Seminar Details:

**LANS Informal Seminar***"Parameter Sensitivity and Uncertainty quantification for Engineering Simulations using the Discrete Adjoint"*

DATE: August 9, 2010

TIME: 15:00:00 - 16:00:00

SPEAKER: Brian Lockwood, *MCS Summer STudent*

LOCATION: Bldg 240 Rm 4301, Argonne National Laboratory

**Description:**

This talk will discuss the use of the discrete adjoint for sensitivity analysis and uncertainty quantification. In the first part of the talk, the use of the adjoint for sensitivity analysis in hypersonic flow simulations will be detailed. The simulation of hypersonic flow is a subject of interest in many engineering fields and is particularly important for evaluating the performance of atmospheric re-entry vehicles. Hypersonic flow (roughly defined as Mach number greater than 5) is typically characterized by the presence of strong shocks, chemical reactions and the excitation of internal molecular energy modes, such as vibrational or electronic energy. The modeling of these phenomena depends on elaborate empirical models and experimentally measured constants. Quantifying the effects of these model parameters on relevant engineering quantities, such as drag or surface heating, is the basis of sensitivity analysis and can provide valuable insights for improving the predictive and design capability of a solver. In order to calculate sensitivity derivatives with respect to a large number of model parameters, a discrete adjoint approach is used. By exploiting similarities between the adjoint problem and the flow problem and making use of automatic differentiation, the flow adjoint can be calculated with minimal developer effort and computational expense roughly equivalent to that of the flow solve. With the sensitivity derivatives calculated, the relative importance of parameters for a given output can be compared. Additionally, these derivatives can be used for uncertainty quantification purposes by aiding in the construction of computationally inexpensive surrogate models. The use of gradient information in constructing inexpensive surrogate models will be the focus of the second part of this talk. The traditional approach to uncertainty quantification, particularly for hypersonic flow simulations, is Monte Carlo sampling. In order to collect reliable statistics for the output, thousands of code evaluations are required. For high fidelity simulations, this requirement can be prohibitively expensive and alternative approaches must be considered. One alternative is to replace the expensive code evaluation with an inexpensive model of the design space which can be sampled exhaustively. The particular models examined in this work are extrapolation based models and Kriging based models. For each of these models, the inclusion of gradient information can substantially reduce the number of code evaluations required to accurately build a model of the design space. In this talk, the use of these response models for quantifying uncertainty in hypersonic flows will be demonstrated. Time permitting, the use of combined regression/Kriging based models will be outlined and applications for nuclear engineering will be discussed.

Please send questions or suggestions to Krishna: snarayan at mcs.anl.gov.