Events

Jan 16 - Jan 10, 2021

• 

  Overcoming the curse of dimensionality: from nonlinear Monte Carlo to deep learning

  Arnulf Jentzen, Professor, Applied Mathematics Münster: Institute for Analysis and Numerics, University of Münster

  Jan 10, 14:00 - 15:00

  KAUST

  nonlinear Deep learning monte carlo algorithms

  In this talk we prove that suitable deep neural network approximations do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs and we thereby prove, for the first time, that a general semilinear parabolic PDE can be solved approximatively without the curse of dimensionality.

Jan 9 - Jan 3, 2021

• 

  Mean Field Games: Numerical Methods and Applications

  Mathieu Laurière, Postdoc, Department of Operations Research and Financial Engineering, Princeton University

  Jan 5, 15:00 - 16:00

  KAUST

  mean-field games numerical methods

  In this talk, several numerical methods will be presented and illustrated on examples. Borrowing tools from stochastic analysis, optimization, partial differential equations and machine learning, these methods enable us to solve mean field games with possibly complex sources of noise or high dimensional state variables.

Dec 12 - Dec 6, 2020

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  Geospatial Data Science for Public Health Surveillance - Graduate Seminar

  Dec 10, 12:00 - 13:00

  KAUST

  Geospatial health data are essential to inform public health and policy. These data can be used to quantify disease burden, understand geographic and temporal patterns, identify risk factors, and measure inequalities. In this talk, I will give an overview of my research which focuses on the development of geospatial methods and interactive visualization applications for health surveillance. I will present disease risk models where environmental, demographic and climatic data are used to predict the risk and identify targets for intervention of lymphatic filariasis in sub-Saharan Africa, and leptospirosis in a Brazilian urban slum. I will also show the R packages epiflows for risk assessment of travel-related spread of disease, and SpatialEpiApp for disease mapping and the detection of clusters. Finally, I will describe my future research and how it can inform better surveillance and improve population health globally.

Dec 5 - Nov 29, 2020

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  Mini Courses by Prof Piermarco Cannarsa - Session 2

  Professor Piermarco Cannarsa, Mathematical Analysis at the University of Rome Tor Vergata, Italy

  Dec 3, 15:00 - 18:00

  KAUST

  The theory of Mean Field Games (MFG) has been developed in the last two decades by economists, engineers, and mathematicians in order to study decision making in very large populations of “small" interacting agents. This short course will be focused on deterministic MFG, which are associated with a first order PDE system. We will address the problem assuming that agents are subject to state constraints, when classical PDE techniques are of little help. First, we will show how to prove the existence of solutions by the so-called Lagrangian approach, which interprets equilibria as certain measures on the space of paths that each agent can choose. Then, we will address regularity issues for such generalized solutions, deriving point-wise properties that allow to recover the typical MFG system. Finally, we will study the asymptotic behavior of solutions to the constrained MFG system as time goes to infinity, borrowing ideas from weak KAM theory.
• 

  Modelling and Simulation of Biological Systems - 2020-12-03

  Gabriel Wittum, Professor (former), Applied Mathematics and Computational Science

  Dec 3, 12:00 - 13:00

  KAUST

  Biological systems are distinguished by their enormous complexity and variability. That is why mathematical modeling and computational simulation of those systems is very difficult, in particular thinking of detailed models which are based on first principles. The difficulties start with geometric modeling which needs to extract basic structures from highly complex and variable phenotypes, on the other hand also has to take the statistic variability into account. Moreover, the models of the processes running on these geometries are not yet well established, since these are equally complex and often couple many scales in space and time. Thus, simulating such systems always means to put the whole frame to test, from modelling to the numerical methods and software tools used for simulation. These need to be advanced in connection with validating simulation results by comparing them to experiments.
• 

  Mean Field Games with State Constraints - Session 1

  Professor Piermarco Cannarsa, Mathematical Analysis at the University of Rome Tor Vergata, Italy

