# Events

# SSD - Koumoutsakos Seminar

## Prof. Dr. Petros Koumoutsakos - Computing and Data Science Interfaces for Fluid Mechanics

Chair of Computational Sciences, ETH Zürich, Switzerland

### Abstract

We live in exciting times characterized by a unique convergence of Computing and Data Sciences. Novel frameworks fuse data with numerical methods while learning algorithms are deployed on computers with unprecedented capabilities. Can we harness these new capabilities to solve some of the long standing problems in Fluid Mechanics such as turbulence modeling, flow control and energy cascades ? I will discuss our efforts to answer this question, celebrate successes as well as outline failures and open problems. I will demonstrate how Bayesian reasoning can assist model selection in molecular simulations, how long-shirt memory networks (may fail to) predict chaotic systems and how deep reinforcement learning can produce powerful flow control methodologies. I will argue that, while Data and Computing offer wonderful capabilities, it is human thinking that remains the central element in our effort to solve Fluid Mechanics problems.

# CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Willcox Seminar

## Prof. Karen Willcox, Ph.D. - Projection-based Model Reduction: Formulations for Scientific Machine Learning

### Abstract

The field of model reduction encompasses a broad range of methods that seek efficient low-dimensional representations of an underlying high-fidelity model. A large class of model reduction methods are projection-based; that is, they derive the low-dimensional approximation by projection of the original large-scale model onto a low-dimensional subspace. Model reduction has clear connections to machine learning. The difference in fields is perhaps largely one of history and perspective: model reduction methods have grown from the scientific computing community, with a focus on reducing high-dimensional models that arise from physics-based modeling, whereas machine learning has grown from the computer science community, with a focus on creating low-dimensional models from black-box data streams. This talk will describe two methods that blend the two perspectives and provide advances towards achieving the goals of Scientific Machine Learning. The first method combines lifting--the introduction of auxiliary variables to transform a general nonlinear model to a model with polynomial nonlinearities--with proper orthogonal decomposition (POD). The result is a data-driven formulation to learn the low-dimensional model directly from data, but a key aspect of the approach is that the lifted state-space in which the learning is achieved is derived using the problem physics. The second method combines a low-dimensional POD parametrization of quantities of interest with machine learning methods to learn the map between the input parameters and the POD expansion coefficients. The use of particular solutions in the POD expansion provides a way to embed physical constraints, such as boundary conditions. Case studies demonstrate the importance of embedding physical constraints within learned models, and also highlight the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models.

# SSD - Grossmann Seminar

## Prof. Ignacio Grossmann, Ph.D. - Advances in Nonlinear Mixed-integer and Generalized Disjunctive Programming and Applications to the Optimization of Engineering Systems

Department of Chemical Engineering, Carnegie Mellon University, USA

### Abstract

In this seminar, we first review recent advances in MINLP (Mixed-Integer Nonlinear Programming) and GDP (Generalized Disjunctive Programing) algorithms. We first describe the quadratic outer-approximation algorithm in which scaled second order approximations that provide valid bounds are incorporated into the master problem in order to reduce the number of major iterations in highly nonlinear convex MINLP problems. Applications are presented in safety layout problems, and in reliability design problems. Here the goal is to determine the number of standby units in serial systems with units that have pre-specified probabilities of failure, with the objectives being to minimize cost and to maximize availability. We apply the proposed models to the design of reliable air separation plants. We next address global optimization of nonconvex GDP problems for which bounds of the global optimum are strengthened through basic steps for the convex GDP approximations, and for which a logic based algorithm is proposed that relies on the use of cutting planes to avoid the increased dimensionality due to the use of hull relaxations. We illustrate the application of this algorithm to the optimal multiperiod blending problem for crude oil. We also address a nonconvex GDP problem corresponding to the design of centralized and distributed facilities. Given the number and location of suppliers and markets, the goal is to determine the number of facilities and their location in a two-dimensional space so as to minimize investment and transportation costs. We develop a special purpose method to solve this GDP problem and apply it to the design of biomass network facilities.

# EU Regional School - Fröhlich Seminar

## Prof. Dr. Holger Fröhlich - From Hype to Reality: Data Science Enabling Innovation in Biomedicine

Bonn-Aachen International Center for Information Technology (B-IT), University of Bonn, Germany

## Abstract

Recent years have witnessed a dramatic increase of interest in Data Science and Artificial Intelligence in biomedical and pharmaceutical research. This increasing interest is accompanied by an often uncritical and hype generating debate in the main stream media, which is driven by a lack of understanding, hence pointing out the necessity for better education.

My talk will be divided into two parts: In the first part I want clarify terminology and give a general introduction into Data Science by briefly explaining some of the commonly used concepts. The second part will focus on the impact of Data Science in biomedical research. In particular, I want to demonstrate this connection by selected examples from own work. I will conclude my talk by reflecting on the strength and limitations of data driven modeling approaches and how future developments may help to overcome them.

# EU Regional School - Reali Seminar

## Prof. Alessandro Reali, Ph.D. - Isogeometric Analysis: An Introduction and Some Recent Advances

Department of Civil Engineering and Architecture - Structures and Materials Section, University of Pavia, Italy

## Abstract

Isogeometric Analysis (IGA) is a recent simulation framework, originally proposed by T.J.R. Hughes and coworkers in 2005, to bridge the gap between Computational Mechanics and Computer Aided Design (CAD). The basic IGA paradigm consists of adopting the same basis functions used for geometry representations in CAD systems - such as, e.g., Non-Uniform Rational B-Splines (NURBS) - for the approximation of field variables, in an isoparametric fashion. This leads to a cost-saving simplification of the typically expensive mesh generation and refinement processes required by standard finite element analysis. In addition, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per-degree-of-freedom and an enhanced robustness with respect to standard finite elements in a number of applications ranging from solids and structures to fluids, opening also the door to geometrically flexible discretizations of higher-order partial differential equations in primal form, as well as to highly efficient (strong-form) collocation methods.

The first part of this short course is devoted to the introduction of the basic concepts of IGA (including a brief primer on B-Splines and NURBS). The unique potential of IGA is then shown through some convincing applications, mainly belonging to the field of structural mechanics and of fluid-structure interaction, where the superior results that can be provided by IGA with respect to standard finite elements are clearly pointed out.

The lecture is finally concluded by a brief presentation of further IGA works in progress and new ideas.