Events

Oct 25 - Nov 1, 2020

• 

  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 18 - Oct 25, 2020

• 

  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 11 - Oct 18, 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 Sciences

  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 Sciences

  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 4 - Oct 11, 2020

• 

  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, Research Scientist, Hierarchical Computations on Manycore Architectures

  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.

Sep 27 - Oct 4, 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.
• 

  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 13 - Sep 20, 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.
• 

  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 6 - Sep 13, 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 Sciences

  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.

Aug 30 - Sep 6, 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.

Jul 26 - Aug 2, 2020

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

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

  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 12 - Jul 19, 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 5 - Jul 12, 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.
• 

  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.

Jun 28 - Jul 5, 2020

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  Hierarchical Approximation Methods for Option Pricing and Stochastic Reaction Networks

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

  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.
• 

  Two-Scale Homogenization and Numerical Methods for Stationary Mean-Field Games

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

  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.
• 

  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 21 - Jun 28, 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.
• 

  Mean field games with local coupling (Session I)

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

  Jun 22, 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.

May 31 - Jun 14, 2020

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  Trajectory Planning for Autonomous Underwater Vehicles: A Stochastic Optimization Approach

  Sultan Albarakati, Director, KAUST Academy

  Jun 7, 16:00 - 18:00

  KAUST

  optimization

  In this work, we develop a new framework of trajectory planning for AUVs in realistic ocean scenarios. We divide this work into three parts. In the first part, we provide a new approach for deterministic trajectory planning in steady current, described using Ocean General Circulation Model (OGCM) data. The latter are used to specify both the ocean current and the bathymetry. We apply a NLP to the optimal-time trajectory planning problem. To demonstrate the effectivity of the resulting model, we consider the optimal time trajectory planning of an AUV operating in the Red Sea and the Gulf of Aden. In the second part, we generalize our 3D trajectory planning framework to time-dependent ocean currents. We also extend the framework to accommodate multi-objective criteria, focusing specifically on the Pareto front curve between time and energy. The scheme is demonstrated for time-energy trajectory planning problems in the Gulf of Aden. In the last part, we address uncertainty in the ocean current field. The uncertainty in the current is described in terms of a finite ensemble of flow realizations. The proposed approach is based on a non-linear stochastic programming methodology that uses a risk-aware objective function, accounting for the full variability of the flow ensemble. Advanced visualization tools are used to amplify simulation results.

Apr 26 - May 3, 2020

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  On Optimal Regularization in Estimation, Detection, and Classification

  Tareq Al-Naffouri, Professor, Electrical and Computer Engineering

  Apr 30, 12:00 - 13:00

  KAUST

  linear systems computational Complexity Convex Gaussian Min-max theorem

  In many problems in statistical signal processing, regularization is employed to deal with uncertainty, ill-posedness, and insufficiency of training data. It is possible to tune these regularizers optimally asymptotically, i.e. when the dimension of the problem becomes very large, by using tools from random matrix theory and Gauss Process Theory. In this talk, we demonstrate the optimal turning of regularization for three problems : i) Regularized least squares for solving ill-posed and/or uncertain linear systems, 2) Regularized least squares for signal detection in multiple antenna communication systems and 3) Regularized linear and quadratic discriminant binary classifiers.

Apr 19 - Apr 26, 2020

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  Efficient and Physics-Preserving Discretization Schemes for Multiphase Flow Problems

  Shuyu Sun, Professor, Earth Science and Engineering

  Apr 23, 12:00 - 13:00

  KAUST

  No summary is available.

Apr 12 - Apr 19, 2020

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  Quantitative understanding of transcription factor regulation at network- and molecular-levels through optimization and deep learning

  Xin Gao, Program Chair, Computer Science

  Apr 16, 12:00 - 13:00

  KAUST

  transcription factor optimization Deep learning

  Transcription factors are an important family of proteins that control the transcription rate from DNAs to messenger RNAs through the binding to specific DNA sequences. Transcription factor regulation is thus fundamental to understanding not only the system-level behaviors of gene regulatory networks, but also the molecular mechanisms underpinning endogenous gene regulation. In this talk, I will introduce our efforts on developing novel optimization and deep learning methods to quantitatively understanding transcription factor regulation at network- and molecular-levels. Specifically, I will talk about how we estimate the kinetic parameters from sparse time-series readout of gene circuit models, and how we model the relationship between the transcription factor binding sites and their binding affinities.