  Dec 1, 15:00 - 18:00

  KAUST

  The theory of Mean Field Games (MFG) has been developed in the last two decades by economists, engineers, and mathematicians in order to study decision making in very large populations of “small" interacting agents. This short course will be focused on deterministic MFG, which are associated with a first order PDE system. We will address the problem assuming that agents are subject to state constraints, when classical PDE techniques are of little help. First, we will show how to prove the existence of solutions by the so-called Lagrangian approach, which interprets equilibria as certain measures on the space of paths that each agent can choose. Then, we will address regularity issues for such generalized solutions, deriving point-wise properties that allow to recover the typical MFG system. Finally, we will study the asymptotic behavior of solutions to the constrained MFG system as time goes to infinity, borrowing ideas from weak KAM theory.
• 

  Enabling Accurate and Efficient Simulation in Visual Computing - Public Colloquium

  Dominik L. Michels, Associate Professor, Computer Science

  Nov 30, 14:30 - 16:00

  KAUST

  visual computing

  The overarching goal of Prof. Michels' Computational Sciences Group within KAUST's Visual Computing Center is enabling accurate and efficient simulations for applications in Scientific and Visual Computing. Towards this goal, the group develops new principled computational methods based on solid theoretical foundations. This talk covers a selection of previous and current work presenting a broad spectrum of research highlights ranging from simulating stiff phenomena such as the dynamics of fibers and textiles, over liquids containing magnetic particles, to the development of complex ecosystems and weather phenomena. Moreover, connection points to the growing field of machine learning are addressed and an outlook is provided with respect to selected technology transfer activities.
• 

  Aggregation-Diffusion PDEs: Gradient Flows, Long Time asymptotics and bifurcations - Session 3

  José A. Carrillo, Professor, Applied Mathematics at The Queen’s College, University of Oxford, UK

  Nov 29, 13:00 - 15:00

  KAUST

  The main goal of this mini course is to discuss the state-of-the-art in understanding the phenomena of long time asympotitcs and phase transitions for a range of nonlinear Fokker-Planck equations with linear and nonlinear diffusion. They appear as natural macroscopic PDE descriptions of the collective behavior of particles such as Cucker-Smale models for consensus, the Keller Segel model for chemotaxis, and the Kuramoto model for synchronization. We will discuss the existence of phase transitions in a variety of these models using the natural free energy of the system and their interpretation as natural gradient flow structure with respect to the Wasserstein distance in probability measures. We will discuss both theoretical aspects as well as numerical schemes and simulations keeping those properties at the discrete level.

Nov 28 - Nov 22, 2020

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  Aggregation-Diffusion PDEs: Gradient Flows, Long Time asymptotics and bifurcations - Session 2

  José A. Carrillo, Professor, Applied Mathematics at The Queen’s College, University of Oxford, UK

  Nov 26, 13:00 - 15:00

  KAUST

  The main goal of this mini course is to discuss the state-of-the-art in understanding the phenomena of long time asympotitcs and phase transitions for a range of nonlinear Fokker-Planck equations with linear and nonlinear diffusion. They appear as natural macroscopic PDE descriptions of the collective behavior of particles such as Cucker-Smale models for consensus, the Keller Segel model for chemotaxis, and the Kuramoto model for synchronization. We will discuss the existence of phase transitions in a variety of these models using the natural free energy of the system and their interpretation as natural gradient flow structure with respect to the Wasserstein distance in probability measures. We will discuss both theoretical aspects as well as numerical schemes and simulations keeping those properties at the discrete level.
• 

  The Tetracopter: A modular, self-similar flying robot

  Eric Feron, Professor, Electrical and Computer Engineering

  Nov 26, 12:00 - 13:00

  KAUST

  Modular robotics deals with robots that are an assemblage of smaller sized and often identical robots. The benefits of modular robots are many, chief among them being how easily they can be transported from one location to another. Moreover, their size can be adjusted according to the task at hand without requiring extensive redesign or specialization, therefore making them the object of significant research efforts.
• 

  Aggregation-Diffusion PDEs: Gradient Flows, Long Time asymptotics and bifurcations - Session 1

  José A. Carrillo, Professor, Applied Mathematics at The Queen’s College, University of Oxford, UK

