Dynamic Average Diffusion With Randomized Coordinate Updates

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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 ...

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

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 ...

As power grids transition towards low-inertia net-works based on converter-interfaced renewable energy resources, they become increasingly vulnerable to extreme dynamics. Currently, the most advanced methods for signal processing in power systems are embed ...

Motivated by the recent successes of neural networks that have the ability to fit the data perfectly \emph{and} generalize well, we study the noiseless model in the fundamental least-squares setup. We assume that an optimum predictor fits perfectly inputs ...

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 ...

Network information theory studies the communication of information in a network and considers its fundamental limits. Motivating from the extensive presence of the networks in the daily life, the thesis studies the fundamental limits of particular network ...

The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...

This work proposes a novel strategy for social learning by introducing the critical feature of adaptation. In social learning, several distributed agents update continually their belief about a phenomenon of interest through: i) direct observation of strea ...

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an under-damped form of the Langevin algorithm perfor ...

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 ...

This paper introduces a new algorithm for consensus optimization in a multi-agent network, where all agents collaboratively find a minimizer for the sum of their private functions. All decentralized algorithms rely on communications between adjacent nodes. ...

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...

The ever-growing number of edge devices (e.g., smartphones) and the exploding volume of sensitive data they produce, call for distributed machine learning techniques that are privacy-preserving. Given the increasing computing capabilities of modern edge de ...

In this paper, we develop a stochastic-gradient learning algorithm for situations involving streaming data that arise from an underlying clustered structure. In such settings, the variance of gradient noise can be decomposed into the in-cluster variance si ...

We study an optimization program over nonnegative Borel measures that encourages sparsity in its solution. Efficient solvers for this program are in increasing demand, as it arises when learning from data generated by a "continuum-of-subspaces" model, a re ...

This thesis work focuses on optimal control of partial differential equations (PDEs) with uncertain parameters, treated as a random variables. In particular, we assume that the random parameters are not observable and look for a deterministic control which ...

In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...

Dynamic Average Diffusion With Randomized Coordinate Updates

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Residual-based attention in physics-informed neural networks

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Preconditioners for robust optimal control problems under uncertainty

Characterization of Real-World Power System Signals in Non-Stationary Conditions using a Dictionary Approach

Last iterate convergence of SGD for Least-Squares in the Interpolation regime

Data-Driven Convergence Prediction of Astrobots Swarms

Feedback and Common Information: Bounds and Capacity for Gaussian Networks

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Adaptive Social Learning

Is there an analog of Nesterov acceleration for gradient-based MCMC?

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

Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization

Strong convergence of multivariate maxima

Novel corrector problems with exponential decay of the resonance error for numerical homogenization

Private and Secure Distributed Learning

Cover: A Cluster-Based Variance Reduced Method For Online Learning

Sparse Inverse Problems Over Measures: Equivalence Of The Conditional Gradient And Exchange Methods

Stochastic approximation methods for PDE constrained optimal control problems with uncertain parameters

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Numerical Homogenization And Model Order Reduction For Multiscale Inverse Problems