Adjunct Prof. Levon Nurbekyan, Department of Mathematics at UCLA
Wednesday, June 16, 2021, 19:00
- 21:00
https://kaust.zoom.us/j/99650559855
Contact Person
I will focus on the envelope formula, an essential tool and a unifying framework for the first-order analysis of value functions in parameter-dependent optimization problems. In particular, I will discuss formal differentiation rules of value functions and derive a few familiar examples as particular cases of this technique, such as the Hamilton-Jacobi-Bellman PDE and the adjoint method. I will then discuss how to turn these formal differentiation rules into rigorous theorems via perturbation analysis of optimization problems. Finally, I will apply these ideas to parameter identification problems based on optimal transportation distances and variational analysis of mean-field games.
Adjunct Prof. Levon Nurbekyan, Department of Mathematics at UCLA
Monday, June 14, 2021, 19:00
- 21:00
https://kaust.zoom.us/j/94185848606
Contact Person
I will focus on the envelope formula, an essential tool and a unifying framework for the first-order analysis of value functions in parameter-dependent optimization problems. In particular, I will discuss formal differentiation rules of value functions and derive a few familiar examples as particular cases of this technique, such as the Hamilton-Jacobi-Bellman PDE and the adjoint method. I will then discuss how to turn these formal differentiation rules into rigorous theorems via perturbation analysis of optimization problems. Finally, I will apply these ideas to parameter identification problems based on optimal transportation distances and variational analysis of mean-field games.
Marco Cirant, Assistant Professor, Mathematic Department, University of Padova, Italy
Thursday, June 10, 2021, 14:00
- 17:00
https://kaust.zoom.us/j/97279416022
Contact Person
In this short course I will introduce some elements of bifurcation theory, such as the Lyapunov-Schmidt reduction, the bifurcation from the simple eigenvalue, and the Krasnoselski bifurcation theorem. Then, I will discuss some applications to the theory of MFG systems: existence of periodic in time solutions, and multi-population problems.
Adjunct Prof. Levon Nurbekyan, Department of Mathematics at UCLA
Wednesday, June 09, 2021, 19:00
- 21:00
https://kaust.zoom.us/j/96385321063
Contact Person
I will focus on the envelope formula, an essential tool and a unifying framework for the first-order analysis of value functions in parameter-dependent optimization problems. In particular, I will discuss formal differentiation rules of value functions and derive a few familiar examples as particular cases of this technique, such as the Hamilton-Jacobi-Bellman PDE and the adjoint method. I will then discuss how to turn these formal differentiation rules into rigorous theorems via perturbation analysis of optimization problems. Finally, I will apply these ideas to parameter identification problems based on optimal transportation distances and variational analysis of mean-field games.
Marco Cirant, Assistant Professor, Mathematic Department, University of Padova, Italy
Tuesday, June 08, 2021, 15:00
- 18:00
https://kaust.zoom.us/j/94665268072
Contact Person
In this short course I will introduce some elements of bifurcation theory, such as the Lyapunov-Schmidt reduction, the bifurcation from the simple eigenvalue, and the Krasnoselski bifurcation theorem. Then, I will discuss some applications to the theory of MFG systems: existence of periodic in time solutions, and multi-population problems.
Wilfrid Gangbo, Professor of mathematics at the University of California, Los Angeles
Tuesday, May 25, 2021, 19:00
- 21:00
https://kaust.zoom.us/j/95232883217
Contact Person
We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim).
Wilfrid Gangbo, Professor of mathematics at the University of California, Los Angeles
Tuesday, May 11, 2021, 19:00
- 21:00
https://kaust.zoom.us/j/94916518261
Contact Person
We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim).
Thursday, May 06, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person

Abstract

As simulation and analytics enter the exascale era, numerical algorithms must span a wide

Wilfrid Gangbo, Professor of mathematics at the University of California, Los Angeles
Tuesday, May 04, 2021, 19:00
- 21:00
https://kaust.zoom.us/j/96125002593
Contact Person
We recall the state of the art and the role of polyconvexity in the calculus of variations. Then we keep our focus on a particular polyconvex function, applicable to the study of Euler incompressible fluids. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional which corresponds to the H1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the Lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. We introduce a minimizing movement scheme to construct Lr-solutions of the Navier-Stokes equation (NSE) for a short time interval. Our scheme is an improved version of the split scheme introduced in Ebin–Marsden in 1970, and allows us to solve the equation with less regular initial data as opposed to more regular initial data requirement in the 1970 Ebin–Marsden’s work. (Most of the material of these lectures is based on a joint work with M. Jacobs and I. Kim)
Georgiy L. Stenchikov, Professor, Earth Science and Engineering
Thursday, April 29, 2021, 12:00
- 13:00
https://kaust.zoom.us/j/94262797011?pwd=ZXBBcnltQ3JvZkdhWFZjTEptL3FmUT09
Contact Person
Explosive volcanic eruptions are magnificent events that in many ways affect the Earth’s natural processes and climate. They cause sporadic perturbations of the planet’s energy balance, activating complex climate feedbacks and providing unique opportunities to better quantify those processes. We know that explosive eruptions cause cooling in the atmosphere for a few years, but we have just recently realized that they affect the major climate variability modes and volcanic signals can be seen in the subsurface ocean for decades. The volcanic forcing of the previous two centuries offsets the ocean heat uptake and diminishes global warming by about 30%. In the future, explosive volcanism could slightly delay the pace of global warming and has to be accounted for in long-term climate predictions. The recent interest in dynamic, microphysical, chemical and climate impacts of volcanic eruptions is also excited by the fact these impacts provide a natural analog for climate geoengineering schemes involving the deliberate development of an artificial aerosol layer in the lower stratosphere to counteract global warming. In this talk, I will discuss these recently discovered volcanic effects and specifically pay attention to how we can learn about the hidden Earth-system mechanisms activated by explosive volcanic eruptions.
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.