  Nov 23, 13:00 - 15:00

  KAUST

  The main goal of this mini course is to discuss the state-of-the-art in understanding the phenomena of long time asympotitcs and phase transitions for a range of nonlinear Fokker-Planck equations with linear and nonlinear diffusion. They appear as natural macroscopic PDE descriptions of the collective behavior of particles such as Cucker-Smale models for consensus, the Keller Segel model for chemotaxis, and the Kuramoto model for synchronization. We will discuss the existence of phase transitions in a variety of these models using the natural free energy of the system and their interpretation as natural gradient flow structure with respect to the Wasserstein distance in probability measures. We will discuss both theoretical aspects as well as numerical schemes and simulations keeping those properties at the discrete level.

Nov 21 - Nov 15, 2020

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  On Unbiased Estimation of the Score Function for a Class of Partially Observed Diffusions

  Nov 19, 12:00 - 13:00

  KAUST

  In this talk we consider the problem of estimating the score function (or gradient of the log-likelihood) associated to a class of partially observed diffusion processes, with discretely observed, fixed length, data and finite dimensional parameters. We construct an estimator that is unbiased with no time-discretization bias. Using a simple Girsanov change of measure method to represent the score function, our methodology can be used for a wide class of diffusion processes and requires only access to a time-discretization method such as Euler-Maruyama. Our approach is based upon a novel adaptation of the randomization schemes developed by Glynn and co-authors along with a new coupled Markov chain simulation scheme. The latter methodology is an original type of coupling of the coupled conditional particle filter. We prove that our estimator is unbiased and of finite variance. We then illustrate our methodology on several challenging statistical examples. This is a joint work with Jeremy Heng (ESSEC, Singapore) and Jeremie Houssineau (Warwick, UK)
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  Start your Research Journey at KAUST - Master and Ph.D. degrees in Applied Mathematics, Computer Science, Electrical Engineering and Statistics

  Aigars Ekers, Dean, University of Latvia, Faculty of Science and Technology

  Nov 18, 16:00 - 17:00

  KAUST

  Did you know that courses are taught in English at KAUST? Did you know that the faculty and students are from more than 100 countries? Did you know that you will be fully funded when studying at KAUST? What you will learn from this webinar: Life at KAUST: What are KAUST and CEMSE? Degrees and Academic Programs Research Areas and Lab Facilities Eligibility and Admission Requirements KAUST Fellowship: Benefits of studying at KAUST How to Apply?
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  Federated Learning of a Mixture of Global and Local Models

  Filip Hanzely, Ph.D., Applied Mathematics and Computational Science

  Nov 16, 12:00 - 13:00

  KAUST

  We propose a new optimization formulation for training federated learning models. The standard formulation has the form of an empirical risk minimization problem constructed to find a single global model trained from the private data stored across all participating devices. In contrast, our formulation seeks an explicit trade-off between this traditional global model and the local models, which can be learned by each device from its own private data without any communication. Further, we develop several efficient variants of SGD (with and without partial participation and with and without variance reduction) for solving the new formulation and prove communication complexity guarantees.

Nov 14 - Nov 8, 2020

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  The method of intrinsic scaling - Session 4

  Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal

  Nov 12, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
• 

  Optimization applied to energy systems, autonomous vehicles, and matching

  Ricardo Manuel Pinto de Lima, Research Scientist, Applied Mathematics and Computational Science

  Nov 12, 12:00 - 13:00

  KAUST

  In this talk, we start by introducing optimization and interesting optimization applications. We review some optimization formulations and focus on applications studied in our research, such as energy systems, and trajectory planning of autonomous underwater vehicles. After the introduction, we address the self-scheduling and market involvement of a virtual power plant using adaptive robust optimization under uncertainty in the wind speed and electricity prices.
• 

  The method of intrinsic scaling - Session 3

  Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal

  Nov 10, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
• 

  The equations of polyconvex thermoelasticity

  Myrto Galanopoulou, Ph.D. Student, Applied Mathematics and Computational Science

  Nov 9, 17:00 - 19:00

  KAUST

  In my thesis, I consider the system of thermoelasticity endowed with polyconvex energy. After presenting the equations in their mathematical and physical context, I embed the equations of polyconvex thermoviscoelasticity into an augmented, symmetrizable, hyperbolic system which possesses a convex entropy. This allows to prove many important stability results, such as convergence from thermoviscoelasticity (with Newtonian viscosity and Fourier heat conduction) to smooth solutions of the system of adiabatic thermoelasticity, and convergence from thermoviscoelasticity to smooth solutions of thermoelasticity in the zero-viscosity limit. In addition, I establish a weak-strong uniqueness result in the class of entropy weak solutions and in a suitable class of measure-valued solutions, defined by means of generalized Young measures that describe both oscillatory and concentration effects. Also, I construct a variational scheme for isentropic processes of adiabatic polyconvex thermoelasticity: I establish existence of minimizers which converge to a measure-valued solution that dissipates the total energy, while the scheme converges when the limiting solution is smooth.

Nov 7 - Nov 1, 2020

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  The method of intrinsic scaling - Session 2

  Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal

  Nov 5, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.
• 

  Exploring Non-Linear Interactions in Multivariate Time Series

  Hernando Ombao, Professor, Statistics

  Nov 5, 12:00 - 13:00

  KAUST

  Linear Multivariate extremes Bayesian computational statistics

  Advances in imaging technology have given neuroscientists unprecedented access to examine various facets of how the brain “works”. Brain activity is complex. A full understanding of brain activity requires careful study of its multi-scale spatial-temporal organization (from neurons to regions of interest; and from transient events to long-term temporal dynamics). Motivated by these challenges, we will explore some characterizations of dependence between components of a multivariate time series and then apply these to the study of brain functional connectivity.
• 

  The method of intrinsic scaling - Session 1

  Jose Urbano, Professor of Mathematics at the University of Coimbra, Portugal

  Nov 3, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular parabolic PDEs. The local Hölder continuity of bounded weak solutions will be derived from scratch for the model case of the degenerate p-Laplace equation. Our approach is entirely self-contained and focused on the essence of the method, leaving aside technical refinements needed to deal with more general equations.

Oct 31 - Oct 25, 2020

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  On the approximation of the spectrum of differential operators

  Daniele Boffi, Associate Dean for Faculty, Computer, Electrical and Mathematical Sciences and Engineering

  Oct 29, 12:00 - 13:00

  KAUST

  Eigenvalue problems associated with partial differential equations are key ingredients for the modeling and simulation of a variety of real world applications, ranging from fluid-dynamics, structural mechanics, acoustics, to electromagnetism and medical problems. We review some properties related to the approximation of eigenvalue problems. Starting from matrix algebraic problems, we present a series of examples and counterexamples showing that even extremely simple situations can produce unexpected results.

Oct 24 - Oct 18, 2020

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  Efficiency Assessment of Approximated Spatial Predictions for Large Datasets

  Yiping Hong, Postdoctoral Research Fellow, Statistics

  Oct 22, 12:00 - 13:00

  KAUST

  mathematics applied statistics Social Network Analysis

  Our suggested criteria are more useful for the determination of tuning parameters for sophisticated approximation methods of spatial model fitting. To illustrate this, we investigate the trade-off between the execution time, estimation accuracy, and prediction efficiency for the TLR method with intensive simulation studies and suggest proper settings of the TLR tuning parameters.

Oct 17 - Oct 11, 2020

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  The Infinity Laplacian (Session IV)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Oct 15, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.
• 

  Epidemiological modeling and optimal control

  David Ketcheson, Professor, Applied Mathematics and Computational Science

  Oct 15, 12:00 - 13:00

  KAUST

  optimal control optimal control theory

  Compartmental epidemiological models are one of the simplest models for the spread of a disease. They are based on statistical models of interactions in large populations and can be effective in the appropriate circumstances. Their application historically and in the present pandemic has sometimes been successful and sometimes spectacularly wrong. In this talk I will review some of these models and their application. I will also discuss the behavior of the corresponding dynamical systems, and discuss how the theory of optimal control can be applied to them. I will describe some of the challenges in using such a theory to make decisions about public policy.
• 

