Events

Sep 4 - Aug 29, 2021

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  Sequential Monte Carlo Algorithms for Agent-Based Models of Disease Transmission

  Jeremy Heng, Applied Mathematics and Computational Sciences (AMCS), ESSEC Business School, Singapore

  Sep 1, 13:00 - 14:00

  KAUST

  We consider statistical inference for a class of agent-based SIS and SIR models. In these models, agents infect one another according to random contacts made over a social network, with an infection rate that depends on individual attributes. Infected agents might recover according to another random mechanism that also depends on individual attributes, and observations might involve occasional noisy measurements of the number of infected agents. Likelihood-based inference for such models presents various computational challenges. In this talk, I will present various sequential Monte Carlo algorithms to address these challenges.

Aug 21 - Aug 15, 2021

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  Machine Learning in Healthcare: When Low Sample Size is not a Limitation

  Dr. Ricardo Henao, Biostatistics and Bioinformatics, Duke University

  Aug 17, 14:30 - 15:30

  KAUST

  In this talk, I will describe three use cases that highlight present challenges and opportunities for the development of machine learning methodology for applications in healthcare. First, I will describe the development of simple word embedding approaches for bag of-documents classification and its applications to diagnosis of peripheral artery disease from clinical narratives. Second, I will present an approach for volumetric image classification that leverages attention mechanisms, contrastive learning and feature-encoding sharing for geographic atrophy prognosis from optical coherence tomography images. Third, I will discuss machine learning approaches for multi-modal and multi-dataset integration for biomarker discovery from molecular (omics) data. To conclude, I will summarize the contributions and insights in each of these different directions in which relatively low sample sizes are the common denominator.
• 

  AMCS Workshop for Higher Education Instructors

  Aug 15, 10:00 - Aug 26, 16:00

  KAUST Campus

  linear algebra Programming language

  Workshop's Agenda View Workshop's Agenda. Topics for the event: Core sessions on Linear Algebra Core sessions on applications on emerging teaching methodologies Programming language (practical applications) Keynote lectures on emerging teaching methodologies and current research applications Core lab and research center visits and presentations Networking sessions and social activities with KAUST faculty, researchers, alumni, and students This workshop is for TAs and lecturers from in-Kingdom Universities. It is not open to KAUST students and the community. Applications are closed now!

Jun 19 - Jun 13, 2021

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  The envelope formula and its applications in variational analysis - Session 3

  Adjunct Prof. Levon Nurbekyan, Department of Mathematics at UCLA

  Jun 16, 19:00 - 21:00

  KAUST

  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.
• 

  The envelope formula and its applications in variational analysis - Session 2

  Adjunct Prof. Levon Nurbekyan, Department of Mathematics at UCLA

  Jun 14, 19:00 - 21:00

  KAUST

  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.

Jun 12 - Jun 6, 2021

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  An introduction to bifurcation theory and applications to MFG - Session 2

  Marco Cirant, Assistant Professor, Mathematic Department, University of Padova, Italy

  Jun 10, 14:00 - 17:00

  KAUST

  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.
• 

  The envelope formula and its applications in variational analysis - Session 1

  Adjunct Prof. Levon Nurbekyan, Department of Mathematics at UCLA

  Jun 9, 19:00 - 21:00

  KAUST

  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.
• 

  An introduction to bifurcation theory and applications to MFG - Session 1

  Marco Cirant, Assistant Professor, Mathematic Department, University of Padova, Italy

  Jun 8, 15:00 - 18:00

  KAUST

  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.

May 29 - May 23, 2021

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  Minimization problems involving polyconvex functionals and an H1-projection problem - Session 3

  Wilfrid Gangbo, Professor of mathematics at the University of California, Los Angeles

  May 25, 19:00 - 21:00

  KAUST

  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).

May 15 - May 9, 2021

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  Minimization problems involving polyconvex functionals and an H1-projection problem - Session 2

  Wilfrid Gangbo, Professor of mathematics at the University of California, Los Angeles

  May 11, 19:00 - 21:00

  KAUST

  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).

May 8 - May 2, 2021

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  Scalable Solvers: Universals and Innovations

  David Keyes, Professor, Applied Mathematics and Computational Science

  May 6, 12:00 - 13:00

  KAUST

  Abstract As simulation and analytics enter the exascale era, numerical algorithms must span a widening gap between ambitious applications and austere architectures. We present fifteen universals for researchers in scalable solvers and some innovations that allow approaching lin-log complexity in storage and operation count in many important algorithmic kernels. Applications are becoming ambitious in many senses: large physical space, phase space or parameter dimensions; resolution of many scales of space and/or time; high fidelity physical modeling; linking together of multiple complex models
• 

  Minimization problems involving polyconvex functionals and an H1-projection problem - Session 1

  Wilfrid Gangbo, Professor of mathematics at the University of California, Los Angeles

  May 4, 19:00 - 21:00

  KAUST

  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)

May 1 - Apr 25, 2021

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  The Role of Volcanic Activity in Climate and Global Change

  Georgiy L. Stenchikov, Professor, Earth Science and Engineering

  Apr 29, 12:00 - 13:00

  KAUST

  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.

