In this talk we propose and validate a Space Multiscale model for the description of particle diffusion in the presence of trapping boundaries. We start from a drift diffusion equation in which the drift term describes the effect of bubble traps, and it is simulated by the Lennard–Jones potential.

Abstract

The goal of the least squares method is to find the best linea

The degenerate Cahn-Hilliard equation, initially introduced in material science, is nowadays used in several different fields, including biology (tumor growth, cell-cell adhesion) and fluid dynamics (high-friction limit in the Euler-Korteweg equation).

We study theoretical problems of fault diagnosis in circuits and switching networks, which are among the most fundamental models for computing Boolean functions.

Cross-validation is an algorithmic technique extensively used for estimating the prediction error, tuning the regularization parameter, and choosing between competing predictive rules.

Breiman (2001) urged statisticians to provide tools when the data, X=s(θ,Y); sampler s is available as Black-Box, parameter θεΘ, Y is random, either observed or latent. The paper’s discussants, D. R. Cox and B. Efron, looked at the problem as X-prediction, surprisingly neglecting the statistical inference for θ, and disagreed with the main thrust of the paper.

This talk is devoted to additive Schwarz methods for convex optimization. First, we propose an abstract framework for additive Schwarz methods for convex optimization. The framework's flexibility allows it to handle composite optimization problems and inexact local solvers. Moreover, it establishes a sharp convergence theory that agrees with the classical theory when addressing linear problems.

In this talk, I will review the fundamentals and application of this technology in various areas, ranging from the inverse design of ultra-flat optical components to HyplexTM, an innovative camera for acquiring and processing high-resolution hyperspectral videos in real-time at 30 frames per second.

Goodness-of-fit tests determine how well a set of observed data fits a particular probability distribution. They can also show if some categorical variable follows a hypothesized family of distributions.

This dissertation focuses on the relative energy analysis of two-species fluids composed of charged particles. In particular, it explores several applications of the relative energy method to Euler-Poisson systems, enabling a comprehensive stability analysis of these systems.

I will review some works on the high-friction limit (or small mass approximation) from Euler flows to advection-diffusion systems that are gradient flows, and related asymptotic problems in fluid mechanics. The formulation exploits the variational structure of compressible Euler flows and is connected to the interpretation of nonlinear Fokker-Planck systems as gradient flows in Wasserstein distance.

This thesis studies mean-field games (MFGs) models of price formation. The thesis focuses explicitly on a MFGs price formation model proposed by Gomes and Saúde. The thesis is divided into two parts. The first part examines the deterministic supply case, while the second part extends the model to incorporate a stochastic supply function. We explore different approaches, such as Aubry-Mather theory, to study the properties of the MFGs price formation model and alternative formulations using a convex variational problem with constraints. We propose machine-learning-based numerical methods to approximate the solution of the MFGs price formation model in the deterministic and stochastic setting.

In this talk, I will describe a surprising application for a known online learning problem and its optimal algorithm.

Estimating first-order intensity functions is crucial in the analysis of point patterns on linear networks, but selecting suitable bandwidths for non-parametric methods remains challenging. We propose an adaptive intensity estimator for the heating kernel that adjusts bandwidths based on data points, a novel approach in this context.

We propose a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. A number of challenges are encountered when discretizing such problems. The first is the heterogeneous kernel singularity in the fractional integral operator. The second comes from the dense discrete operator with its quadratic growth in memory footprint and arithmetic operations. To address these challenges, we propose a strategy that decomposes the system matrix into three components. The first is a sparse matrix that handles the singular near-field separately and is computed by adapting singular quadrature techniques available for the homogeneous case to the case of spatially variable order.

Abstract

We consider the incompressible axisymmetric Navier-Stokes equations as an idealized model of tornado-like flows. Assuming that an infinite vortex line that interacts with a boundary surface resembles the tornado core, we look for stationary self-similar solutions of the axisymmetric Euler and the axisymmetric Navier-Stokes equations emphasizing the connection among them as the viscosity ν → 0.

Coffee Time: 15:30 - 16:00. Kernel matrices can be found in computational physics, chemistry, statistics, and machine learning. Fast algorithms for matrix-vector multiplication for kernel matrices have been developed, and is a subject of continuing interest, including here at KAUST. One also often needs fast algorithms to solve systems of equations involving large kernel matrices. Fast direct methods can sometimes be used, for example, when the physical problem is 2-dimensional. In this talk, we address preconditioning for the iterative solution of kernel matrix systems. The spectrum of a kernel matrix significantly depends on the parameters of the kernel function used to define the kernel matrix, e.g., a length scale.

“Practical fusion power is thirty years off and always will be.” Most people are instantly enraptured at the thought that a single glass of water will provide enough fusion fuel for their lifetime – if only it could be safely unlocked – and most of us have heard, as well, that we should not set our watches for when this will occur.

Generating fusion power from a stellarator is an exciting scientific and engineering challenge, one that promises to produce a stable, green, and nearly perennial energy source for mankind. To do so economically and safely will require a combination of several interdisciplinary breakthroughs including extreme scale computing (with adroit use of artificial intelligence and machine learning), high-temperature superconductors, materials science research, and robotics, to name a few. Overcoming this challenge will need a worldwide effort, involving academia, national laboratories, and industry, and contributions from diverse economies and people.

The most compelling transformational use of magnetically confined, high-temperature plasma is to realize sustained fusion energy. The tokamak, which is the leading magnetic confinement concept in the world today, first realized in 1958, has the geometry of a torus and toroidal symmetry, giving it good confinement properties. Nevertheless, the tokamak has a number of unresolved stability issues related to its current-carrying plasma that may be obstacles to its ultimate success.  In contrast, in the stellarator, the confining magnetic field is mostly produced by external current-carrying coils.

In this talk, I will talk about general approaches for multiscale modeling (closely related to porous media applications). I will mainly focus on numerical approaches, where multiscale finite element basis functions are constructed and used in approximating the solution. In these approaches, macroscopic equations are formed via some variational formulations of the problem. I will discuss how these approaches are used in deriving, so called upscaling techniques and the relation to well known upscaling methods. The concepts discussed in the talk are used for linear and nonlinear problems. I will discuss some applications.

Dear Kaustians, We are excited to announce the upcoming Stochastic Numerics and Statistical Learning: Theory and Applications Workshop 2023, taking place at KAUST, Building 9, from May 21 to June 1, 2023. Following the highly successful 2022 edition, this year's workshop promises to be another engaging and insightful event for researchers, faculty members, and students interested in stochastic algorithms, statistical learning, optimization, and approximation. The 2023 workshop aims to build on the achievements of last year's event, which featured 28 talks, two mini-courses, and two poster sessions, attracting over 150 participants from various universities and research institutes. In 2022, attendees had the opportunity to learn from through insightful talks, interactive mini-courses, and vibrant poster sessions. This year, the workshop will once again showcase contributions that offer mathematical foundations for algorithmic analysis or highlight relevant applications. Confirmed speakers include renowned experts from institutions such as Ecole Polytechnique, EPFL, Université Pierre et Marie Curie - Paris VI, and Imperial College London, among others.

KAUST Research Conference on

Advances in nonlinear elliptic and parabolic PDEs

The theory of mean field games (MFG for short) aims to study limiting behavior of Nash equilibria of (stochastic) differential games when the number of agents tends to infinity. While in general existence of MFG Nash equilibria can be established under fairly general assumptions, uniqueness is the exception rather than the rule.