  Efficient Ensemble Data Assimilation and Forecasting of the Red Sea Circulation

  Habib Toye Mahamadou Kele, Ph.D. Student, Applied Mathematics and Computational Science

  Oct 13, 16:15 - 17:00

  KAUST

  This dissertation presents our efforts to build an operational ensemble forecasting system for the Red Sea, based on the Data Research Testbed (DART) package for ensemble data assimilation and the Massachusetts Institute of Technology general circulation ocean model (MITgcm) for forecasting. The Red Sea DART-MITgcm system efficiently integrates all the ensemble members in parallel, while accommodating different ensemble assimilation schemes. The promising ensemble adjustment Kalman filter (EAKF), designed to avoid manipulating the gigantic covariance matrices involved in the ensemble assimilation process, possesses relevant features required for an operational setting. We developed new schemes aiming at lowering the computational burden while preserving reliable assimilation results. The ensemble data assimilation system is implemented and tested on Shaheen, our world-class supercomputer, and will form the basis of the first ever operational Red Sea forecasting system that is currently being implemented to support Saudi Aramco operations in this basin.
• 

  The Infinity Laplacian (Session III)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Oct 13, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.

Oct 10 - Oct 4, 2020

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  The Infinity Laplacian (Session II)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Oct 8, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.
• 

  ExaGeoStat: Moving Towards Large-Scale Geostatistical Modeling on Manycore Systems

  Sameh Abdulah, Senior Research Scientist, Applied Mathematics and Computational Science

  Oct 8, 12:00 - 13:00

  KAUST

  Adaptive modeling

  We present Exascale GeoStatistics (ExaGeoStat) software, a high-performance library implemented on a wide variety of contemporary hybrid distributed-shared supercomputers whose primary target is climate and environmental prediction applications.
• 

  The Infinity Laplacian (Session I)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Oct 6, 16:00 - 17:30

  KAUST

  The mini-course is an introduction to the analysis of infinity-harmonic functions. We detail the proof of the equivalence between enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense, thus making a seamless connection with the previous mini-course. Further material includes the existence of infinity-harmonic functions in the case of an unbounded domain and an easy and self-contained proof, due to Armstrong and Smart, of the celebrated uniqueness theorem of Jensen.

Oct 3 - Sep 27, 2020

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  Consensus formation models with delay

  Jan Haskovec, AMCS, KAUST

  Oct 1, 12:00 - 13:00

  KAUST

  Models Formation

  Individual-based models of collective behavior represent a very active research field with applications in physics (spontaneous magnetization), biology (flocking and swarming) and social sciences (opinion formation). They are also a hot topic engineering (swarm robotics). A particularly interesting aspect of the dynamics of multi-agent systems is the emergence of global self-organized patterns, while individuals typically interact only on short scales. In this talk I shall discuss the impact of delay on asymptotic consensus formation in Hegselmann-Krause-type models, where agents adapt their „opinions“ (in broad sense) to the ones of their close neighbors. We shall understand the two principial types/sources of delay - information propagation and processing - and explain their qualitatively different impacts on the consensus dynamics. We then discuss various mathematical methods that provide asymptotic consensus results in the respective settings: Lyapunov functional-type approach, direct estimates, convexity arguments and forward-backward estimates.
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  Nonlinear and dispersive waves: Theory, computations and applications

  Dr. Dimitrios Mitsotakis, Senior Lecturer, Victoria University of Wellington

  Sep 30, 12:00 - 13:00

  KAUST

  oceanic waves dispersive waves

  The study of waves in fluids is one of the most significant branches of fluid mechanics. Part of this study is the theory of nonlinear and dispersive waves which has recently emerged and is still under development. Nonlinear and dispersive waves appear in fluids of any form and have significant role in the fields of oceanic waves (surface and internal), atmospheric modelling, electromagnetism, nonlinear optics, ultra-cold matter and even in blood flow problems. In this presentation we will review relevant applications, such as tsunami waves, the El Nino southern oscillation, blood flow in arteries and solitons propagating in optical fibres. Mathematical modelling techniques for deriving equations that describe such phenomena will be introduced in the context of surface water waves. We will also review the minimum required theoretical background in order to proceed with safe numerical simulations. Finally, we will discuss the numerical modelling of such problems where methods such as standard and mixed Galerkin / Finite element methods are of central focus. We close this presentation by showcasing a topic of much current interest, namely, the development of modern mathematical models for nonlinear and dispersive waves by combining machine learning techniques with classical methodologies.