Apr 24 - Apr 18, 2021

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  Distributed second order methods with fast rates and compressed communication

  Peter Richtarik, Professor, Computer Science

  Apr 22, 12:00 - 13:00

  KAUST

  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.

Apr 17 - Apr 11, 2021

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  Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining - 2021

  Mikhail Moshkov, Professor, Applied Mathematics and Computational Science

  Apr 15, 12:00 - 13:00

  KAUST

  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.
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  Continuous-time optimal control on discrete spaces. Applications to inventory management in commerce and finance - Session 2

  Olivier Guéant, Professor, Applied Mathematics at Université Paris 1 Panthéon-Sorbonne, France

  Apr 13, 15:00 - 18:00

  KAUST

  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).

Apr 10 - Apr 4, 2021

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  A Rapid, Accurate and Machine-agnostic Segmentation and Quantification Method for CT-based COVID-19 Diagnosis

  Xin Gao, Professor, Computer Science

  Apr 8, 12:00 - 13:00

  KAUST

  COVID-19

  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.
• 

  Continuous-time optimal control on discrete spaces. Applications to inventory management in commerce and finance - Session 1

  Olivier Guéant, Professor, Applied Mathematics at Université Paris 1 Panthéon-Sorbonne, France

  Apr 6, 15:00 - 18:00

  KAUST

  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).

Apr 3 - Mar 28, 2021

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  Waves Functional Materials - 2021-04-01

  Ying Wu, Program Chair, Applied Mathematics and Computational Science

  Apr 1, 12:00 - 13:00

  KAUST

  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.
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  Numerical Methods for Mean Field Games- Session 2

  Mathieu Laurière, Postdoc, Operations Research and Financial Engineering, Princeton University, USA

  Mar 30, 14:30 - 17:30

  KAUST

  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).

Mar 27 - Mar 21, 2021

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  The Convex Gaussian Min-Max Theorem: A Powerful Tool for the Analysis of Regularized Convex Optimization Problems

  Tareq Al-Naffouri, Professor, Electrical and Computer Engineering

  Mar 25, 12:00 - 13:00

  KAUST

  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.
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  International Seminar on Mathematical Models and Numerical Methods for Flow and Transport in Porous Media

  Speakers from KAUST, CEMSE, PSE, G-CSC, IBRAE and INM RAS

  Mar 25, 10:30 - Mar 26, 17:00

  KAUST

  numerical methods Mathematical modeling flow problems porous media

  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.
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  Numerical Methods for Mean Field Games - Session 1

  Mathieu Laurière, Postdoc, Operations Research and Financial Engineering, Princeton University, USA

  Mar 23, 14:30 - 17:30

  KAUST

  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)
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  Minimal-time Mean Field Games

  Samer Dweik, Postdoctoral Fellow, University of British Columbia

  Mar 22, 11:00 - 12:00

  KAUST

  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.

Mar 20 - Mar 14, 2021

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  Multicomponent flows: overview of the models and results on the existence of global in time solutions - Part 2

  Ewelina Zatorska, Senior Lecturer, Applied and Numerical Analysis, Imperial College London, UK

  Mar 18, 14:00 - 16:00

  KAUST

  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.
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  On Discovering Nature’s Equations from Observations

  Jesper Tegner, Professor, BESE Division, KAUST

  Mar 18, 12:00 - 13:00

  KAUST

  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.
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  Fully nonlinear degenerate elliptic equations: qualitative properties of viscosity solutions - Session 3

  Martino Bardi, Professor, Mathematical Sciences, University of Padova, Italy

  Mar 17, 15:00 - 17:00

  KAUST

  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.
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  Mathematical Modeling and Analysis of Emergent Phenomena

  Jan Haskovec, Research Scientist, AMCS, KAUST

  Mar 15, 12:00 - 13:00

  KAUST

  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.

