Events

Mar 23 - Mar 29, 2025

Dimension Liftings for Quantum Computation of Partial Differential Equations and Related Problems

Shi Jin, Director of Institute of Natural Sciences, Chair Professor of Mathematics, Shanghai Jiao Tong University

Mar 25, 16:00 - 17:00

B1 L3 R3119

PDEs Schrödinger equation quantum simulation quantum computing

This lecture presents a systematic framework for developing quantum simulation algorithms for general differential equations, using dimension lifting to transform nonlinear and time-dependent problems into forms solvable by simulating the Schrödinger equation.

Jan 12 - Jan 18, 2025

Dec 22 - Dec 28, 2024

SDE, BSDE under Nonlinear Expectation and Fully Nonlinear Path-dependent Parabolic PDE

Shige Peng, Academician of the Chinese Academy of Sciences, Professor of Mathematics, and Chairman of the Research Center for Mathematics and Interdisciplinary Sciences at Shandong University

Dec 22, 11:00 - 12:00

B1, L3, R3119

In this talk we begin with stochastic differential equations (SDE, or FSDE) and backward stochastic differential equations (BSDE) driven by a d-dimensional G-Brownian motion defined on a nonlinear expectation space. The corresponding BSDE is then a path-solution of the corresponding (deterministic) path-dependent fully nonlinear partial differential equation of second order. This, combined with the powerful deep learning approach, provides an important tool for solving numerical solutions of a system of high dimensional partial differential equations of parabolic type.

Dec 8 - Dec 14, 2024

Dec 1 - Dec 7, 2024

Causal Recommender Systems

Xiao-Hua (Andrew) Zhou

Dec 5, 16:00 - 17:00

B1, L3, R3119

In this presentation, I will give an overview of the recommender systems (RS) from causal prospective and discuss my team works on the causal recommendation. First, I introduce the potential outcome framework in recommender system. Second, I provide a brief overview for the debiasing strategies. Then I introduce our woks to address the bias in RS from causal perspective. FinallyI discuss some open problem and future direction in recommender systems.

Nov 24 - Nov 30, 2024

Constraint Maps and their free boundaries

Henrik Shahgholian

Nov 26, 16:00 - 17:00

Building 1, Level 3, Room 3119

I shall give an introduction to the topic of constraint maps, which sits on the intersection of free boundaries, and harmonic maps. The talk will start at level of graduate and will also smoothly merge current work that has been developed recently.

Nov 17 - Nov 23, 2024

Oct 27 - Nov 2, 2024

Fundamentals of flow of fluids and transport of solutes and colloids in porous media

Oct 31, 14:00 - Dec 5, 16:30

B1, L3, R3119

In this short course, we will cover the fundamentals of fluid flow and the transport of solutes and colloids in porous media.

Jun 9 - Jun 15, 2024

On the Natural Gradient Descent

Prof. Levon Nurbekyan

Jun 11, 16:00 - 17:00

KAUST

gradient methods

Abstract 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. Nevertheless, neural networks and deep learning techniques are often opaque and resistant to precise control of their mathematical properties in terms of architectures, hyperparameters, etc. Consequently, optimizing neural network models can result in a laborious hyperparameter tuning process that

May 26 - Jun 1, 2024

A Whole-genome Model of DNA Replication in Human Cells

Dr. Francisco Berkemeier, University of Cambridge

May 28, 16:00 - 17:00

B5 L5 R5209

genome biological models

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.

May 12 - May 18, 2024

Models, Methods, Applications: HPC in Medicine, Science, Engineering, and AI

Rolf Krause, Professor, Applied Mathematics and Computational Sciences

May 14, 16:00 - 17:00

B3 L5 R5209

machine learning medicine AI

Abstract The accurate numerical prediction of complex processes in medicine, science, and engineering requires a well balanced interplay of mathematical models, numerical methods, and scientific software. In this talk, we discuss along different examples from engineering, earth-sciences, and medicine the various challenges in building predictive models. Our focus will be on the algorithmic aspects, i.e. on the numerical methods, -may it be finite elements or neural networks in the context of massive parallelism. We will present in particular parallel preconditioners for non-linear problems

May 5 - May 11, 2024

Apr 28 - May 4, 2024

Cell-centered extrapolation cascadic multigrid method for solving diffusion equation with discontinuous coeffcients

Xiaoxin Wu, Central South University, China

May 2, 09:00 - 10:00

https://meeting.tencent.com/dm/bpUiLe2AlgBC

Multigrid

This seminar is an online interview for a postdoctoral position in KAUST.
Virtual Element Approximation of Eigenvalue Problems

Prof. Francesca Gardini, Università di Pavia

Apr 30, 16:00 - 17:00

B1 L3 R3119

Virtual Element Method Elgenvalue FEMSimulation PDE

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.

