Prof. Marco Picasso, Ph.D. - Adaptive Finite Element with Large Aspect Ratio

Mathematics Institute of Computational Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

Abstract

Adaptive finite elements with large aspect ratio have shown to be extremely efficient whenever the solution to the underlying pde has internal or boundary layers. The adaptive criteria can be based on anisotropic a posteriori error estimates, the involved interpolation constants being aspect ratio independent.

In this talk, some a posteriori error estimates and adaptive algorithms will be presented on academic problems (elliptic, parabolic and hyperbolic pde's). Numerical results on more challenging CFD problems will also be discussed.

Dr. Norbert Hosters - Spline-based Methods for Fluid-structure Interaction

Abstract

The numerical advantages of the presented combination of isogeometric analysis and the NURBS-enhanced 

Prof. Filippo Lipparini, Ph.D. - Multiscale Modeling: a Chemical Perspective to an Interdisciplinary Problem

Abstract

Computational chemistry is the branch of chemistry that uses models and computer simulations in order to predict or rationalize the molecular behavior of chemical systems. Methods based on quantum mechanics are nowadays extensively used in order to study molecular properties, structures or reactivity and are becoming a standard technique in the toolbox of a chemist. Many different methods exist, that differ in accuracy and applicability, due to their computational cost. Unfortunately, the size of the systems to which such methodologies can be applied is limited. Processes that involve large biomolecules, or that happen in solution, can not be described in a naive way by just increasing the size of the model system. Focused multiscale models, that divide the system in a core, where the interesting process mainly happens, and an environment, which plays a spectator role to the process, but influences it by tuning the properties of the core, are one of the most successful strategies to deal with such complex phenomena. In this presentation, I will quickly present two of such multiscale models, namely, continuum solvation models and QM/MM models, and describe some of the challenges that they introduce, with particular attention on numerical and computational aspects. I will present some new algorithmic or technical solutions recently proposed, one of which is the results of a collaboration between chemists and applied mathematicians.

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.

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.