Mar 13 - Mar 7, 2021

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  Programming curvature into flat sheets

  Mar 11, 12:00 - 13:00

  KAUST

  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.
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  Fully nonlinear degenerate elliptic equations: qualitative properties of viscosity solutions - Session 2

  Martino Bardi, Professor, Mathematical Sciences, University of Padova, Italy

  Mar 10, 15:00 - 17:00

  KAUST

  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.
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  Analysis of the compressible two-phase flow

  Dr. Ewelina Zatorska, Senior Lecturer in the Applied and Numerical Analysis, Imperial College London

  Mar 9, 15:00 - 16:00

  KAUST

  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.
• 

  Fully nonlinear degenerate elliptic equations: qualitative properties of viscosity solutions - Session 1

  Martino Bardi, Professor, Mathematical Sciences, University of Padova, Italy

  Mar 8, 15:00 - 17:00

  KAUST

  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.

Mar 6 - Feb 28, 2021

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  A proof of the C^p'-regularity conjecture in the plane

  Prof. José Miguel Urbano, Mathematics at the University of Coimbra (Portugal)

  Mar 4, 12:00 - 13:00

  KAUST

  Abstract We establish a new oscillation estimate for solutions of nonlinear partial differential equations of degenerate elliptic type, which yields a precise control on the growth rate of solutions near their set of critical points. We then apply this new tool to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C^p'=C^{1,1/p-1}, an optimal regularity result. This is joint work with Eduardo Teixeira (University of Central Florida, USA) and Damião Araújo (Universidade Federal da Paraíba
• 

  Title: Introduction to free boundary problems - Session 2

  Aram Karakhanyan, Professor, School of Mathematics, University of Edinburgh, UK

  Mar 2, 15:00 - 18:00

  KAUST

  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

Feb 27 - Feb 21, 2021

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  On Adversarial Network Attacks, Robustness, and Certification

  Bernard Ghanem, Professor, Electrical and Computer Engineering

  Feb 25, 12:00 - 13:00

  KAUST

  Abstract The outstanding performance of deep neural networks (DNNs), for visual recognition tasks in particular, has been demonstrated on many large-scale benchmarks. This performance has immensely strengthened the line of research that aims to understand and analyze the driving reasons behind the effectiveness of these networks. One important aspect of this analysis has gained much attention, namely the sensitivity of a DNN to perturbations. This has spawned a thrust in the research community, which focuses on developing adversarial attacks that fool a DNN, training strategies that make DNNs
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  Title: Introduction to free boundary problems - Session 1

  Aram Karakhanyan, Professor, School of Mathematics, University of Edinburgh, UK

  Feb 23, 15:00 - 18:00

  KAUST

  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.

Feb 20 - Feb 14, 2021

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  Forward-prediction and Backward-design by Machine Learning

  Prof. Xiangliang Zhang

  Feb 18, 12:00 - 13:00

  KAUST

  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.
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  Recent developments for stochastic processes and their applications

  Ahmed Kebaier, Associate Professor, Laboratory Analysis, Geometry and Application (LAGA), University Sorbonne Paris Nord (USPN)

  Feb 16, 12:00 - 13:00

  KAUST

  stochastic

  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.
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  Existence theory for non-separable mean field games - Session 3

  David Ambrose, Professor, Department of Mathematics at Drexel University, USA

  Feb 15, 17:00 - 19:00

  KAUST

  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.

Feb 13 - Feb 7, 2021

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  Proper scoring rules and model selection for stochastic processes

  David Bolin, Professor, Statistics

  Feb 11, 12:00 - 13:00

  KAUST

  In this talk, we begin by a brief introduction to proper scoring rules and their use in statistics. Then, we discuss an often overlooked problem: the up-weighting of observations with large uncertainty, which can lead to unintuitive rankings of models, by some of the most popular proper scoring rules, such as the continuously ranked probability score (CRPS), the MAE, and the MSE.
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  High Order Numerical Methods for Acoustic and Elastic Scattering

  Prof. Vianey Villamizar, Department of Mathematics, Brigham Young University, USA

  Feb 9, 14:00 - 15:00

  KAUST

  A focus of my current research is to develop numerical methods for the accurate simulation of sound and seismic waves. This waves usually occur in very large domains. For the computational purpose, the original unbounded wave problems need to be transformed into bounded ones. To accomplish this goal artificial boundaries are chosen to truncate the infinite domains. The challenge is to define absorbing boundary conditions (ABC) on these artificial boundaries such that the solutions of the new bounded problems approximate to a reasonable degree the solutions of the original unbounded problems in their common domains. In part, my efforts and those of my students and collaborators have been in deriving computational advantageous ABC and the formulation of a high order and high accurate numerical methods inside the truncated domain. In this talk, I will describe in some details our work. Also, I will include numerical results which demonstrate the improved accuracy and simplicity of our formulation when compared with commonly used ABC.
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  Existence theory for non-separable mean field games - Session 2

  David Ambrose, Professor, Department of Mathematics at Drexel University, USA

  Feb 8, 17:00 - 19:00

  KAUST

  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.

