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.

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.

This scientific meeting will concentrate on stochastic algorithms and their rigorous numerical analysis for various problems, including statistical learning, optimization, and approximation. Stochastic algorithms are valuable tools when addressing challenging computational problems.

This thesis studies novel and efficient computational sampling methods for applications in three types of stochastic inversion problems: seismic waveform inversion, filtering problems, and static parameter estimation.

In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this thesis, we design novel efficient simulation techniques, based on multilevel Monte Carlo methods and importance sampling, for a reliable and fast estimation of various statistical quantities for stochastic biological and chemical systems under the framework of Stochastic Reaction Networks (SRNs). In the second part of this thesis, we design novel numerical methods for pricing financial derivatives. Option pricing is usually challenging due to a combination of two complications: 1) The high dimensionality of the input space, and 2) The low regularity of the integrand on the input parameters. We address these challenges by using different techniques for smoothing the integrand to uncover the available regularity and improve quadrature methods' convergence behavior. We develop different ways of smoothing that depend on the characteristics of the problem at hand. Then, we approximate the resulting integrals using hierarchical quadrature methods combined with Brownian bridge construction and Richardson extrapolation.

Optimal experimental design for parameter estimation is a fast-growing area of research. Let us consider the experimental goal to be the inference of some attributes of a complex system using measurement data of some chosen system responses, and the optimal designs are those that maximize the value of measurement data. The value of data is quantified by the expected information gain utility, which measures the informativeness of an experiment. Often, a mathematical model is used that approximates the relationship between the system responses and the model parameters acting as proxies for the attributes of interest.

Hierarchical porous media that feature properties and processes at multiple scales arise in many engineering applications including the design of novel materials for energy storage devices. Microscopic (pore-scale) properties of the media impact their macroscopic (continuum- or Darcy-scale) counterparts and understanding the relationships between processes on these two scales is essential for informing engineering decision tasks.

I​n the field of uncertainty quantification, the effects of parameter uncertainties on scientific simulations may be studied by integrating or approximating a quantity of interest as a function over the parameter space. If this is done numerically, using regular grids with a fixed resolution, the required computational work increases exponentially with respect to the number of uncertain parameters -- a phenomenon known as the curse of dimensionality.

The probability that a sum of random variables (RVs) exceeds (respectively falls below) a given threshold, is often encountered in the performance analysis of wireless communication systems. Generally, a closed-form expression of the sum distribution does not exist and a naive Monte Carlo (MC) simulation is computationally expensive when dealing with rare events. An alternative approach is represented by the use of variance reduction techniques, known for their efficiency in requiring less computations for achieving the same accuracy requirement.

This work employs statistical and Bayesian techniques to analyze mathematical forward models with several sources of uncertainty. The forward models usually arise from phenomenological and physical phenomena and are expressed through regression-based models or partial differential equations (PDEs) associated with uncertain parameters and input data. One of the critical challenges in real-world applications is, for any proposed model, to estimate and quantify uncertainties of its unknown parameters using the available observations.

A feasible, nonparametric, probabilistic approach for modeling and quantifying model-form uncertainties associated with a High-Dimensional Computational Model (HDM) and/or a corresponding Hyperreduced Projection-based Reduced-Order Model (HPROM) [1,2] designed for the solution of computational mechanics problems is presented.

Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.

Ms. Soumaya ElKantassi is a master student in Applied Mathematics and Computational Science and a member of the Stochastic Numerics Group at KAUST. She obtained her Bachelor's degree in Engineering from Tunisia Polytechnic School majoring in Economic and Scientific Management.

Most problems in engineering and natural sciences involve parametric equations in which the parameters are not known exactly due to measurement errors, lack of measurement data, or even intrinsic variability. In such problems, one objective is to compute point or aggregate values, called "quantities of interest".

Abstract:

Time inconsistent performance crit

Chebyshev nodes are well-known for their near-optimal polynomial interpolation and quadrature properties on intervals. In particular, the associated Lebesgue constant grows only logarithmically, whereas that associated to equispaced nodes grows exponentially.

We present a novel regularizing ensemble Kalman method for solving PDE-constrained inverse problems. By merging ideas from iterative regularisation approaches and ensemble Kalman algorithms we design a derivative-free solver for generic inverse problems. The proposed method can be used to estimate parameters of large-scale PDE models in a black-box fashion.

This thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in dense communication networks. The first part of this work proposes novel numerical methods to estimate, in an efficient and accurate way, observables from realizations of Markovian jump processes.

In biochemical systems, stochastic effects can be caused by the presence of small numbers of certain reactant molecules. In this setting, discrete state-space and stochastic simulation approaches were proved to be more relevant than continuous state-space and deterministic ones.

Experimental design can be vital when experiments are resource exhaustive and time-consuming. In this work, we carry out experimental design in the Bayesian framework. To measure the amount of information, which can be extracted from the data in an experiment, we use the expected information gain as the utility function, which specifically is the expected logarithmic ratio between the posterior and prior distributions.

Jacques DUYSENS, 47 years old, obtained his Civil Engineer Diploma in Electricity & Mechanics, and in Aerospace, from the University of Liège (Belgium) with the highest distinction. His prior responsibility was as R&D Engineer in Powertrains Groups dynamics at RENAULT SA (France) in 1990. Three years later, he served as Director of the Simulation of Manufacturing Processes department (Assembly & Machining) within the Mechanical Process Direction.

Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs) that have been mainly developed to model biochemical reactions. SRNs also have applications in neural networks, virus kinetics, and dynamics of social networks, among others.

Core flooding experiments are always needed to be conducted before the application of Enhanced Oil Production (EOR) in the field, which is a great way to improve the oil recovery. In order to optimize existing resources and obtain the information efficiently, it is necessary to optimize these experiments.