Dear Kaustians, We are excited to announce the upcoming Stochastic Numerics and Statistical Learning: Theory and Applications Workshop 2024, taking place at KAUST, Building 9, from May 19-30, 2024. Following the highly successful 2022 and 2023 editions, 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 2024 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 previous two years 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.

Numerical approximation of partial differential equations involves parameter dependencies from problem formulation and numerical methods. We focus on two areas: least-squares finite element method with linear elasticity, studying its dependence on the Lamé parameter, and the Virtual Element Method, known for handling complex geometries where the stabilization parameter is analyzed.

Rare, low-probability events often lead to the biggest impacts. Therefore, the development of statistical approaches for modeling, predicting and quantifying environmental risks associated with natural hazards is of utmost importance. In this seminar, I will show how statistical deep-learning methods can help solve challenges that arise when modeling complex and massive spatiotemporal extremes data.

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.

Growth is a fundamental process in biological systems and various technological applications, including epitaxial deposition and additive manufacturing. The interaction between growth and mechanics in deformable bodies leads to a wealth of very challenging mathematical questions. I will give a short overview of the key concepts of morphoelasticity, namely, the theory of elastic deformations in growing bodies.

Traveling wave solutions of reaction-diffusion systems have been studied to explain wave propagation phenomena in biological organisms.

Abstract

Neural operator methods provide a novel approach for solving or learning the complex mapp

Despite being small and simple structured in comparison to their victims, virus particles have the potential to harm severly and even kill highly developed species such as humans. To face upcoming virus pandemics, detailed quantitative biophysical un- derstanding of intracellular virus replication mechanisms is crucial. Unveiling the relationship of form and function will allow to determine putative attack points relevant for the systematic development of direct antiviral agents (DAA) and potent vacci- nes. Biophysical investigations of spatio-temporal dynamics of intracellular virus replication so far are rare.

Predicting the paths of animals poses a significant challenge, given the intricate nature of their behaviors, the impact of unpredictable environmental elements, individual differences, and the scarcity of precise data on their movements.

As more and more modern time series data sets are becoming high dimensional, the problem of classification in this context has received increasing attention. We propose a statistical framework for classifying multivariate stationary Gaussian time series where the number of covariates, the length of the series, and the sample size, all grow to infinity.

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.

In this work, we employ importance sampling (IS) techniques to track a small over-threshold probability of a running maximum associated with the solution of a stochastic differential equation (SDE) within the framework of ensemble Kalman filtering (EnKF).

Artificial materials represent composite media that can be meticulously engineered to exhibit unique wave propagation behaviors. Our research endeavors are driven by the intriguing principles underlying these materials, such as effective models, and their broad applications, including perfect absorption. In this presentation, I will outline our recent advancements in our innovative design strategies for novel artificial materials from both forward first-principle physics-based modeling and data-driven approaches. Specifically, I will highlight our pioneering work in the designs of double-zero-index materials for both electromagnetic and acoustic waves. Additionally, I will discuss our discovery of the acoustic Purcell effect for enhanced emission, as well as our development of analytic and numerical solutions for space-time modulated wave systems. Furthermore, I will delve into our practical solution for achieving broad frequency cloaking of invisibility. These accomplishments hold significant promise for a wide range of applications spanning sound control, communication, sensing, imaging and more.

In this work, we analyze the convergence rate of randomized quasi-Monte Carlo (RQMC) methods under Owen's boundary growth condition [Owen, 2006] via spectral analysis.

In 2019, diabetes caused 1.5 million global deaths, with 48% occurring before age 70. While Type 1 diabetes strongly depends on genetic components and is usually diagnosed in childhood, Type 2 diabetes is primarily caused by long term consumption of high calories foods. Lifestyle choices significantly influence the risk of Type 2 diabetes and obesity, including energy intake, diet composition, physical activity, and smoking.

When pressure acoustic waves interact with rotating scatterers, they undergo peculiar and intriguing characteristics. In this talk, I will discuss our recent findings on the physics of acoustic scattering and propagation in spinning fluids.

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.

Until very recently, distribution-led local flexibility markets were exclusively an academic endeavor, with few practical applications, mostly limited to small-scale innovation projects. However, with European regulation finally catching up with the realities of modern distribution networks, local flexibility markets are slowly becoming a reality - new ones popping up across the continent, or some even becoming a BAU option in the most advanced countries.

The Pauli-Poisswell equation models fast-moving charges in semiclassical semi-relativistic quantum dynamics. It is at the center of a hierarchy of models from the Dirac-Maxwell equation to the Euler-Poisson equation that is linked by asymptotic analysis of small parameters such as the Planck constant or inverse speed of light. We discuss the models and their application in plasma and accelerator physics as well as the many mathematical problems they pose

We consider the widely used continuous $Q_{k+1}-Q_k$ quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions.

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.

A subtle difference in a diffusion model can lead to an opposite conclusion. We need to understand how each component involved in the diffusion phenomenon contributes to the diffusion model. In this talk, we will discuss how nonconstant persistence and permeability play a role in the diffusion phenomenon.

The term doubly nonlinear refers to the fact that the diffusion part depends nonlinearly both on the gradient and the solution itself. Such equations describe several physical phenomena and were introduced by Lions and Kalashnikov. These equations have an intrinsic mathematical interest because they represent a natural bridge between the more natural generalizations of the heat equation: the p-Laplacian and the porous medium equation.

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.