Sep 19 - Sep 13, 2020

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  The Lipschitz Extension Problem (Session IV)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Sep 17, 16:00 - 17:30

  KAUST

  We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.
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  Estimating High-Resolution Red Sea Surface Temperature Hotspots, Using a Low-Rank Semiparametric Spatial Model

  Arnab Hazra, Postdoctoral Research Fellow, Statistics

  Sep 17, 12:00 - 13:00

  KAUST

  High Resolution X-ray Diffraction spatial modulation

  In this work, we estimate extreme sea surface temperature (SST) hotspots, i.e., high threshold exceedance regions, for the Red Sea, a vital region of high biodiversity. We analyze high-resolution satellite-derived SST data comprising daily measurements at 16703 grid cells across the Red Sea over the period 1985–2015. We propose a semiparametric Bayesian spatial mixed-effects linear model with a flexible mean structure to capture spatially-varying trend and seasonality, while the residual spatial variability is modeled through a Dirichlet process mixture (DPM) of low-rank spatial Student-t processes (LTPs). By specifying cluster-specific parameters for each LTP mixture component, the bulk of the SST residuals influence tail inference and hotspot estimation only moderately. Our proposed model has a nonstationary mean, covariance and tail dependence, and posterior inference can be drawn efficiently through Gibbs sampling. In our application, we show that the proposed method outperforms some natural parametric and semiparametric alternatives.
• 

  The Lipschitz Extension Problem (Session III)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Sep 15, 16:00 - 17:30

  KAUST

  We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.

Sep 12 - Sep 6, 2020

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  The Lipschitz Extension Problem (Session II)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Sep 10, 16:00 - 17:30

  KAUST

  We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.
• 

  A cheap rotated characteristic decomposition technique for high-order reconstructions in multi-dimensions with application to instabilities in direct initiation of gaseous detonations in free space

  Matteo Parsani, Associate Professor, Applied Mathematics and Computational Science

  Sep 10, 12:00 - 13:00

  KAUST

  When constructing high-order schemes for solving hyperbolic conservation laws with multi-dimensional finite volume schemes, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For multi-dimensional finite volume schemes, we need to perform the characteristic decomposition several times in different normal directions of the target cell, which is very time-consuming. We propose a rotated characteristic decomposition technique that requires only one-time decomposition for multi-dimensional reconstructions. This technique not only reduces the computational cost remarkably, but also controls spurious oscillations effectively. We take a third-order weighted essentially non-oscillatory finite volume scheme for solving the Euler equations as an example to demonstrate the efficiency of the proposed technique. We apply the new methodology to the simulation of instabilities in direct initiation of gaseous detonations in free space.
• 

  The Lipschitz Extension Problem (Session I)

  Prof. José Miguel Urbano, Department of Mathematics, University of Coimbra, Portugal

  Sep 8, 16:00 - 17:30

  KAUST

  We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions, and its several drawbacks, leading to the notion of AMLE (Absolutely Minimizing Lipschitz Extension). We then present a rigorous and detailed analysis of the equivalence between being absolutely minimizing Lipschitz and enjoying comparison with cones. Finally, we explore some consequences of this geometric notion, chiefly the derivation of a Harnack inequality.

Sep 5 - Aug 30, 2020

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  The two faces of correlation

  Haavard Rue, Program Chair, Statistics

  Sep 3, 12:00 - 13:00

  KAUST

  Statistical Modeling computing

  Discussing the concept of correlation and how to interpret it alone (marginally) or within a more complex environment (conditionally). This rather simple observation is the key observation behind a lot of exciting developments and connections in statistics that can be leveraged for improved computations and better motivated statistical models.

