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.

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GPT, Stable Diffusion, AlphaFold 2, etc., all these state-of-t

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

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.

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 In this presentation, we initially discuss the approxima

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.

Coffee time: 15:30–16:00. We consider high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems, which release the work of body-fitted mesh generation and allow us to design adaptive finite element methods for solving curved geometric singularities.

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In this presentation, I will share

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Multiscale elliptic equations with

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In this study, we aim to solve Biot’s consolidation models by

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We propose an unconditionally energy-stable, orthonormality-pr

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Deep neural networks have brought transformative changes in areas such as image recogniti

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Rather than a talk, this firstmost is an invitation to discussion.

Coffee Time: 15:30 - 16:00. The phase-field model, a powerful modeling tool for dealing with interface problems, has been widely used in various fields such as computational physics, computational biology, materials engineering, and even image processing. The dissipation of free energy is an important and fundamental property of the phase-field model.

Splitting methods have been shown to a useful tool in solving phase field equations. However, rigorous nonlinear stability analysis has not been available. In this short course, we will discuss some recent development in this direction.

A fascination with symmetric forms seems to be an innate feature of human perception and for millennia it has influenced art and natural philosophy. The concept of symmetry is one of the very few on which mathematicians and physicists agree, namely that Symmetry ≡ Groups. We describe some special symmetries and related problems including symmetric polynomials and monstrous moonshine.

We will give an overview of the development of Abstract Algebra from Galois to our time. The talk will be accessible to general audience with basic mathematical background.

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Cells make fate decisions in response to dynamic environments, and multicellular structur

Arabic, being one of the six official languages of the United Nations and the sixth most commonly spoken language across the globe, holds a significant stance in the linguistic landscape. The diglossic nature of Arabic, where Classical Arabic (CA), Modern Standard Arabic (MSA), and various dialects coexist, coupled with its complex morphological structure, presents a unique set of challenges and opportunities for the domain of Natural Language Processing (NLP).

This talk begins with the problem of pricing American basket options in a multivariate setting. In high dimensions, nonlinear PDE methods for solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation become expensive due to the curse of dimensionality.

In the next months, KAUST expects to place into service Shaheen-3, a supercomputer with a GPU partition whose planned 1 Exaflop/s HPL AI capability would rank it in the Top 6 globally if delivered today.

This talk is devoted to additive Schwarz methods for convex optimization. First, we propose an abstract framework for additive Schwarz methods for convex optimization. The framework's flexibility allows it to handle composite optimization problems and inexact local solvers. Moreover, it establishes a sharp convergence theory that agrees with the classical theory when addressing linear problems.