Topics

<> approximation (2) <> architectural geometry (2) <> architecture (2) <> astronomy (2) <> Automous Vehicles (2) <> award (2) <> Bayesian and computational Statistics (2) <> Bayesian Inversion (2) <> bioinformatics (2) <> biomechanics (2) <> biomedical devices (2) <> cancer (2) <> climate change (2) <> collective (2) <> communication (2) <> communication networks (2) <> computation (2) <> Computational biology (2)

Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks

-

KAUST

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.

Chiheb Ben Hammouda

Chiheb Ben Hammouda is a Ph.D. candidate at Stochastic Numerics Research Group (STOCHNUM) under the supervision of Professor Raul F. Tempone at King Abdullah University of Science and Technology (KAUST). Prior to joining Ph.D., Chiheb obtained a Master's degree in Applied Mathematics and Computational Sciences from KAUST, and a Bachelor's degree in multidisciplinary engineering from Ecole Polytechnique de Tunisie, Tunisia. Research Interests Chiheb's research interests include Stochastic modeling, Numerical simulation and analysis, Quantitative finance in particular option pricing, Stochastic
<> computational fluids mechanics (2) <> Computational Neuroscience (2) <> Computational Photography (2) <> computational physics (2) <> computational probability (2) <> computational science and engineering (2) <> computer graphics (2) <> Computer simulations (2) <> Conservation Laws (2) <> Control Theory (2) <> coral reefs (2) <> Cross-layer protocol design (2) <> Data Analytics (2) <> Deep generative models (2) <> deep neural networks (2) <> desalination (2) <> Differential Equation (2) <> Differential equations (2) <> differential geometry (2)

Discrete conformal mappings and Riemann Surfaces: Theory and Applications

-

B9 L2 H2

The general idea of discrete differential geometry is to find and investigate discrete models that exhibit properties and structures characterisitic of the corresponding smooth geometric objects. This is a challenging problem, since equivalent points of view in the smooth setting may lead to a number of inequivalent treatments in the discrete setting. We will illustrate the paradigm of structure-preserving discretizations on the example of conformal maps by showing how simple definitions lead to surprisingly rich theories.

Anthony Ramos

Anthony Ramos is an MS/PhD Student at Visual Computing Center (VCC) in King Abdullah University of Science and Technology (KAUST), studying under the supervision of Professor Helmut Pottman in his research group. Education and Early Career Anthony have obtained Bachelor's degree in Physicist from Yachay Tech University, Urcuqui, Ecuador - government project with the idea of making an international university for the country, from which he was part of the second generation of students. Research Interest Anthony Ramos is passionate about geometry and programming. He loves to bring problems to
<> Diffusion Models (2) <> Digital signal processing (2) <> digital twins (2) <> discrete maximum principle (2) <> Domain Decomposition (2) <> ecology (2) <> elasticity (2) <> energy security (2) <> Energy-efficient wireless multihop networks (2) <> Euler equations (2)

Weak solutions of the 2D Euler equations

-

B1 L3 R3119

In this talk we consider the Cauchy problem for the 2D Euler equations for incompressible inviscid fluids. It is well-known that given a smooth initial datum, the Cauchy problem is well-posed and in particular the energy is conserved and the vorticity is transported by the flow of the velocity. When we consider weak solutions this might not be the case anymore. We will review some recent results obtained in collaboration with Gianluca Crippa and Gennaro Ciampa where we extend those properties to the case of irregular vorticities. In particular, under low integrability assumptions on the vorticity we show that certain approximations important from a physical and a numerical point of view converge to solutions satisfying those properties.

A Variational Theory of Aero-hydrodynamics

Haithem Taha, Associate Professor

-

B5 L5 R5209

The Euler equation does not possess a unique solution for the flow over a two-dimensional object. This problem has serious repercussions in aerodynamics; it implies that the inviscid aero-hydrodynamic lift force over a two-dimensional object cannot be determined from first principles; a closure condition must be provided. The Kutta condition has been ubiquitously considered for such closure in the literature, even in cases where it is not applicable (e.g. unsteady).
<> exascale (2) <> extreme-value theory (2) <> finite element method (2) <> flow problems (2) <> Fluid Mechanics (2) <> forecasting (2) <> FPGA (2) <> Free-space optical communications (2) <> Functional (2) <> functional data analysis (2) <> Fusion (2) <> game theory (2) <> generative models (2) <> geometric modeling (2) <> Geometry (2)

Geometry and Computational Design

-

KAUST

An important stream of research in computational design aims at digital tools which support users in realizing their design intent in a simple and intuitive way, while simultaneously taking care of key aspects of function and fabrication. Such tools are expected to shorten the product development cycle through a reduction of costly feedback loops between design, engineering and fabrication. The strong coupling between shape generation, function and fabrication is a rich source for the development of new geometric concepts, with an impact to the original applications as well as to geometric theory. This will be illustrated at hand of applications in architecture and fabrication with a mathematical focus on discrete differential geometry and geometric optimization problems.