Apr 5 - Apr 12, 2020

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  Geometry and Computational Design

  Apr 9, 12:00 - 13:00

  KAUST

  Geometry computational design

  An important stream of research in computational design aims at digital tools which support users in realizing their design intent in a simple and intuitive way, while simultaneously taking care of key aspects of function and fabrication. Such tools are expected to shorten the product development cycle through a reduction of costly feedback loops between design, engineering and fabrication. The strong coupling between shape generation, function and fabrication is a rich source for the development of new geometric concepts, with an impact to the original applications as well as to geometric theory. This will be illustrated at hand of applications in architecture and fabrication with a mathematical focus on discrete differential geometry and geometric optimization problems.

Mar 29 - Apr 5, 2020

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  Classification of Functional Data by Detecting the Discrepancy of Second Moment Structure of Scaled functions

  Shuhao Jiao, Postdoctoral Research Fellow, Statistics

  Apr 2, 12:00 - 13:00

  KAUST

  Functional data

  This talk presents a new classification method for functional data. We consider the case where different groups of functions have similar means so that it is difficult to classify them based on only the mean function. To overcome this limitation, we propose the second moment based functional classifier (SMFC). Here, we demonstrate that the new method is sensitive to divergence in the second moment structure and thus produces lower rate of misclassification compared to other competitor methods. Our method uses the Hilbert-Schmidt norm to measure the divergence of second moment structure. One important innovation of our classification procedure lies in the dimension reduction step. The method data-adaptively discovers the basis functions that best capture the discrepancy between the second moment structures of the groups, rather than uses the functional principal component of each individual group, and good performance can be achieved as unnecessary variability is removed so that the classification accuracy is improved. Consistency properties of the classification procedure and the relevant estimators are established. Simulation study and real data analysis on phoneme and rat brain activity trajectories empirically validate the superiority of the proposed method.

Mar 8 - Mar 15, 2020

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  Functional data depth and its application in the visualization of spatio-temporal covariance structures

  Mar 12, 12:00 - 13:00

  KAUST

  functional data analysis spatio-temporal statistics

  Functional data analysis is a very active research area due to the overwhelming existence of functional data. In the first part of this talk, I will introduce how functional data depth is used to carry out exploratory data analysis and explain recently-developed depth techniques. In the second part, I will discuss spatio-temporal statistical modeling. It is challenging to build realistic space-time models and assess the validity of the model, especially when datasets are large. I will present a set of visualization tools we developed using functional data analysis techniques for visualizing covariance structures of univariate and multivariate spatio-temporal processes. I will illustrate the performance of the proposed methods in the exploratory data analysis of spatio-temporal data.

Mar 1 - Mar 8, 2020

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  Simulation of Neuronal Signal Processing - 2020-03-05

  Gabriel Wittum, Professor, Applied Mathematics and Computational Sciences

  Mar 5, 12:00 - 13:00

  B9 L2 R2322

  Neuronal ensembles Stochastiic Variability neuroscience

  In the lecture we present a three dimensional mdoel for the simulation of signal processing in neurons. To handle problems of this complexity, new mathematical methods and software tools are required. In recent years, new approaches such as parallel adaptive multigrid methods and corresponding software tools have been developed allowing to treat problems of huge complexity. Part of this approach is a method to reconstruct the geometric structure of neurons from data measured by 2-photon microscopy. Being able to reconstruct neural geometries and network connectivities from measured data is the basis of understanding coding of motoric perceptions and long term plasticity which is one of the main topics of neuroscience. Other issues are compartment models and upscaling.

Feb 23 - Mar 1, 2020

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  Deterministic particle approximation for nonlinear transport equations

  Marco Di Francesco, Associate Professor, Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila (Italy)

  Feb 25, 14:00 - 15:00

  Building L3 R3119

  PDE numerical methods nonlinear models

  Approximating the solution to an evolutionary partial differential equation by a set of "moving particles" has several advantages. It validates the use of a continuity equation in an "individuals-based" modeling setting, it provides a link between Lagrangian and Eulerian description, and it defines a "natural" numerical approach to those equations. I will describe recent rigorous results in that context. The main one deals with one-dimensional scalar conservation laws with nonnegative initial data, for which we prove that the a suitably designed "follow-the-leader" particle scheme approximates entropy solutions in the sense of Kruzkov in the many particle limit. Said result represents a new way to solve scalar conservation laws with bounded and integrable initial data. The same method applies to second order traffic flow models, to nonlocal transport equations, and to the Hughes model for pedestrian movements.

