We will discuss the solution of eigenvalue problems associated with partial differential equations (PDE)s that can be written in the generalised form Ax = λMx, where the matrices A and/or M may depend on a scalar parameter. Parameter dependent matrices occur frequently when stabilised formulations are used for the numerical approximation of PDEs. With the help of classical numerical examples we will show that the presence of one (or both) parameters can produce unexpected results.

Hessian-dependent functionals play a pivotal role in a wide latitude of problems in mathematics. Arising in the context of differential geometry and probability theory, this class of problems find applications in the mechanics of deformable media (mostly in elasticity theory) and the modelling of slow viscous fluids. We study such functionals from three distinct perspectives.

We present a theoretical analysis of the Weak Adversarial Networks (WAN) method, recently proposed in [1, 2], as a method for approximating the solution of partial differential equations in high dimensions and tested in the framework of inverse problems. In a very general abstract framework.

Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas.

Wave propagation and scattering problems are of huge importance in many applications in science and engineering - e.g., in seismic and medical imaging and more generally in acoustics and electromagnetics.

In this short course, we will introduce some elements in deriving the hp a posteriori error estimate for a high-order unfitted finite element method for elliptic interface problems. The key ingredient is an hp domain inverse estimate, which allows us to prove a sharp lower bound of the hp a posteriori error estimator.

I will present an overview of our activities around estimation problems for partial and fractional differential equations. I will present the methods and the algorithms we develop for the state, source and parameters estimation and illustrate the results with some simulations and real applications.

We consider the problem of recovering a low-rank signal matrix in the presence of a general, unknown additive noise; more specifically, noise where the eigenvalues of the sample covariance matrix have a general bulk distribution. We assume given an upper bound for the rank of the assumed orthogonally invariant signal, and develop a selector for hard thresholding of singular values, which adapts to the unknown correlation structure of the noise.

A variety of intriguing patterns in eigenvalues were observed and speculated about in ML conference papers. We describe the work of Vardan Papyan showing that the traditional subdisciplines, properly deployed, can offer insights about these objects that ML researchers had.

Abstract

The talk will present the integrate

The Center of Excellence for NEOM Research at KAUST presents a lecture on the NEOM Food Sector by KAUST Professor and NEOM Food Sector Head, Mark Tester.

Flash floods are one of the most common natural disasters worldwide, causing thousands of casualties every year. The emergence of Unmanned Aerial Vehicles (UAVs) gives the possibility to monitor these events over large geographical areas. In this talk, we focus on the problem of trajectory planning for a swarm of unmanned aerial vehicles sensing flooding conditions.

We will present some new methods for source and parameters estimation for partial and fractional differential equations and illustrate the results with some simulations and real applications.

The Conference is inspired by the surging interest in smart cities and smart environmental systems worldwide. The ever-increasing capabilities of sensing, communications, and computation will be key enablers of future destinations that are designed for livability, efficiency, and affordability, all the while ensuring sustainability and environmental stewardship. The conference will feature research presentations on smart solutions for energy, transportation, urban planning, and monitoring, as well as the supporting foundational areas of networks and communications; signal processing and big data; high performance computing; and cyberphysical systems.