Abstract:

Time inconsistent performance crit

Chebyshev nodes are well-known for their near-optimal polynomial interpolation and quadrature properties on intervals. In particular, the associated Lebesgue constant grows only logarithmically, whereas that associated to equispaced nodes grows exponentially.

We present a novel regularizing ensemble Kalman method for solving PDE-constrained inverse problems. By merging ideas from iterative regularisation approaches and ensemble Kalman algorithms we design a derivative-free solver for generic inverse problems. The proposed method can be used to estimate parameters of large-scale PDE models in a black-box fashion.

In this talk, I explore the application of single level and multilevel Monte Carlo methods for computing key quantities in a stochastic particle system within the mean-field framework.

This thesis focuses on the development and analysis of efficient simulation and inference techniques for Markovian pure jump processes with a view towards applications in dense communication networks. The first part of this work proposes novel numerical methods to estimate, in an efficient and accurate way, observables from realizations of Markovian jump processes.

In biochemical systems, stochastic effects can be caused by the presence of small numbers of certain reactant molecules. In this setting, discrete state-space and stochastic simulation approaches were proved to be more relevant than continuous state-space and deterministic ones.

Experimental design can be vital when experiments are resource exhaustive and time-consuming. In this work, we carry out experimental design in the Bayesian framework. To measure the amount of information, which can be extracted from the data in an experiment, we use the expected information gain as the utility function, which specifically is the expected logarithmic ratio between the posterior and prior distributions.

Jacques DUYSENS, 47 years old, obtained his Civil Engineer Diploma in Electricity & Mechanics, and in Aerospace, from the University of Liège (Belgium) with the highest distinction. His prior responsibility was as R&D Engineer in Powertrains Groups dynamics at RENAULT SA (France) in 1990. Three years later, he served as Director of the Simulation of Manufacturing Processes department (Assembly & Machining) within the Mechanical Process Direction.

Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs) that have been mainly developed to model biochemical reactions. SRNs also have applications in neural networks, virus kinetics, and dynamics of social networks, among others.

Core flooding experiments are always needed to be conducted before the application of Enhanced Oil Production (EOR) in the field, which is a great way to improve the oil recovery. In order to optimize existing resources and obtain the information efficiently, it is necessary to optimize these experiments.

Marco Iglesias received his PhD in 2008 from the Institute for Computational Engineering and Sciences, University of Texas at Austin. From 2008 and 2013 Iglesias held postdoctoral positions at the Department of Civil and Environmental Engineering at MIT as well as the Mathematics Institute at the University of Warwick . Since October 2013 Iglesias is an assistant professor in scientific computation at the University of Nottingham, U.K.

We provide a quick glance into recently developed Adaptive Multilevel Monte Carlo (MLMC) Methods for the following widely applied mathematical models: (i) Itô Stochastic Differential Equations, (ii) Stochastic Reaction Networks modeled by Pure Jump Markov Processes and (iii) Partial Differential Equations with random inputs.

In this talk, I will describe the main features that characterize a Bayesian framework for experimental design. A special emphasis will be devoted to the description of how to measure the information, conveyed by an experiment, about the unknown parameters of the statistical model used to describe the data uncertainty.

This talk will provide a tutorial style introduction to sequential Monte Carlo methods, attempting to start from a basic introduction, to a coverage of some of the latest research developments.

Last year I provided a quick glance into the research of my KAUST Stochastic Numerics group, giving particular emphasis on the activities of my KAUST students. There I also connected our KAUST research and our educational activities, including the Numerical Methods for Stochastic Differential Equations (AMCS 336) and Stochastic Methods for Engineers (AMCS 308) KAUST courses.

In many Computational Science and Engineering applications, uncertainties in model, parameters, and initial condition, in concert with increasing computational power, have lead to an increasing interest in probabilistic solutions of large-scale problems.  Even crude approximations of the probabilistic solution require many tens of deterministic solves and accurate ones often require thousands or millions.

Alexander Litvinenko joined the Stochastic Numerics Group and Strategic Initiative in Uncertainty Quantification at KAUST in 2013.  He specializes in efficient numerical methods for stochastic PDEs, uncertainty quantification, and multi-linear algebra.  He is involved in Bayesian update methods for solving inverse problems, with the goal of reducing the complexity both the stochastic forward problem as well as the Bayesian update by a low-rank (sparse) tensor data approximation.

In R1 we discuss the telegraph process and give the main distributional results. We consider also the case of the asymmetric telegraph process and use relativistic transformations for its probabilistic analysis. Random motions in the plane with infinite and with a finite number of possible directions of motion are discussed.

We present, in the simplest possible way, the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields. As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the aim of making the basic philosophy clear.

The seminar will present the basic structure and the fundamental ideas behind the Virtual Element Methods, taking, for simplicity, the Laplace operator as toy example. The main features of the method will be sketched, together with the guidelines for its implementation and the essential mathematical instruments to be used in the analysis.

Alexander Litvinenko joined the Stochastic Numerics Group and Strategic Initiative in Uncertainty Quantification at KAUST in 2013.  He specializes in efficient numerical methods for stochastic PDEs, uncertainty quantification, and multi-linear algebra.  He is involved in Bayesian update methods for solving inverse problems, with the goal of reducing the complexity both the stochastic forward problem as well as the Bayesian update by a low-rank (sparse) tensor data approximation.

Bayesian inference provides a natural framework for quantifying uncertainty in parameter estimates and model predictions, for combining heterogeneous sources of information, and for conditioning sequential predictions on data. Posterior simulation in Bayesian inference often proceeds via Markov chain Monte Carlo (MCMC) or sequential Monte Carlo (SMC), but the associated computational expense and convergence issues can present significant bottlenecks in large-scale or dynamically complex problems.

The widely used Monte Carlo simulation technique where all the particles are independent and statistically identical and their weights are constant is by no means universally applicable. The reason is that particles may wander off to irrelevant parts of the state space, leaving only a small fraction of relevant particles that contribute to the computational task at hand. Therefore it  may require a huge number of particles to obtain a desired precision, resulting in a computational cost that is too high for all practical purposes.

Hierarchy is a key ingredient for achieving optimal arithmetic complexity and scalable communication complexity in algorithms. Fast Multipole Methods (FMM) and H-matrices share many common features that arise from their hierarchical nature. In this talk, Rio Yokota will illustrate the common features between FMM and H-matrices and how these features are favorable on computer architectures of the next generation.