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.

How does an elastic membrane lie on a given obstacle? This naive looking question hides a beautiful mathematical theory integrating powerful tools with far-reaching applications. In this mini-course we will discuss the obstacle problem as a free boundary model. All necessary tools will be carefully constructed from scratch. We will mainly focus on: optimal regularity of solutions, non-degeneracy estimates, weak geometric-measure properties of the free boundary, classification of global profiles, and differentiability of the free boundary.

I consider the vector counterpart of the classical p-Laplace and p-heat equations which are some of the building blocks for the mathematical description of non-linear plasticity, non-Newtonian fluids, and turbulent eddy viscosity models. I will discuss results of “natural regularity” and their role in the study of the well-posedness of the nonlinear pdes as well as in the theory of convergence for space-time discretisation methods. In particular, I will present the “A-approximation" method which generalises results by Necas and which reduces the problem to a family of linear ones. Coffee Time: 15:30 - 16:00

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.

How does an elastic membrane lie on a given obstacle? This naive looking question hides a beautiful mathematical theory integrating powerful tools with far-reaching applications. In this mini-course we will discuss the obstacle problem as a free boundary model. All necessary tools will be carefully constructed from scratch. We will mainly focus on: optimal regularity of solutions, non-degeneracy estimates, weak geometric-measure properties of the free boundary, classification of global profiles, and differentiability of the free boundary.

Abstract

Effective process monitoring is crucial to ensure engineering

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. For finite horizon mean field games uniqueness typically holds if the time horizon is small (or the data satisfies other smallness conditions).

Abstract

How does an elastic membrane lie on a given obstacle?

How does an elastic membrane lie on a given obstacle? This naive looking question hides a beautiful mathematical theory integrating powerful tools with far-reaching applications. In this mini-course we will discuss the obstacle problem as a free boundary model. All necessary tools will be carefully constructed from scratch. We will mainly focus on: optimal regularity of solutions, non-degeneracy estimates, weak geometric-measure properties of the free boundary, classification of global profiles, and differentiability of the free boundary.

Abstract

In this talk, we will discuss the m

Reservoir simulation is an essential tool in reservoir engineering, enabling effective management and optimization of reservoirs. Despite minimal changes in the fundamental sciences since the development of reservoir simulators, advancements in computational power and linear solvers have significantly improved the technology. However, the reliability and ability to improve decision quality of reservoir models remain debatable.

The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution. Consequently, testing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mardia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions.

During the recent pandemic, urgent advances have been made by the scientific community in developing artificial intelligence (AI)-based computer-aided systems for CT-based COVID-19 diagnosis. In this talk, I will introduce our work on a fully-automatic, rapid, accurate, and machine-agnostic method that can segment and quantify the infection regions on CT scans from different sources.

Pore-scale models are valuable tools for the investigation of various flow and transport processes in porous media, and upscaling from pore to core scales. Popular approaches include pore-network models (PNM), Lattice-Boltzman models (LBM), Smooth Particle Hydrodynamics (SPH), volume-of-fluid method (VOF), and grain-scale models (GSM).

We investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by  regions in which $u > 0$ and $u < 0$. The classical point of view of regarding the Prandtl equations as an evolution  equation in $x$ completely breaks down since $u$ changes sign. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. Joint work with Sameer Iyer.

We consider non-conforming discretizations of the stationary Stokes equation in two and three dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit and also contains substantial freedom for a concrete choice.

Reservoir simulation usually involves the fluid flow of partially miscible multi-component multi-phase mixture in porous media.  Phase behavior of fluid mixture is a crucial component of many multi-phase flow framework.  Accurate modeling and robust computation of the phase behavior is essential for optimal design and cost-effective operations in petroleum reservoirs as well as in a petroleum processing plant.  A typical problem formulation in phase behavior is two-phase constant volume flash, i.e., the two-phase  phase-split under the constant temperature, moles, and volume.

"Force-deformation laws, Love numbers, and the Association Principle". This lecture contains a discussion about realistic force-deformation relations used for celestial bodies, their empirical description by means of Love numbers, and their mathematical modelling by means of the "Association Principle''.

In this talk, we discuss problems and numerical methods arising in the calculus of variations and energy minimization. Among numerous applications, energy minimization is a core element of Machine Learning algorithms. Within the field of nonlinear PDEs, the calculus of variations has received a lot of attention from the analysis point of view.  Although quite interesting and challenging,  the numerical analysis of these problems is much less developed.

"Translation, rotation and Deformation". In this lecturer, we will present the simplest possible model for the motion of two extended rigid bodies interacting by gravity.

This talk will review the recent shift in the construction and modern analysis of a large class of spatially and temporally adaptive methods whose properties are very close to our current analytical knowledge about hyperbolic or mixed hyperbolic-parabolic partial differential equations (PDEs) in computational physics. Thus these algorithms can be regarded as the elite methods in the field. Next, we will show examples of how the robustness and efficiency of the fully-discrete representation of PDEs can be enhanced using computational science's smithy, i.e., "modern" numerical analysis. The talk will showcase complex flow problems in aeronautics, aerospace, and automotive sectors, provide preliminary results in other fields, and present an outlook for future research directions where data science can currently be the linesman.

"Qualitative theory of tides and their effects." It contains a qualitative explanation of tides and their effects: phase lags, forces that dissipate energy but do not dissipat angular momentum, circularization of orbits, spin-orbit synchronization and collision.

This talk reviews recent results concerning the inviscid limit for the 2D Euler equations with unbounded vorticity. In particular, by using techniques from the theory of transport equation with no smooth vector fields, we show that the solutions obtained in the vanishing viscosity limit satisfy a representation formula in terms of the flow of the velocity and that the strong convergence of the vorticity holds and we give a rate of convergence.