Feb 16 - Feb 23, 2020

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  Statistical models for long-range dependent climate data

  Sigrunn Sorbye, Associate Professor, UiT The Arctic University of Norway

  Feb 20, 12:00 - 13:00

  B9 L2 R2322

  statistical models climate data

  In this talk I will discuss statistical models which incorporate temperature response to the radiative forcing components. The models can be used to estimate important climate sensitivity measures and give temperature forecasts. Bayesian inference is obtained using the methodology of integrated nested Laplace approximation and Monte Carlo simulations. The resulting approach will be demonstrated in analyzing instrumental data and Earth system model ensembles.

Feb 9 - Feb 23, 2020

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  Energy and Entropy in Numerical Methods

  Hendrik Ranocha, Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences

  Feb 16, 12:00 - 13:00

  B9 L2 H2

  numerical methods

  Secondary quantities such as energy and entropy can be very important for numerical methods. Firstly, preserving these quantities can ensure that non-physical behavior is excluded. Secondly, preserving such quantities can result in stability estimates. Finally, preserving the correct energy/entropy evolution in time can result in additional desirable properties such as lower numerical errors. In this talk, a brief overview of some recent advances concerning energy and entropy preserving numerical methods for ordinary and partial differential equations will be given, together with an outlook on future research directions and applications.

Feb 9 - Feb 16, 2020

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  Unveiling the potential of energy/entropy stable numerical methods for hyperbolic/mixed hyperbolic-parabolic PDEs

  Matteo Parsani, Associate Professor, Applied Mathematics and Computational Sciences

  Feb 13, 12:00 - 13:00

  B9 L2 H1

  algorithm Hyperbolic PDEs PDE parabolic-hyperbolic PDE SBP numerical methods for PDE's

  Abstract The demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future PDEs solvers. At the algorithmic level, hardware compatibility and efficiency are of paramount importance in determining viability on future hardware. However, equally important (if not more so) is provable algorithmic robustness which becomes progressively more challenging to achieve as problem size and physics complexity increase. We show that rigorously designed adaptive semi- and fully-discrete
• 

  Weak solutions of the 2D Euler equations

  Stefano Spirito, Assistant Professor, Department of Mathematics, University of L’Aquila, Italy

  Feb 11, 15:00 - 16:00

  B1 L3 R3119

  Cauchy problem Euler equations

  In this talk we consider the Cauchy problem for the 2D Euler equations for incompressible inviscid fluids. It is well-known that given a smooth initial datum, the Cauchy problem is well-posed and in particular the energy is conserved and the vorticity is transported by the flow of the velocity. When we consider weak solutions this might not be the case anymore. We will review some recent results obtained in collaboration with Gianluca Crippa and Gennaro Ciampa where we extend those properties to the case of irregular vorticities. In particular, under low integrability assumptions on the vorticity we show that certain approximations important from a physical and a numerical point of view converge to solutions satisfying those properties.

Feb 2 - Feb 9, 2020

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  Mathematical modeling of the stochastic climate system

  Georgiy L. Stenchikov, Professor, Earth Science and Engineering

  Feb 6, 12:00 - 13:00

  B9 L2 H1

  weather climate projections

  ​Author of more than 290 journal and conference publications, Professor Stenchikov's research interests are in multi-scale modeling of environmental processes and numerical methods; global climate change, climate downscaling, atmospheric convection; assessment of anthropogenic impacts and geoengineering; air-sea interaction, evaluating environmental consequences of catastrophic events like volcanic eruptions, nuclear explosions, forest and urban fires; and air pollution, transport of aerosols, chemically and optically active atmospheric tracers, their radiative forcing and effect on climate.
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  A regularized shallow-water waves system with slip-wall boundary conditions: Theory and numerical analysis

