SSD - Elber Seminar
Prof.Gershon Elber, Ph.D. - Volumetric Representations: the Geometric Modeling of the Next Generation
he needs of modern (additive) manufacturing (AM) technologies can be satisfied no longer by boundary representations (B-reps), as AM requires the representation and manipulation of interior fields and materials as well. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modeling (GM) has been conceived, contemporary GM systems only offer a loose link between the two, if at all.
For about half a century, (trimmed) Non Uniform Rational B-spline (NURBs) surfaces has been the B-rep of choice for virtually all the GM industry. Fundamentally, B-rep GM has evolved little during this period. In this talk, we seek to examine an extended volumetric representation (V-rep) that successfully confronts the existing and anticipated design, analysis, and manufacturing foreseen challenges. We extend all fundamental B-rep GM operations, such as primitive and
surface constructors and Boolean operations, to trimmed trivariate V-reps. This enables the much needed tight link to (Isogeometric) analysis on one hand and the full support of (heterogeneous and anisotropic) additive manufacturing on the other.
Examples and other applications of V-rep GM, including AM and lattice- and micro-structure synthesis and heterogeneous materials will also be demonstrated.
SSD - Hesthaven Seminar
Prof. Jan Hesthaven Ph.D.- New Directions in Reduced Order Modeling
Chair of Computational Mathematics and Simulation Science, Ecole Polytechnique Fédérale de Lausanne, Switzerland
The development of reduced order models for complex applications, offering the promise for rapid and accurate evaluation of the output of complex models under parameterized variation, remains a very active research area. Applications are found in problems which require many evaluations, sampled over a potentially large parameter space, such as in optimization, control, uncertainty quantification and applications where near real-time
response is needed. However, many challenges remain to secure the flexibility, robustness, and efficiency needed for general large-scale applications, in particular for nonlinear and/or timedependent problems. After giving a brief general introduction to reduced order models, we discuss developments in two different directions. In the first part, we discuss recent developments of reduced methods that conserve chosen invariants for nonlinear time-dependent problems. We pay particular attention to the development of reduced models for Hamiltonian problems and propose a greedy approach to build the basis. As we shall demonstrate, attention to the construction of the basis must be paid not only to ensure accuracy but also to ensure stability of the reduced model. As alternative approach we shall also, time permitting, discuss the importance of using a skew-symmetric form to ensure stability of the reduced models for more general conservation laws.
The second part of the talk discusses the combination of reduced order modeling for nonlinear problems with the use of neural networks to overcome known problems of online efficiency for general nonlinear problems. We discuss the general idea in which training of the neural network becomes part of the offline part and demonstrate its potential through a number of examples, including for the incompressible Navier-Stokes equations with geometric variations and a prototype combustion problem.
This work has been done with in collaboration with B.F. Afkram (EPFL, CH), N. Ripamonti EPFL, CH) and S. Ubbiali (USI, CH), Q. Wang (EPFL, CH).
SSD - Koumoutsako Seminar
Prof. Dr. Petros Koumoutsakos - Computing and Data Science Interfaces for Fluid Mechanics
Chair of Computational Sciences, ETH Zürich, Switzerland
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
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
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.