decentralized Learning

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

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

Randomized low-rank approximation of parameter-dependent matrices

Unlabeled Principal Component Analysis and Matrix Completion

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

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

Graph generative deep learning models with an application to circuit topologies

Optimizing Data Processing for Nanodiamond Based Relaxometry

Harmonization of multi-scanner in vivo magnetic resonance spectroscopy: ENIGMA consortium task group considerations

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains