Thursday, April 22, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
We develop several new communication-efficient second-order methods for distributed optimization. Our first method, NEWTON-STAR, is a variant of Newton's method from which it inherits its fast local quadratic rate. However, unlike Newton's method, NEWTON-STAR enjoys the same per iteration communication cost as gradient descent. While this method is impractical as it relies on the use of certain unknown parameters characterizing the Hessian of the objective function at the optimum, it serves as the starting point which enables us to design practical variants thereof with strong theoretical guarantees. In particular, we design a stochastic sparsification strategy for learning the unknown parameters in an iterative fashion in a communication efficient manner. Applying this strategy to NEWTON-STAR leads to our next method, NEWTON-LEARN, for which we prove local linear and superlinear rates independent of the condition number. When applicable, this method can have dramatically superior convergence behavior when compared to state-of-the-art methods. Finally, we develop a globalization strategy using cubic regularization which leads to our next method, CUBIC-NEWTON-LEARN, for which we prove global sublinear and linear convergence rates, and a fast superlinear rate. Our results are supported with experimental results on real datasets, and show several orders of magnitude improvement on baseline and state-of-the-art methods in terms of communication complexity.
Thursday, April 15, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
Dynamic programming is an efficient technique to solve optimization problems. It is based on decomposing the initial problem into simpler ones and solving these sub-problems beginning from the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. We developed extensions of dynamic programming which allow us (i) to describe the set of objects under consideration, (ii) to perform a multi-stage optimization of objects relative to different criteria, (iii) to count the number of optimal objects, (iv) to find the set of Pareto optimal points for the bi-criteria optimization problem, and (v) to study the relationships between two criteria. The considered applications include optimization of decision trees and decision rule systems as algorithms for problem-solving, as ways for knowledge representation, and as classifiers, optimization of element partition trees for rectangular meshes which are used in finite element methods for solving PDEs, and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths.
Olivier Guéant, Professor, Applied Mathematics at Université Paris 1 Panthéon-Sorbonne, France
Tuesday, April 13, 2021, 15:00
- 18:00
https://kaust.zoom.us/j/97831248001
Contact Person
This 6-hour course covers the theory of optimal control in the case of discrete spaces / graphs. In the first part, we present the dynamic programming principle and the resulting Bellman equations. Bellman equations, which turn out to be a system of backward ordinary differential equations (ODE), are then thoroughly studied: in addition to existence and uniqueness results obtained through classical ODE tools and comparison principles, the long-term behavior of optimal control problems is studied using comparison principles and semi-group tools. The second part of the course focuses on a special case of optimal control problems on graphs for which closed-form solutions can be derived. The link with inventory management problems will be presented in details (in particular the link with the resolution of the Avellaneda-Stoikov problem, a classical problem in finance).
Thursday, April 08, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
COVID-19 has caused a global pandemic and become the most urgent threat to the entire world. Tremendous efforts and resources have been invested in developing diagnosis. Despite the various, urgent advances in developing artificial intelligence (AI)-based computer-aided systems for CT-based COVID-19 diagnosis, most of the existing methods can only perform classification, whereas the state-of-the-art segmentation method requires a high level of human intervention. In this talk, I will introduce our recent work on a fully-automatic, rapid, accurate, and machine-agnostic method that can segment and quantify the infection regions on CT scans from different sources. Our method is founded upon three innovations: 1) an embedding method that projects any arbitrary CT scan to a same, standard space, so that the trained model becomes robust and generalizable; 2) the first CT scan simulator for COVID-19, by fitting the dynamic change of real patients’ data measured at different time points, which greatly alleviates the data scarcity issue; and 3) a novel deep learning algorithm to solve the large-scene-small-object problem, which decomposes the 3D segmentation problem into three 2D ones, and thus reduces the model complexity by an order of magnitude and, at the same time, significantly improves the segmentation accuracy. Comprehensive experimental results over multi-country, multi-hospital, and multi-machine datasets demonstrate the superior performance of our method over the existing ones and suggest its important application value in combating the disease.
Olivier Guéant, Professor, Applied Mathematics at Université Paris 1 Panthéon-Sorbonne, France
Tuesday, April 06, 2021, 15:00
- 18:00
https://kaust.zoom.us/j/93184598804
Contact Person
This 6-hour course covers the theory of optimal control in the case of discrete spaces / graphs. In the first part, we present the dynamic programming principle and the resulting Bellman equations. Bellman equations, which turn out to be a system of backward ordinary differential equations (ODE), are then thoroughly studied: in addition to existence and uniqueness results obtained through classical ODE tools and comparison principles, the long-term behavior of optimal control problems is studied using comparison principles and semi-group tools. The second part of the course focuses on a special case of optimal control problems on graphs for which closed-form solutions can be derived. The link with inventory management problems will be presented in details (in particular the link with the resolution of the Avellaneda-Stoikov problem, a classical problem in finance).
Thursday, April 01, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
Wave functional materials are artificial materials that can control wave propagation as wish. In this talk, I will give a brief review on the progress of wave functional materials and reveal the secret behind the engineering of these materials to achieve desired properties. In particular, I will focus on our contributions on metamaterials and metasurfaces. I will introduce the development of effective medium, a powerful tool in modeling wave functional materials, followed by some illustrative examples demonstrating the intriguing properties, such as redirection, emission rate enhancement, wave steering and cloaking.
Mathieu Laurière, Postdoc, Operations Research and Financial Engineering, Princeton University, USA
Tuesday, March 30, 2021, 14:30
- 17:30
https://kaust.zoomus/j/91484640398
Contact Person
Mean field games and mean field control problems are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative situations with a large finite number of agents, and have found a broad range of applications, from economics to crowd motion, energy production and risk management. The solutions are typically characterized by a forward-backward system of partial differential equations (PDE) or stochastic differential equations (SDE).
Thursday, March 25, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
In modern large-scale inference problems, the dimension of the signal to be estimated is comparable or even larger than the number of available observations. Yet the signal of interest lies in some low-dimensional structure, due to sparsity, low-rankness, finite alphabet, ... etc. Non-smooth regularized convex optimization are powerful tools for the recovery of such structured signals from noisy linear measurements. Research has shifted recently to the performance analysis of these optimization tools and optimal turning of their hyper-parameters in high dimensional settings. One powerful performance analysis framework is the Convex Gaussian Min-max Theorem (CGMT). The CGMT is based on Gaussian process methods and is a strong and tight version of the classical Gordon comparison inequality. In this talk, we review the CGMT and illustrate its application to the error analysis of some convex regularized optimization problems.
Speakers from KAUST, CEMSE, PSE, G-CSC, IBRAE and INM RAS
Thursday, March 25, 2021, 10:30
- 17:00
Zoom invite is sent to registered users by email before the meeting.

To register, please fill form. The workshop will use Zoom. The link will be distributed to registered users by email before the meeting.

This workshop is devoted to numerical simulation of groundwater flow and subsurface contamination transport, as well as related problems. The main topics are mathematical modeling of the processes in porous media and the numerical methods for discretization, solution of the discretized systems and numerical treatment of inverse problems. In particular, fractured porous media and partially saturated aquifers will be concerned.

Mathieu Laurière, Postdoc, Operations Research and Financial Engineering, Princeton University, USA
Tuesday, March 23, 2021, 14:30
- 17:30
https://kaust.zoom.us/j/98430292725
Contact Person
Mean field games and mean field control problems are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative situations with a large finite number of agents, and have found a broad range of applications, from economics to crowd motion, energy production and risk management. The solutions are typically characterized by a forward-backward system of partial differential equations (PDE) or stochastic differential equations (SDE)
Samer Dweik, Postdoctoral Fellow, University of British Columbia
Monday, March 22, 2021, 11:00
- 12:00
https://kaust.zoom.us/j/97760962935
Contact Person
In this talk, we study a mean field game inspired by crowd motion in which agents evolve in a domain and want to reach its boundary minimizing their travel time. Interactions between agents occur through their dynamic, which depends on the distribution of all agents. First, we provide a Lagrangian formulation for our mean field game and prove existence of equilibria, which are shown to satisfy a MFG system. The main result, which relies on the semi-concavity of the value function of this optimal control problem, states that an L^p initial distribution of agents gives rise to an L^p distribution of agents at each time t>0.
Ewelina Zatorska, Senior Lecturer, Applied and Numerical Analysis, Imperial College London, UK
Thursday, March 18, 2021, 14:00
- 16:00
https://kaust.zoom.us/j/94549347967
Contact Person
In this lecture I will present broader spectrum of complex, multicomponent flows. For example, the models of compressible mixtures describe multicomponent fluids that are mixed on the molecular level. They are different from the models of the multi-phase flows from the first lecture, because there is no division of volume occupied by different species. The existence of global in time weak solutions, and global in time strong solutions for such systems will be explained, and some open problems related to singular limits and weak-strong uniqueness of solutions will be mentioned. At the end of the lecture I will also present another model of two-phase flow describing the motion of compressible and incompressible medium with an interphase given by a condition on the density. I will explain how to prove the existence of solutions and give some applications in modelling of crowd evacuation.
Jesper Tegner, Professor, BESE Division, KAUST
Thursday, March 18, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
In essence, science is about discovering regularities in Nature. It turns out that such regularities (laws) are written in the language of mathematics. In many cases, such laws are formulated and refined from fundamental “first principles.” Yet, in phenomenological areas such as biology, we have an abundance of data but lack “first principles.” Machine learning and deep learning, in particular, are remarkably successful in classification and prediction tasks. However, such systems, when trained on data, do not, as a rule, provide compact mathematical laws or fundamental first principles. Here we ask how we can identify interpretable compact mathematical laws from complex data-sets when we don’t have access to first principles. I will give an overview of this problem and provide some vignettes of our ongoing work in attacking this problem.
Martino Bardi, Professor, Mathematical Sciences, University of Padova, Italy
Wednesday, March 17, 2021, 15:00
- 17:00
https://kaust.zoom.us/j/98147555364
Contact Person
I will start recalling the definitions and basic properties of viscosity solutions to fully nonlinear degenerate elliptic equations, in particular the comparison principles. The main goal of the course is discussing two properties of subsolutions: the Strong Maximum Principle (SMP), i.e., if a subsolution in an open connected set attains an interior maximum then it is constant, and the Liouville property, i.e., if a subsolution in the whole space is bounded form above then it is constant. They are standard results for classical solutions of linear elliptic PDEs, and many extensions are known, especially for divergence form equations. My goal is explaining how the viscosity methods allow to turn around the difficulties of non-smooth solutions, fully nonlinear equations, and their possible degeneracies.
Jan Haskovec, Research Scientist, AMCS, KAUST
Monday, March 15, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/92541355313
Contact Person
Emergence of nontrivial patterns via collective actions of many individual entities is an ever-present phenomenon in physics, biology and social sciences. It has numerous applications in engineering, for instance, in swarm robotics. I shall demonstrate how tools from mathematical modeling and analysis help us gain understanding of fundamental principles and mechanisms of emergence. I will present my recent results in consensus formation and flocking models, focusing on the effects of noise and delay on their dynamics. Moreover, I will introduce continuum modeling framework for biological network formation, where emergence takes place through the interaction of structure and medium. The models are formulated in terms of ordinary, stochastic and partial differential equations. I shall explain how mathematical analysis of the respective models contributes to the understanding of how individual rules generate and influence the patterns observed on the global scale. A particular example from biology is development of leaf venation as a result of auxin-PIN interaction in the plant tissue. Here our model supported the hypothesis that a-priori polarization of auxin transport does not play a decisive role in leaf venation.
Thursday, March 11, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
Small-scale cut and fold patterns imposed on sheet material enable its morphing into three-dimensional shapes. This manufacturing paradigm has received much attention in recent years and poses challenges in both fabrication and computation. It is intimately connected with the interpretation of patterned sheets as mechanical metamaterials, typically of negative Poisson ratio. We discuss a fundamental geometric question, namely the targeted programming of a shape morph from a flat sheet to a curved surface, or even between any two shapes. The solution draws on differential geometry, discrete differential geometry, geometry processing and geometric optimization.
Martino Bardi, Professor, Mathematical Sciences, University of Padova, Italy
Wednesday, March 10, 2021, 15:00
- 17:00
https://kaust.zoom.us/j/97385719868
Contact Person
I will start recalling the definitions and basic properties of viscosity solutions to fully nonlinear degenerate elliptic equations, in particular the comparison principles. The main goal of the course is discussing two properties of subsolutions: the Strong Maximum Principle (SMP), i.e., if a subsolution in an open connected set attains an interior maximum then it is constant, and the Liouville property, i.e., if a subsolution in the whole space is bounded form above then it is constant. They are standard results for classical solutions of linear elliptic PDEs, and many extensions are known, especially for divergence form equations. My goal is explaining how the viscosity methods allow to turn around the difficulties of non-smooth solutions, fully nonlinear equations, and their possible degeneracies.