Feb 6 - Jan 31, 2021

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  Effective Literature Search

  Nevena Tomic, Library Subject Specialist, PSE, KAUST

  Feb 4, 12:00 - 13:00

  KAUST

  This session will help you to improve the efficiency of your literature searches. You will learn basic search techniques – using Boolean operators, keyword search, concept search, truncation, etc. Two major interdisciplinary scientific databases – Web of Science and Scopus, as well as CEMSE specific resources in KAUST library collections will be presented.
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  Existence theory for non-separable mean field games - Session 1

  David Ambrose, Professor, Department of Mathematics at Drexel University, USA

  Feb 1, 17:00 - 19:00

  KAUST

  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.
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  Monte Carlo based Inference for State-space Models

  Sumeetpal Singh, Reader, Engineering Statistics, Department of Engineering, University of Cambridge

  Jan 31, 12:00 - 13:00

  KAUST

  Monte Carlo state-space models

  State-space models are widely used for the analysis of time-series data but full Bayesian inference is still elusive. I will review some applications of state-space models and recent endeavours towards efficient Monte Carlo sampling, in particular using Particle filtering and more recent Particle Markov Chain Monte Carlo methods. I will discuss the theoretical scalability of these methods with respect to the length of the observed time-series. Our theoretical results on their efficiency align well with many documented instances of their effectiveness based on extensive numerical studies. The talk will conclude with some open challenges to be pursued.

Jan 30 - Jan 24, 2021

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  Fractional calculus and partial differential equation - Session 2

  Fabio Camilli, Full Professor of Mathematical Analysis, Università di Roma, La Sapienza, Italy

  Jan 28, 15:00 - 18:00

  KAUST

  In this course, we provide a brief introduction to fractional calculus with a view to applying it to the study of time fractional partial differential equations. We will introduce the definitions and main properties of fractional integrals and derivatives, including those of Riemann-Liouville, Caputo and Grunwald-Letnikov. The previous results will serve as the main modeling tools for partial differential equations related to a class of non-Markovian stochastic processes, called subdiffusions. Then we will examine some results regarding time-fractional linear partial differential equations and conclude with a brief introduction to control problems and Mean Field Games for subdiffusion processes.
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  A personal and historical view of computational mathematics

  Tony Chan, President, King Abdullah University of Science and Technology

  Jan 28, 12:00 - 13:00

  KAUST

  Computational mathematics has a millennium long history but its modern incarnation started after the advent of electronic computers about 80 years ago. Scientifically, it lies in the intersection between mathematics, a subject with a long history, and computer sciences, a relatively new discipline. Its motivations, approaches and practitioners have derived from different fields, and it has also had to evolve and adapt to new tools and opportunities. My own scientific career overlaps quite a bit with the field’s modern evolution and in this talk, I’ll give a personal, as well as a “historical” view of the field.
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  Fractional calculus and partial differential equation - Session 1

  Fabio Camilli, Full Professor of Mathematical Analysis, Università di Roma, La Sapienza, Italy

  Jan 26, 15:00 - 18:00

  KAUST

  In this course, we provide a brief introduction to fractional calculus with a view to applying it to the study of time fractional partial differential equations. We will introduce the definitions and main properties of fractional integrals and derivatives, including those of Riemann-Liouville, Caputo and Grunwald-Letnikov. The previous results will serve as the main modeling tools for partial differential equations related to a class of non-Markovian stochastic processes, called subdiffusions. Then we will examine some results regarding time-fractional linear partial differential equations and conclude with a brief introduction to control problems and Mean Field Games for subdiffusion processes.

Jan 23 - Jan 17, 2021

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  Elliptic PDEs: Regularity under minimal assumptions - Session 2

  Giuseppe Di Fazio,Professor of Mathematics at the University of Catania, Italy

  Jan 21, 10:00 - 13:00

  KAUST

  Elliptic PDE are ubiquitous both in Mathematics and in the applications of Mathematics. The regularity of the generalized solutions is a very important issue that it is necessary to handle in proper way if one want to obtain useful information. The goal of my lectures is to introduce the audience to the topic of regularity for elliptic PDE under assumptions on the coefficients that are of minimal requirements.
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  Elliptic PDEs: Regularity under minimal assumptions - Session 1

  Giuseppe Di Fazio, Professor of Mathematics at the University of Catania, Italy

  Jan 19, 10:00 - 13:00

  KAUST

  Elliptic PDE are ubiquitous both in Mathematics and in the applications of Mathematics. The regularity of the generalized solutions is a very important issue that it is necessary to handle in proper way if one want to obtain useful information. The goal of my lectures is to introduce the audience to the topic of regularity for elliptic PDE under assumptions on the coefficients that are of minimal requirements.