Apr 21 - Apr 27, 2024

Structure-conforming Operator Learning via Transformers

Prof. Shuhao Cao, University of Missouri–Kansas City

Apr 22, 16:00 - 17:00

KAUST

transformers

Abstract GPT, Stable Diffusion, AlphaFold 2, etc., all these state-of-the-art deep learning models use a neural architecture called "Transformer". Since the emergence of "Attention Is All You Need", Transformer is now the ubiquitous architecture in deep learning. At Transformer's heart and soul is the "attention mechanism". In this talk, we shall give a specific example the following research program: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? An attention-based deep direct

Apr 14 - Apr 20, 2024

Neural Operators: Theory, Architecture, and Applications for PDEs

Xinliang Liu, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

Apr 16, 16:00 - 17:00

B1 L3 R3119

Neural Operator Multigrid

Abstract Neural operator methods provide a novel approach for solving or learning the complex mappings from parameters to solutions arising from intricate physical systems. In this talk, I will cover the foundational aspects of neural operators, encompassing both theoretical frameworks and algorithmic developments, including some well-known neural operator architectures. Additionally, I will share our recent work on applying the neural operator method to multiscale partial differential equations (PDEs). To tackle the challenges of multiscale PDEs, we have developed a neural operator with a

Mar 24 - Mar 30, 2024

Hessian-dependent Functionals: Mean Field Games, Free Boundaries and Improved Regularity

Prof. Edgard Pimentel, Department of Mathematics of the University of Coimbra

Mar 26, 16:00 - 17:00

B2 L5 R5220

Hessain-dependent elasticity mean-field games Free Boundaries viscous

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.

Feb 25 - Mar 2, 2024

Critical Phenomena in Financial Markets and Social Networks

Prof. Christof Schmidhuber, ZHAW School of Engineering

Feb 27, 16:00 - 17:00

B9 L2 R2322

Financial Market Social Network Analysis Critical Phenomena Arbitrageurs

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.

Feb 11 - Feb 17, 2024

Approximation and Generalization Errors in Deep Neural Networks for Sobolev Spaces measured by Sobolev Norms

Dr. Yahong Yang, Department of Mathematics, Penn State University

Feb 14, 16:00 - 17:00

KAUST

deep neural networks approximation Sobolev Spaces

Abstract In this presentation, we initially discuss the approximation capabilities of deep neural networks (DNNs) with ReLU and the square of ReLU as activation functions for Sobolev functions measured by the Sobolev norms \(W^{m,p}\) where \(m \ge 1\). Subsequently, we consider how to address the issue of the curse of dimensionality for DNNs’ approximation. Finally, we analyze the generalization errors associated with DNNs using such Sobolev loss functions. Additionally, we provide recommendations on when to opt for deeper NNs versus wider NNs, considering factors such as the number of sample

Feb 4 - Feb 10, 2024

Fast Solution Methods for Wave Propagation Problems: From Classical Domain Decomposition Solvers to Learning

Prof. Dr. Victorita Dolean, Mathematics and Computer Science, Scientific Computing, TU Eindhoven

Feb 6, 16:00 - 17:00

B2 L5 R5220

wave propagation numerical methods

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.

Jan 21 - Jan 27, 2024

A Posteriori Error Estimation and Adaptivity for Elliptic Interface Problems

Prof. Zhiming Chen, Academy of mathematics and Systems Science, Chinese Academy of Sciences

Jan 24, 14:30 - 16:00

B4 L5 R5220

adaptive methods linear elliptic equations

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.
Arbitrarily High-order Finite Element Methods for Arbitrarily Shaped Domains with Automatic Mesh Generation

Prof. Zhiming Chen, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Jan 23, 16:00 - 17:00

B2 L5 R5220

High-order FEM adaptive methods

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.