Aug 1 - Jul 26, 2020

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  Optimization for Supervised Machine Learning: Randomized Algorithms for Data and Parameters

  Filip Hanzely, Ph.D., Applied Mathematics and Computational Science

  Jul 30, 16:00 - 18:00

  KAUST

  Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used to formulate these often ill-conditioned optimization tasks, there is a need for new efficient algorithms able to cope with these challenges. In this thesis, we deal with each of these sources of difficulty in a different way. To efficiently address the big data issue, we develop new methods which in each iteration examine a small random subset of the training data only. To handle the big model issue, we develop methods which in each iteration update a random subset of the model parameters only. Finally, to deal with ill-conditioned problems, we devise methods that incorporate either higher-order information or Nesterov's acceleration/momentum. In all cases, randomness is viewed as a powerful algorithmic tool that we tune, both in theory and in experiments, to achieve the best results.

Jul 18 - Jul 12, 2020

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  The Interplay between Mean-Field Games and Machine-Learning (Session III)

  Prof. Levon Nurbekyan, Department of Mathematics, UCLA

  Jul 15, 21:00 - 23:00

  KAUST

  In this short course, I will discuss connections between mean-field games (MFG) systems and modern machine-learning (ML) techniques and problems. In the first part of the course, roughly the first two lectures, I will present how various ML techniques can be applied to solve high-dimensional MFG systems that are far out of reach for traditional methods. In the second part of the course, I will discuss the reverse relation, namely, how the MFG framework can be useful for solving specific ML problems.
• 

  The Interplay between Mean-Field Games and Machine-Learning (Session II)

  Prof. Levon Nurbekyan, Department of Mathematics, UCLA

  Jul 14, 21:00 - 23:00

  KAUST

  In this short course, I will discuss connections between mean-field games (MFG) systems and modern machine-learning (ML) techniques and problems. In the first part of the course, roughly the first two lectures, I will present how various ML techniques can be applied to solve high-dimensional MFG systems that are far out of reach for traditional methods. In the second part of the course, I will discuss the reverse relation, namely, how the MFG framework can be useful for solving specific ML problems.
• 

  The Interplay between Mean-Field Games and Machine-Learning (Session I)

  Prof. Levon Nurbekyan, Department of Mathematics, UCLA

  Jul 13, 21:00 - 23:00

  KAUST

  In this short course, I will discuss connections between mean-field games (MFG) systems and modern machine-learning (ML) techniques and problems. In the first part of the course, roughly the first two lectures, I will present how various ML techniques can be applied to solve high-dimensional MFG systems that are far out of reach for traditional methods. In the second part of the course, I will discuss the reverse relation, namely, how the MFG framework can be useful for solving specific ML problems.

Jul 11 - Jul 5, 2020

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  The Lagrangian Approach to First Order Mean Field Games (Session II)

  Prof. Francisco J. Silva, Applied Mathematics, University of Limoges, France

  Jul 8, 14:00 - 17:00

  KAUST

  In this course, we will consider the so-called Lagrangian approach to mean-field games. We will introduce the problem by recalling some basic results for nonatomic games in a static framework. Next, based on recent results in collaboration with Markus Fischer (University of Padua), I will introduce the analogous setting in the deterministic and dynamic framework. In the second part of the course, I will present the details of a convergence result, obtained in collaboration with Saeed Hadikhanloo, of equilibria of a suitable sequence of discrete-time and finite mean-field games, as introduced by Gomes, Mohr, and Souza in 2010, to an equilibrium of the first-order mean-field game system. The convergence proof relies importantly on the Lagrangian formulation of equilibria.
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  The Lagrangian Approach to First Order Mean Field Games (Session I)

  Prof. Francisco J. Silva, Applied Mathematics, University of Limoges, France

  Jul 6, 14:00 - 17:00

  KAUST

  In this course, we will consider the so-called Lagrangian approach to mean-field games. We will introduce the problem by recalling some basic results for nonatomic games in a static framework. Next, based on recent results in collaboration with Markus Fischer (University of Padua), I will introduce the analogous setting in the deterministic and dynamic framework. In the second part of the course, I will present the details of a convergence result, obtained in collaboration with Saeed Hadikhanloo, of equilibria of a suitable sequence of discrete-time and finite mean-field games, as introduced by Gomes, Mohr, and Souza in 2010, to an equilibrium of the first-order mean-field game system. The convergence proof relies importantly on the Lagrangian formulation of equilibria.

