SSD - Peherstorfer Seminar
Prof. Dr. Benjamin Peherstorfer- Learning Context -aware Reduced Models for Multifidelity Computations
Courant Institute of Mathematical Sciences, New York University, USA
Traditional model reduction constructs reduced models with the aim of replacing expensive, high-fidelity models to speed up computations. However, reduced and high-fidelity models are increasingly used together in multifidelity methods, which means that the purpose of reduced models becomes supporting computations with the high-fidelity models rather than approximating and replacing them. In this presentation, we propose context-aware reduced models that are explicitly constructed for being used together with high-fidelity models in multifidelity computations. In the first part of the presentation, we introduce the adaptive multifidelity Monte Carlo (AMFMC) method that constructs reduced models that optimally support the multifidelity estimation of statistics of high-fidelity model outputs. Our analysis shows that our context-aware reduced models optimally reduce the runtime of multifidelity estimation, even though they are less accurate in the sense of traditional model reduction. In the second part, we present a multifidelity approach to dynamically couple reduced models with high-fidelity models, where the reduced models are adapted in a context-aware sense with sparse data from the high-fidelity model. Our numerical examples demonstrate that the dynamic coupling is particularly beneficial in case of convection-dominated problems, where our context-aware approach achieves significant speedups, whereas traditional reduced models are even more costly to evaluate than the high-fidelity models.
CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Ghattas Seminar
Prof. Omar Ghattas, Ph.D. - Large-Scale Bayesian Inversion with Applications to the Flow of the Antarctic Ice Sheet
Institute for Computational Engineering Sciences (ICES)
Many physical systems are characterized by complex nonlinear behavior coupling multiple physical processes over a wide rang of length and time scales. Mathematical and computational models of these systems often contain numerous uncertain parameters, making high-reliability predictive modeling a challenge. Rapidly expanding volumes of observational data--along with tremendous increases in HPC capability--present opportunities to reduce these uncertainties via solution of large-scale inverse probles. Bayesian inference provides a systematic framework for inferring model parameters with associated uncertainties from (possibly noisy) data and any prior information. However, solution of Bayesian inverse problems via conventional Markov chain Monte Carlo (MCMC) methods remains prohibitive for expensive models and high-dimensional parameterizations, as result from discretization of infinite dimensional problems with uncertain fields. Despite the large size of observational datasets, typically they inform only low dimensional manifolds in parameter space, due to ill-posedness of the inverse problem. Based on this property we design scalable Bayesian inversion algorithms that adapt to the structure and geometry of the posterior probability, thereby exploiting an effectively-reduced parameter dimension and making Bayesian inference tractable for some large-scale, high-dimensional inverse problems. We discuss an inverse problem for the flow of the Antarctic ice sheet, which has been solved for as many as one million uncertain parameters at a cost (measured in forward ice sheet flow solves) that is independent of both the parameter and data dimensions. This work is joint with Tobin Isaac, Noemi Petra, and Georg Stadler.
SSD - Frison Seminar
Dr. Gianluca Frison - BLASFEO and its Use in Structure-Exploiting Algorithms for Optimal Control
Systems Control and Optimization Laboratory, University of Freiburg
BLASFEO is a newly developed dense linear algebra library, which differentiate itself being optimized for the rather small matrix sizes (up to a couple hundreds) typically encountered in embedded optimization and control. In this talk, I will introduce the main concepts behind the implementation of the library, and show the results of benchmarks against state-of-the-art BLAS libraries (e.g. MKL, OpenBLAS, BLIS) or code-generated linear algebra (e.g. libxsmm, Eigen). Subsequently, I will introduce the embedded optimization framework, and show how the combination of structure-exploiting algorithms with an high-performance dense linear algebra library like BLASFEO allows to obtain very fast optimization algorithms, outperforming current state-of-the-art software based on code-generation.
SSD - Vedula Seminar
Vijay Vedula, Ph.D. - Ventricular Hemodynamics in Disease and Development
Department of Pediatrics, Stanford University, USA
Despite continuous advancements in medical technologies and imaging, cardiovascular disease forms the leading cause of mortality and death. Computational modeling provides a low cost, non-invasive modality that complements animal testing and routine clinical care. Simulation-based diagnosis has demonstrated a growing impact in the clinic, ultimately leading to improved decision-making and patient outcomes. While this translation was successfully achieved in vascular flow applications, cardiac hemodynamics (representing blood flow in the heart chambers) has remained distant, partly due to the significant cost and complexity involved in modeling the underlying blood dynamics. These include high Reynolds number flows, moving boundaries and fluid-structure interaction effects, in addition to the complex multiphysics interactions and the valve dynamics. In this talk, I will present a robust and efficient framework to perform patient-specific modeling of ventricular hemodynamics with examples from single ventricle physiology (children born with a single `functional’ ventricle). I will then present the utility of the framework in embryonic cardiac flow modeling to understand shear regulated mechanotransduction during cardiac morphogenesis. Finally, I will discuss future directions, both from computational modeling and clinical translation perspective.
* funded by Theodore-von-Kármán-Fellowship
SSD- Palazoglu Seminar
Prof. Ahmet Palazoglu, Ph.D. - A new Design Paradigm to Address Demand Response Objectives in Process Systems
Department of Chemical Engineering, University of California, Davis, USA
With the continuing penetration of renewable sources into the power grid, the energy picture presented to the process industries has changed dramatically within the last 10 years. The most visible consequence is the ability to offer real-time electricity pricing by the grid operators as they manage a number of distributed power sources including renewables. If power is available directly from the renewables such as solar and wind, their intermittency challenges the operation of process systems as the available energy varies during the day. This leads to the use of hybrid systems where renewable sources are complemented with storage systems (batteries) and the process has the flexibility to draw energy from the grid or sell back to it when appropriate . The variations on the supply side both in terms of price and availability result in a search for optimal allocation of loads (demand) during the day. Accordingly, demand response (DR) is defined as the ability of the operators to modify process conditions in real-time to take advantage of and respond to such variations and to formulate load shifting strategies. In this talk, I will summarize our ongoing work towards the goal of developing demand responsive process designs. Such designs are not only expected to accommodate variations in price and availability by modifying (scheduling) process steady-states  but also consider re-configuring the process flowsheet in real-time for a more holistic DR strategy . The formulation of the design problem leads to a mixed integer nonlinear programming (MINLP) problem in which the objective function quantifies the capital and operating costs (CAPEX and OPEX) subject to recourse constraints that express scenario-dependent costs. Our recent studies include both deterministic and stochastic versions which present significant algorithmic challenges and these will be briefly discussed. The methodology will be illustrated by examples of process networks.
 Wang, X., H. Teichgraber, A. Palazoglu N.H. El-Farra, “An Economic Receding Horizon Optimization Approach for Energy Management in the Chlor-Alkali Process with Hybrid Renewable Energy Generation,” J. Process Control, 24, 1318-1327 (2014).
 Tong, C., A. Palazoglu, N.H. El-Farra, X. Yan, “Energy Demand Management for Process Systems through Production Scheduling and Control,” AIChE J., 61(11), 3756–3769 (2015).
 Wang, X., N.H. El-Farra, A. Palazoglu, “Proactive Reconfiguration of Heat-Exchanger Super Networks,” Ind. & Eng. Chemistry Research, 54, 9178−9190 (2015).