Dr. Felix Fritzen - Model Order Reduction and Data-assisted Surrogates in Materials Science

Abstract

In engineering applications the use of manufactured or natural composite materials is a key technology enabling leight-weight constructions and outstanding physical properties. However, the prediction of the impact of changes of the microstructural configuration on the physical properties are nontrivial to foresee. In order to better understand the microstructure-property relations, the use of model order reduction can be of great use. First, it enables parametric studies that account for deviations of the phase properties. Second, it allows for the consideration of nonlinearities at a fraction of the compute time of fully resolved models. The link between model reduction and computational homogenization in linear and nonlinear settings will be explored in this lecture. Further, the use of state of the art data-assisted techniques for the surrogation of nonlinear material models will be discussed. Here the use of reduced order models for the generation of the samples of the full order model are found to be rather useful.

Prof. Christoph Geuzaine, Ph.D. - Recent Developments in Gmsh

Department of Electrical Engineering and Computer Science, University of Liege, Belgium

Abstract

Gmsh (http://gmsh.info) is an open source finite element mesh generator with built-in pre- and post-processing facilities. Under continuous development for the last two decades, it has become the de facto standard for open source finite element mesh generation, with a large user community in both academia and industry. In this talk I will present an overview of Gmsh, and highlight recent developments including the support for constructive solid geometry, new robust and parallel meshing algorithms, flexible solver integration and a new multi-language Application Programming Interface. Time permitting I will also present an overview of current research directions for meshing based on the solution of partial differential equations: from surface remeshing to frame-based hex-meshing.

Prof. Dariusz Uciński Ph.D. - Optimum Experimental Design for Distributed Parameter System Identification

Institute of Control and Computation Engineering, University of Zielona Góra, Poland

Abstract

The impossibility of observing the states of distributed parameter systems over the entire spatial domain raises the question of where to locate measurement sensors so as to estimate the unknown system parameters as accurately as possible. Both researchers and practitioners do not doubt that making use of sensors placed in an ‘intelligent’ manner may lead to dramatic gains in the achievable accuracy of the parameter estimates, so efficient sensor location strategies are highly desirable. In turn, the complexity of the sensor location problem implies that there are few sensor placement methods which are readily applicable to practical situations. What is more, they are not well known among researchers. The aim of the minicourse is to give account of both classical and recent original work on optimal sensor placement strategies for parameter identification in dynamic distributed systems modeled by partial differential equations. The reported work constitutes an attempt to meet the needs created by practical applications, especially regarding environmental processes, through the development of new techniques and algorithms or adopting methods which have been successful in akin fields of optimal control and optimum experimental design. While planning, real-valued functions of the Fisher information matrix of parameters are primarily employed as the performance indices to be minimized with respect to the sensor positions. Particular emphasis is placed on determining the ‘best’ way to guide moving and scanning sensors, and making the solutions independent of the parameters to be identified. A couple of case studies regarding the design of air quality monitoring networks are adopted as an illustration aiming at showing the strength of the proposed approach in studying practical problems. The course will be complemented by a discussion of more advanced topics including the related problem of optimum input design and the Bayesian approach to deal with the ill-posedness of parameter estimation.

Prof. Dr. Philippe Renard - Stochastic Modeling of Karstic Systems

Centre d'Hydrogéologie et de Géothermie, University of Neuchâtel, Paris

Abstract

Karstic aquifers are characterized by the presence of rare but highly permeable karstic conduits embedded in a carbonate matrix of lower permeability. This highly heterogeneous structure results from the dissolution of the matrix by acidic water and a self-reinforcing process. Karst aquifers can present very fast flow and contaminant transfer in the conduits. Consequently, these aquifers are often highly vulnerable to groundwater pollution and extremely sensitive to climate fluctuations. In recent years, significant progresses have been made to model karstic reservoirs. In this presentation, we will discuss several of these modeling aspects, including techniques that can be used to simulate the geometry of karstic networks (often only partially known), flow and transport simulation methods, but also the speleogenesis processes.

Prof. Youssef Marzouk, Ph.D. - Transport Methods for Sampling: Preconditioning and Low-dimensional Structure

Department of Aeronautics and Astronautics,Massachusetts Institute of Technology, USA

Abstract

Integration against an intractable probability measure is a fundamental challenge in Bayesian inference and well beyond. A useful approach to this problem seeks a deterministic coupling of the measure of interest with a tractable “reference” measure (e.g., a standard Gaussian). Such couplings are induced by transport maps, and enable direct simulation from the desired measure simply by evaluating the transport map at samples from the reference. In recent years, an enormous variety of representations and constructions for such transport maps have been proposed­—ranging from monotone polynomials or invertible neural networks to the flows of ODEs. Approximate transports can also be used to “precondition” and accelerate standard Monte Carlo schemes. Within this framework, one can describe many useful notions of low-dimensional structure: for instance, sparse or decomposable transports underpin modeling and computation with non-Gaussian Markov random fields, and low-rank transports arise frequently in inverse problems.

I will present a broad overview of this framework, describing how to construct suitable classes of transport maps, and then focus on two recent developments: adaptive MCMC schemes that use transport to create more favorable target geometry, and greedy variational methods that build high-dimensional transport maps by composing multiple low-dimensionalmaps or flows.

This is joint work with Daniele Bigoni, Matthew Parno, Alessio Spantini, and Olivier Zahm.

Speaker bio: Youssef Marzouk is an associate professor in the Department of Aeronautics and Astronautics at MIT, and co-director of the MIT Center for Computational Engineering. He is also director of MIT’s Aerospace Computational Design Laboratory and a core member of MIT's Statistics and Data Science Center. His research interests lie at the intersection of physical modeling with statistical inference and computation. In particular, he develops methodologies for uncertainty quantification, inverse problems, large-scale Bayesian computation, and optimal experimental design in complex physical systems. His methodological work is motivated by a wide variety of engineering, environmental, and geophysics applications. He received his SB, SM, and PhD degrees from MIT and spent several years at Sandia National Laboratories before joining the MIT faculty in 2009. He is a recipient of the Hertz Foundation Doctoral Thesis Prize (2004), the Sandia Laboratories Truman Fellowship (2004-2007), the US Department of Energy Early Career Research Award (2010), and the Junior Bose Award for Teaching Excellence from the MIT School of Engineering (2012). He is an Associate Fellow of the AIAA and currently serves on the editorial boards of the SIAM Journal on Scientific Computing, Advances in Computational Mathematics, and the SIAM/ASA Journal on Uncertainty Quantification, among other journals. He is also an avid coffee drinker and occasional classical pianist.