Jan 14 - Jan 20, 2024

Unveiling Insights from "Gradient Descent Converges Linearly for Logistic Regression on Separable Data"

Bang An, Ph.D. Student, Applied Mathematics and Computational Sciences

Jan 17, 10:00 - 11:00

B1 L0 R0118

gradient methods Regression Models

Abstract In this presentation, I will share a paper titled "Gradient Descent Converges Linearly for Logistic Regression on Separable Data", a work highly related to my ongoing research. I will explore its relevance to my current research topic and discuss the inspiration for our future works. Abstract of the paper: We show that running gradient descent with variable learning rate guarantees loss f(x) \leq 1.1f(x^*)+\epsilon for the logistic regression objective, where the error \epsilon decays exponentially with the number of iterations and polynomially with the magnitude of the entries of an

Jan 7 - Jan 13, 2024

Physics-informed Neural Networks for Learning the Homogenized Coefficients of Multiscale Elliptic Equations

Dr. Jun Sur Richard Park, Korea Institute for Advanced Study

Jan 10, 10:00 - 11:00

KAUST

Physics-informed Neural Networks multiscale methods Homogenization

Abstract Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodicity of the multiscale coefficients, thus finding the G-limits often requires sophisticated techniques in more general settings even when multiscale coefficient is known, if possible. Alternatively, we propose a simple approach to estimate the G-limits from (noisy-free or noisy) multiscale solution data, either from the existing forward

Dec 31 - Jan 6, 2023

A Combination of Physics-informed Neural Networks with the Fixed-stress Splitting Iteration for Solving Biot’s Model

Prof. Mingchao Cai, Department of Mathematics, Morgan State University

Jan 3, 16:00 - 17:00

KAUST

Physics-informed Neural Networks

Abstract In this study, we aim to solve Biot’s consolidation models by employing physics-informed neural networks. Based on the fixed-stress splitting method, loss functions are designed for the displacement variable and the pressure variables separately. Such a strategy enables us to train two independent and smaller neural networks. The coupling of different variables is realized via the fixed-stress iterative algorithm. Numerical experiments are provided to show that the fixed-stress iterative algorithm can improve the performance of neural network approximations of the solution of Biot’s

Dec 24 - Dec 30, 2023

An Unconditionally Energy-stable and Orthonormality-preserving Iterative Scheme for the Kohn-Sham Gradient Flow Based Model

Xiuping Wang, AMCS, CEMSE, KAUST

Dec 27, 10:00 - 11:00

B1 L0 R0118

Kohn-Sham gradient flow Orthonormality-preserving

Abstract We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in time but still continuous in space. The component-wise splitting iterative scheme changes one wave function at a time, similar to the Gauss-Seidel iteration for solving a linear equation system. At the time step n, the orthogonality of the wave function being updated to other wave functions is preserved by projecting the gradient of the Kohn-Sham

Dec 17 - Dec 23, 2023

Deep Neural Network Approximation via Function Compositions

Dr. Shijun Zhang, Department of Mathematics, Duke University

Dec 20, 19:00 - 20:00

KAUST

deep neural networks approximation

Abstract Deep neural networks have brought transformative changes in areas such as image recognition and healthcare, yet their underlying theoretical principles remain somewhat elusive. The main emphasis of this presentation is to explore the theoretical dimensions of deep neural networks, with a special focus on evaluating their approximation capabilities. We begin by assessing the approximation errors in ReLU networks when they attempt to approximate various target functions, including (Lipschitz) continuous functions, polynomials, and smooth functions. Utilizing the concept of Vapnik

Dec 10 - Dec 16, 2023

Arabic NLP @ AI Initiative

Oleg Serikov, AI Initiative, KAUST

Dec 13, 09:00 - 10:00

B1 L3 R3309

Arabic natural language processing

Abstract Rather than a talk, this firstmost is an invitation to discussion. We’re working on pre-training LLMs for Arabic and evaluation at AI Init and will share the progress, as well as some afterthoughts. Right now our efforts comprise two directions of work: pre-training (we learn to pretrain various models from scratch) and evaluation (just have it in-house + to not only observe perplexity on the pretraining dashboard). Figuring out the potential collaboration directions is our key interest for this meeting.

Dec 3 - Dec 9, 2023

Nov 26 - Dec 2, 2023

Nov 12 - Nov 18, 2023

Multiscale Learning of High-dimensional Cell Fate

Prof. Qing Nie, Department of Mathematics, Department of Developmental and Cell Biology, NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine

Nov 16, 15:30 - 17:00

B9 L4 R4225

Abstract Cells make fate decisions in response to dynamic environments, and multicellular structures emerge from multiscale interplays among cells and genes in space and time. The recent single-cell genomics technology provides an unprecedented opportunity to profile cells for all their genes. While those measurements provide high-dimensional gene expression profiles for all cells, it requires fixing individual cells that lose many important spatiotemporal information. Is it possible to infer temporal relationships among cells from single or multiple snapshots? How to recover spatial

Nov 5 - Nov 11, 2023

A Brief Overview of Arabic NLP

Prof. Sakhar B. Alkhereyf

Nov 7, 15:30 - 17:00

B5 L5 R5209

nlp Arabic natural language processing

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).