Jul 4 - Jun 28, 2020

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  Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks

  Chiheb Ben Hammouda, Ph.D., Applied Mathematics and Computational Science

  Jul 2, 14:00 - 16:00

  KAUST

  hierarchical approximation methods option pricing Computational biology

  In biochemically reactive systems with small copy numbers of one or more reactant molecules, stochastic effects dominate the dynamics. In the first part of this thesis, we design novel efficient simulation techniques, based on multilevel Monte Carlo methods and importance sampling, for a reliable and fast estimation of various statistical quantities for stochastic biological and chemical systems under the framework of Stochastic Reaction Networks (SRNs). In the second part of this thesis, we design novel numerical methods for pricing financial derivatives. Option pricing is usually challenging due to a combination of two complications: 1) The high dimensionality of the input space, and 2) The low regularity of the integrand on the input parameters. We address these challenges by using different techniques for smoothing the integrand to uncover the available regularity and improve quadrature methods' convergence behavior. We develop different ways of smoothing that depend on the characteristics of the problem at hand. Then, we approximate the resulting integrals using hierarchical quadrature methods combined with Brownian bridge construction and Richardson extrapolation.
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  Regularity Theory for MFG Systems (Session II)

  Prof. Marco Cirant, Department of Mathematics, University of Padova, Italy

  Jul 2, 09:00 - 12:00

  KAUST

  In this short course, I will address some regularity aspects in the theory of Mean-Field Games systems, with special emphasis on stationary and uniformly elliptic problems. I will first describe some regularity results for linear uniformly elliptic PDEs and semi-linear PDEs of Hamilton-Jacobi type. Then, I will show how to use these tools to prove the existence (and in some cases uniqueness) of solutions to MFG systems.
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  Two-Scale Homogenization and Numerical Methods for Stationary Mean-Field Games

  Xianjin Yang, Ph.D. Student, Applied Mathematics and Computational Science

  Jul 1, 16:00 - 18:00

  KAUST

  mean-field games

  Mean-field games (MFGs) study the behavior of rational and indistinguishable agents in a large population. Agents seek to minimize their cost based upon statistical information on the population's distribution. In this dissertation, we study the homogenization of a stationary first-order MFG and seek to find a numerical method to solve the homogenized problem. More precisely, we characterize the asymptotic behavior of a first-order stationary MFG with a periodically oscillating potential. Our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems. Moreover, we prove the existence and uniqueness of the solution to these limit problems. Next, we notice that the homogenized problem resembles the problem involving effective Hamiltonians and Mather measures, which arise in several problems, including homogenization of Hamilton--Jacobi equations, nonlinear control systems, and Aubry--Mather theory. Thus, we develop algorithms to solve the homogenized problem, effective Hamiltonians, and Mather measures.
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  Regularity Theory for MFG Systems (Session I)

  Prof. Marco Cirant, Department of Mathematics, University of Padova, Italy

  Jun 30, 09:00 - 12:00

  KAUST

  In this short course, I will address some regularity aspects in the theory of Mean-Field Games systems, with special emphasis on stationary and uniformly elliptic problems. I will first describe some regularity results for linear uniformly elliptic PDEs and semi-linear PDEs of Hamilton-Jacobi type. Then, I will show how to use these tools to prove the existence (and in some cases uniqueness) of solutions to MFG systems.

Jun 27 - Jun 21, 2020

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  Mean Field Games with Local Coupling (Session II)

  Prof. Alessio Porretta, Mathematical Analysis, University of Rome Tor Vergata, Italy

  Jun 25, 14:00 - 17:00

  KAUST

  We introduce several PDE tools which are useful in the study of mean field game systems with local couplings. Due to the lack of regularity of solutions, refined compactness and renormalization arguments are needed for a general approach leading to existence and uniqueness results. If time is enough, congestion models will be treated by similar techniques.