Dr. Ewelina Zatorska, Senior Lecturer in the Applied and Numerical Analysis, Imperial College London
Tuesday, March 09, 2021, 15:00
- 16:00
https://kaust.zoom.us/j/92756762717
Contact Person
In this talk, I will present the recent developments in the topic of the existence of solutions to the two-fluid systems. The compensated compactness technique of P.-L. Lions and E. Feireisl for single-component fluids has certain limitations, distinctly in the context of multi-component flow models. A particular example of such a model is the two-fluids Stokes system with a single velocity field and two densities, and with an algebraic pressure law closure. The first result that I will present is the existence of weak solutions for such a system, using the compactness criterion introduced recently by D. Bresch and P.-E. Jabin. I will also outline an innovative construction of solutions relying on the G. Crippa and C. DeLellis stability estimates for the transport equation. In the last part of my talk, I will relate to a couple of more recent results: the existence of solutions to the one-dimensional system, non-uniqueness of solutions to the inviscid system, and I will comment on issues around weak-strong uniqueness.
Martino Bardi, Professor, Mathematical Sciences, University of Padova, Italy
Monday, March 08, 2021, 15:00
- 17:00
https://kaust.zoom.us/j/92420134266
Contact Person
I will start recalling the definitions and basic properties of viscosity solutions to fully nonlinear degenerate elliptic equations, in particular the comparison principles. The main goal of the course is discussing two properties of subsolutions: the Strong Maximum Principle (SMP), i.e., if a subsolution in an open connected set attains an interior maximum then it is constant, and the Liouville property, i.e., if a subsolution in the whole space is bounded form above then it is constant. They are standard results for classical solutions of linear elliptic PDEs, and many extensions are known, especially for divergence form equations. My goal is explaining how the viscosity methods allow to turn around the difficulties of non-smooth solutions, fully nonlinear equations, and their possible degeneracies.
Aram Karakhanyan, Professor, School of Mathematics, University of Edinburgh, UK
Tuesday, March 02, 2021, 15:00
- 18:00
https://kaust.zoom.us/j/91736661597
Contact Person
In this course I will discuss the basics of the classical theory of free boundary problems. We will focus on two problems; the Alt-Caffarelli and obstacle problem. In the first part of the course we will discuss the regularity of the solutions, and in the remainder the full and partial regularity of the free boundary
Aram Karakhanyan, Professor, School of Mathematics, University of Edinburgh, UK
Tuesday, February 23, 2021, 15:00
- 18:00
https://kaust.zoom.us/j/92984769007
Contact Person
In this course I will discuss the basics of the classical theory of free boundary problems. We will focus on two problems; the Alt-Caffarelli and obstacle problem. In the first part of the course we will discuss the regularity of the solutions, and in the remainder the full and partial regularity of the free boundary.
Thursday, February 18, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Machine learning has been widely applied to diverse problems of forwarding prediction and backward design. The former problem of forwarding prediction is to predict the reaction of a system given the input x, i.e., y=f(x). This talk will introduce several groups of algorithms for learning the prediction function f. The backward design is an inverse problem, predicting the input x according to the system reaction y, i.e., x=g(y). This is an important problem for the design of chemical material and optical devices. This talk will introduce several successful application examples of machine learning algorithms on the backward design problems.
Ahmed Kebaier, Associate Professor, Laboratory Analysis, Geometry and Application (LAGA), University Sorbonne Paris Nord (USPN)
Tuesday, February 16, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/93976998457
Contact Person
In this talk, we present our theoretical results recently developed around various types of applications. These results cover asymptotic and non-asymptotic analysis, functional limit theorems, concentration inequalities, and Malliavin calculus techniques elaborated for several classes of stochastic processes. We showcase through concrete examples the role of these results in taking up various challenges at the cutting-edge of modern applied probability.
David Ambrose, Professor, Department of Mathematics at Drexel University, USA
Monday, February 15, 2021, 17:00
- 19:00
https://kaust.zoom.us/j/93687627308
Contact Person
The time-dependent PDE system for mean field games is a coupled pair of parabolic equations, one forward in time and the other backward in time. The lecturer will demonstrate two techniques for proving existence and uniqueness of solutions for this system. The first of these techniques is inspired by work in fluid dynamics, as a similar forward-backward structure for vortex sheets was discovered by Duchon and Robert in the 1980s. Adapting the ideas of Duchon and Robert gives existence and uniqueness of solutions for the time-dependent mean field games system in function spaces based on the Wiener algebra. The second technique to be demonstrated by the speaker uses Sobolev spaces, and is an adaptation of the energy method to the forward-backward setting.