Oct 29 - Nov 4, 2023

Stochastic Optimal Control with Exercise Rate Optimization and Markovian Projections: Pricing American Options and Importance Sampling Applications

Raul Tempone, Professor, Applied Mathematics and Computational Sciences

Oct 31, 15:30 - 17:00

B5 L5 R5209

sampling Markovian projection

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.

Sep 24 - Sep 30, 2023

Device accelerated solvers for PDEs. Current status and future perspectives

Stefano Zampini, Senior Research Scientist, Hierarchical Computations on Manycore Architectures

Sep 26, 16:00 - 17:00

B5 L5 R5220

Shaheen GPU supercomputing petsc PDEs

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.

Sep 17 - Sep 23, 2023

Additive Schwarz Methods for Convex Optimization - Theory and Applications

Jongho Park, Research Scientist, Applied Mathematics and Computational Sciences

Sep 19, 16:00 - 17:00

B5 L5 R5209

Additive Schwarz methods convex optimization

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.

Apr 9 - Apr 15, 2023

High-order non-conforming finite elements for the Stokes equation

Stefan Sauter, Professor, Institute of Mathematics, University of Zurich

Apr 11, 16:00 - 17:00

B2 L5 R5220

High-order non-confirming Finite elements stokes equation

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.

Apr 2 - Apr 8, 2023

Numerical Methods for Energy Minimisation: Application to Machine Learning Algorithms

Prof. Charalambos Makridakis, Director of the Institute of Applied and Computational Mathematics of FORTH, Greece

Apr 4, 16:00 - 17:00

B2 L5 R5220

numerical methods energy minimization Applied Machine Learning

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.

Mar 26 - Apr 1, 2023

Scalable parallel solvers for cardiac reaction-diffusion models and applications

Luca F. Pavarino, Professor, Department of Mathematics, Università degli Studi di Pavia

Mar 28, 16:00 - 17:00

B2 L5 R5220

Applied Partial Differential Equations parallel simulations

After a brief introduction to the field of Computational Cardiology and cardiac reentry, we introduce and study some scalable domain decomposition preconditioners for cardiac reaction-diffusion models, discretized with splitting semi-implicit techniques in time and isoparametric finite elements in space.

Feb 5 - Feb 11, 2023

Theoretical understanding of learning dynamics in modern deep learning

Dr. Zhanxing Zhu, Senior Research Professor. Changping National lab, Beijing

Feb 7, 16:00 - 17:00

B2 L5 R5209

Coffee Time: 15:30-16:00. It has been a long-standing debate that “Is deep learning alchemy or science? ”, since the success of deep learning mainly relies on various engineering design and tricks, and lack of theoretical foundation. Unfortunately, the underlying mechanism of deep learning is still mysterious, severely limiting its further development from both theoretical and application aspects.

Sep 11 - Sep 17, 2022

On the resolution of a theoretical question related to the nature of local training in federated learning

Peter Richtarik, Professor, Computer Science

Sep 13, 15:30 - 17:00

B1 L3 R3119

machine learning mathematical optimization communications algorithms

In this talk, I will explain the problem, its solution, and some subsequent work generalizing, extending and improving the ProxSkip method in various ways. We study distributed optimization methods based on the local training (LT) paradigm - achieving improved communication efficiency by performing richer local gradient-based training on the clients before parameter averaging - which is of key importance in federated learning. Looking back at the progress of the field in the last decade, we identify 5 generations of LT methods: 1) heuristic, 2) homogeneous, 3) sublinear, 4) linear, and 5) accelerated. The 5th generation, initiated by the ProxSkip method of Mishchenko et al (2022) and its analysis, is characterized by the first theoretical confirmation that LT is a communication acceleration mechanism.

Aug 28 - Sep 3, 2022

Emergence of transportation networks as a self-regulated process

Jan Haskovec, Senior Research Scientist, Applied Mathematics and Computational Sciences

Aug 30, 15:30 - 17:00

B1 L3 R3119

random process transportation networks

In this talk, we shall explain how transportation networks emerge as a self-regulating process, with a particular focus on applications in biology (leaf venation in plants, neuronal networks in animals). We start by introducing a purely diffusive model with tensor-valued diffusivity, derived as a gradient flow of a broad class of entropy dissipations. The introduction of a prescribed electric potential leads to the Fokker-Planck equation. We show that with quadratic entropy density modeling Joule heating, the model is convex with respect to the diffusivity tensor.