Geometry and Computational Design of Equilibrium Structures

-

B1 L3 R3119

Freeform structures play a prominent role in contemporary architecture. In order to stay within reasonable cost limits, computational shape design has to incorporate aspects of structural analysis and fabrication constraints. The talk discusses solutions to important problems in this area. They concern the design of polyhedral surfaces with nearly rectangular faces, polyhedral surfaces in static equilibrium, the smoothest visual appearance of polyhedral surfaces and the closely related problem of finding material-minimizing forms and structures. From a methodology perspective, there is an interplay of geometry, mechanics and optimization. Classical subjects such as isotropic geometry, a simple Cayley-Klein geometry, play a role as well as most recent developments in discrete differential geometry. We also show how practical requirements have led to new results and open problems in geometry.
<> GPU (2) <> GPU Algorithms (2) <> Graphene (2) <> information security (2) <> International Supercomputing Conference (2) <> Inverse problem (2) <> Kinetic Theory (2) <> knowledge discovery (2) <> laser (2) <> light (2) <> Localization (2) <> machine learning for wireless communication (2) <> markov chains (2) <> MCMC (2) <> medicine (2) <> ML (2) <> Multi-Modal Large Language Models (2) <> multimodal AI (2) <> multimodal sensing (2) <> Multiphase flows (2) <> Multiphysics Simulation (2)

Multi-physics Simulation of Plasmonic Photoconductive Devices and Antennas

-

B9 L2 R2322 H1

Terahertz (THz) frequency electromagnetic fields have numerous applications ranging from wireless communications to imaging systems and nondestructive testing, to material characterization. One of the main obstacles in the way of widespread industrial use of THz technologies is the difficulty of implementing compact and frequency-stable THz sources that can operate at room temperatures. Among a variety of possible options, photoconductive devices (PCDs) satisfy these conditions. Indeed, they have become one of the most promising candidates for THz source generation since recent advances in fabrication techniques, such as metasurface integration and nanostructured surface inclusions have significantly increased their optical-to-THz conversion efficiency and made them polarization insensitive.

Rolf Krause

Professor Rolf Krause is an experienced researcher and educator specializing in designing and analyzing algorithms to solve complex problems in scientific computing and machine learning.
<> multivariate analysis (2) <> Navier-Stokes (2) <> Network Design (2) <> neural network (2) <> Non-Terrestrial Networks (2) <> nonlinear (2) <> nonlinear models (2)

Mathematical Design and Analysis of Iterative Methods for Linear and Nonlinear Problems

-

B1 L3 R3119

This talk presents a systematic approach to the design and analysis of iterative methods for solving linear and nonlinear problems.

Deterministic particle approximation for nonlinear transport equations

-

Building L3 R3119

Approximating the solution to an evolutionary partial differential equation by a set of "moving particles" has several advantages. It validates the use of a continuity equation in an "individuals-based" modeling setting, it provides a link between Lagrangian and Eulerian description, and it defines a "natural" numerical approach to those equations. I will describe recent rigorous results in that context. The main one deals with one-dimensional scalar conservation laws with nonnegative initial data, for which we prove that the a suitably designed "follow-the-leader" particle scheme approximates entropy solutions in the sense of Kruzkov in the many particle limit. Said result represents a new way to solve scalar conservation laws with bounded and integrable initial data. The same method applies to second order traffic flow models, to nonlocal transport equations, and to the Hughes model for pedestrian movements.
<> nonlinear stability (2) <> nonlinearity (2)

Statistical Analysis of Multi-day Solar Irradiance using a Threshold Time Series model

-

B9 H2 R2325

Abstract The analysis of solar irradiance has important applications in predicting solar energy production from solar power plants. Although the sun provides every day more energy than we need, the variability caused by environmental conditions affects electricity production. Most of the existing statistical models to forecast solar irradiance are linear and highly depend on normality assumptions. However, solar irradiance shows strong non-linearity and is only measured during the day time. Thus, we propose a new multi-day threshold autoregressive (TAR) model to quantify the variability of the

Manifold Markov Chain Monte Carlo Methods for Bayesian Inference In Diffusion Models

Prof. Alexandros Beskos, the Dept of Statistical Science, University College London (UCL)

-

KAUST

Bayesian inference for nonlinear diffusions, observed at discrete times,is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology - borrowing ideas from statistical physics and computational chemistry - for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process
<> numeric simulations (2) <> numerical discretization (2) <> Numerical Modeling (2) <> Numerical simulation and analysis (2)

KAUST Ph.D. student wins Society for Industrial and Applied Mathematics award

1 min read ·
Chiheb Ben Hammouda, a KAUST Ph.D. student in the University's Stochastic Numerics Research Group, recently won the best poster award at the Society for Industrial and Applied Mathematics (SIAM) Conference on Financial Mathematics & Engineering (FM19) held at the University of Toronto from June 4 to 7. His winning poster, titled "Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model," is one of several research projects carried out by Ben Hammouda under the supervision of KAUST Professor Raul Tempone.

Chiheb Ben Hammouda

Chiheb Ben Hammouda is a Ph.D. candidate at Stochastic Numerics Research Group (STOCHNUM) under the supervision of Professor Raul F. Tempone at King Abdullah University of Science and Technology (KAUST). Prior to joining Ph.D., Chiheb obtained a Master's degree in Applied Mathematics and Computational Sciences from KAUST, and a Bachelor's degree in multidisciplinary engineering from Ecole Polytechnique de Tunisie, Tunisia. Research Interests Chiheb's research interests include Stochastic modeling, Numerical simulation and analysis, Quantitative finance in particular option pricing, Stochastic
<> Numerical Solution of Partial Differential Equations (2) <> ocean circulation (2) <> oceanography (2) <> ODEs (2)