  Dimitrios Mitsotakis, Senior Lecturer, School of Mathematics and Statistic Victoria University of Wellington, New Zealand

  Feb 5, 16:00 - 17:00

  B1 L4 R4214

  In this talk we present the derivation of a new Boussinesq-type system to describe the propagation of long waves of small amplitude in a basin with mildly varying bottom topography. We prove the existence and uniqueness of weak solutions for maximal times that do not depend on the amplitude of the waves. We then present the numerical solution of the new system using Galerkin finite element methods and prove the convergence of the semidiscrete solution to the exact solution. The system appears to describe well water waves even in benchmark experiments that involve also general bathymetries.
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  Algebraic flux correction for finite element discretizations of hyperbolic conservation laws

  Prof. Dmitri Kuzmin, Applied Mathematics, TU Dortmund University

  Feb 3, 14:00 - 15:00

  B1 L4 R4214

  algebraic flux correction hyperbolic problems stabilization techniques flux-corrected transport

  In this talk, we review some recent advances in the analysis and design of algebraic flux correction (AFC) schemes for hyperbolic problems. In contrast to most variational stabilization techniques, AFC approaches modify the standard Galerkin discretization in a way which provably guarantees the validity of discrete maximum principles for scalar conservation laws and invariant domain preservation for hyperbolic systems. The corresponding inequality constraints are enforced by adding diffusive fluxes, and bound-preserving antidiffusive corrections are performed to obtain nonlinear high-order approximations. After introducing the AFC methodology and the underlying theoretical framework in the context of continuous piecewise-linear finite element discretizations, we present some of the limiting techniques that we use in high-resolution AFC schemes. This presentation is based on joint work with Dr. Manuel Quezada de Luna (KAUST) and other collaborators.

Jan 26 - Feb 2, 2020

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  Dynamics and Convergence of Weight Normalization for Training Neural Networks

  Guido Montufar, Assistant Professor, Departments of Mathematics and Statistics, University of California, Los Angeles (UCLA)

  Jan 29, 13:00 - 14:30

  B1 L3 R3119

  machine learning neural network optimization ReLUs

  We present a result on the convergence of weight normalized training of artificial neural networks. In the analysis, we consider over-parameterized 2-layer networks with rectified linear units (ReLUs) initialized at random and trained with batch gradient descent and a fixed step size. The proof builds on recent theoretical works that bound the trajectory of parameters from their initialization and monitor the network predictions via the evolution of a ''neural tangent kernel'' (Jacot et al. 2018). We discover that training with weight normalization decomposes such a kernel via the so called ''length-direction decoupling''. This in turn leads to two convergence regimes. From the modified convergence we make a few curious observations including a natural form of ''lazy training'' where the direction of each weight vector remains stationary.

Jan 19 - Jan 26, 2020

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  A very short introduction to regularity theory for linear elliptic equations - Part 4

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

  Jan 22, 14:00 - 15:30

  B1 L3 R3119

  PDE regularity

  Mini Course Part 4 of 4. The course is a very short introduction to regularity for linear elliptic pdes of second order. We start with equations with regular coefficients and the difference quotient method of Nirenberg. We then treat the case of coefficients that are merely measurable and bounded, putting forward the basics of De Giorgi-Nash-Moser theory. If time permits, we present some characterizations of Hölder spaces which are very useful in regularity theory.
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  A very short introduction to regularity theory for linear elliptic equations - Part 3

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

  Jan 20, 14:00 - 15:30

  B1 L3 R3119

  PDE regularity

  Mini Course Part 3 of 4. The course is a very short introduction to regularity for linear elliptic pdes of second order. We start with equations with regular coefficients and the difference quotient method of Nirenberg. We then treat the case of coefficients that are merely measurable and bounded, putting forward the basics of De Giorgi-Nash-Moser theory. If time permits, we present some characterizations of Hölder spaces which are very useful in regularity theory.
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  KAUST Research Conference Digital Health 2020

  Takashi Gojobori, Ibn Sina Distinguished Professor, Bioscience

  Jan 20, 08:00 - Jan 22, 17:00

  B19 L2 H1

  digital health artificial intelligence computational science big data analytics Omics

  Computational Bioscience Research Center at King Abdullah University of Science and Technology is pleased to announce the KAUST Research Conference on Digital Health 2020.