Abstract

Due to the influence of geological activities, fractures are c

Numerous problems in scientific computing can be formulated as optimization problems of suitable parametric models over parameter spaces. Neural network and deep learning methods provide unique capabilities for building and optimizing such models, especially in high-dimensional settings.

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Digital geometry processing technology is widely used in compu

DNA replication is a fundamental cellular process and its precise regulation is crucial for maintaining genomic integrity. Inspired by the mathematical parallelism between DNA replication and the nucleation problem in one-dimensional crystal growth kinetics, we introduce a model that maps whole-genome replication dynamics based on the firing rate profiles of replication origins and fork movement.

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The accurate numerical prediction of complex processes in medicine, science, and engineer

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This seminar is an online interview for a postdoctoral position in KAUST.

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.