O. Roderick and M. Anitescu, "Intrusive Uncertainty Quantification for NeK5000: Development of Intrusive Uncertainty Quantification for High-Dimensional, High-Fidelity Codes," Argonne Report ANL/MCS-TM-329, September 2012. [pdf]
We study the use of lower-fidelity training data for uncertainty quantification of complex simulation models. In our approach, computationally expensive full-model outputs are approximated applying proper orthogonal-decomposition-based dimensionality reduction to the full model.
A Gaussian-processes-based machine learning approach is then used to model the difference (or, rather, the correspondence) between the higher-fidelity and the lower fidelity data. This stochastic model can be constructed by using few additional full code evaluations; it is used to calibrate arbitrarily many lower-quality outputs in order to create additional training data for sampling-based analysis. In effect, an adequate approximation of the simulation model's response to uncertainty can be constructed at a modest computational cost. In fact, we aim at the number of full-model evaluations comparable to that required for a linear approximation (as opposed to numbers traditionally associated with sampling in high-dimensional spaces).
In this report, we explain the basic algorithm, suggest some performance tuning options, and give a first characterization for the class of simulation models of nuclear engineering for which the suggested report is effective.
The primarily goal of our work was to demonstrate the effectiveness of multifidelity analysis on high-performance fluid dynamics simulation code Nek5000. We have been successful at estimating statistics for an output of interest at low cost. While further demonstration exercises may be helpful, the information provided here clearly argues for the effectiveness of the approach. Logically, the next stage of work is to explore the full range of tasks related to Nek5000 code development and verification that could be made more computationally accessible with the use of calibrated lower fidelity data.
The suggested approach can be generalized to multiple levels of fidelity, enabling uncertainty analysis based on many different model approximations. The long-term goal of our research is to fit the developed method into a larger context of advanced uncertainty analysis tools for nuclear engineering applications. We foresee implementation as a suite of analysis tools that can become a component of SHARP/NEAMS codes.