MECHANICAL ENGINEERING & MATERIALS SCIENCE
Hessam Babaee, PhD
1102 Benedum Hall | 3700 O’Hara Street | Pittsburgh, PA 15261
Assistant Professor
P: 412-383-0560 h.babaee@pitt.edu
A Stochastic Framework for Computation of Sensitivities in Chaotic Flows
The work of Dr. Babaee’s research group is at the intersection of high performance computing, uncertainty quantification and predictive modeling. Advances in the field of machine learning provide a rigorous mathematical framework that have begun to allow combining data with variable fidelities from different sources to generate or improve predictive models. Furthermore, the advent of efficient numerical techniques, particularly in the field of stochastic differential equations and high performance computing have paved the way for quantifying uncertainty in complex engineering systems. The combination of these components is just starting to bear fruit and unprecedented opportunities exist for constructing predictive models endowed with rigorous certificates of fidelity in multi-physics/multi-scale engineering systems. This is the scope of Dr. Babaee’s research group.
Uncertainty Quantification and Stochastic Modeling Complex thermo-fluid systems are often poorly understood due to the uncertainties in the models, parameters, experimental measurements and numerical simulations, and operating conditions. Propagating and managing uncertainty in these systems is a daunting task. These systems are often governed by multi-physics/multiscale phenomenon – described by highdimensional coupled differential/integral equations – such as heat transfer in gas turbines or turbulent two-phase flows.
Time-Dependent Basis
Low-dimensional Attractor
Our group develops stochastic reduced order models (ROM) by exploiting the correlations among the different (a) (b) realizations of a physical system. ROM has orders of magnitude smaller dimension Figure 1 Figure 2: PI Babaee’s research on a minimization principle for bui than the full-dimensional model and it (a) Featured on the Cover Page of Proceedings of the Royal Society serves two main purposes: (1) ROM is a diagnostic tool that can be used to characterize Physical and Engineering Sciences [33]; (b) Smoke: volume rendering o and analyze the behavior of complex dynamical systems; (2) ROM can be used instead time-dependent (OTD) modes. of the full-dimensional model to significantly reduce the computational burden of propagating uncertainty in high-dimensional dynamical systems.
increases the influence of the unresolved fluctuations becomes more s the non-linearity of dynamical system results in growth of the unresolv prediction of the flow structure, it is essential to account for the e↵ Multi-Fidelity Modeling for Design and Optimization not, the aliasing errors will surely lead to non-physical results. This Engineering designs and resilient systems require management of compressible flow research for over 60 yeas now [34–38]. The crux of data from a variety of sources, efficient allocation of interaction of pressure and vorticity modes, with escalated complexity a
computational resources, and, most importantly, quantification of uncertainty inherent in multi-physics models of variable We fidelity would like to examine several means of accounting for the e↵ect and operating conditions, as well as utilization of such information high Reynolds number flows. We recognize that there are certain simi in risk-averse decision making. Even for classical engineering modal decomposition and the filtering operation as employed in LES systems that can be described at various levels of fidelity and that some of the ideas is subgrid scale (SGS) modeling may be useful for which experimental data may exist, currently there are no the issue is closure of the correlation: Tij = E[ui uj ] E[ui ]E[uj ]. Th mathematically rigorous methods to combine these disparate many of such closures [39–41]. Some of them appear promising for our p information sources into a viable framework for the purpose of Figure 2 design and optimization. In our group we develop multi-fidelity First, we would like to examine the scale-similarity model (SSM) [42–4 framework by employing modern elements of machine learning provide an information-fusion framework, in which prediction natural for our purpose. With this model, simulations will be conduct – such as non-parametric Bayesian regression – that are capable for quantities of interest and their associated uncertainties resolutions. This can be achieved by increasing r. These results will b of blending information from sources of different fidelity, and can are determined.
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the unresolved fluctuations. Another possibility would be the mixed m based on the combination of the SSM and the general SGS viscosity ty simulations with varying resolutions neededAND to determine the e↵ects DEPARTMENT OF MECHANICAL are ENGINEERING MATERIALS SCIENCE
We will also consider a stochastic methodology. Since this method is n
