Abstract
Computational simulation allows scientists to explore, observe, and test physical regimes thought to be unattainable. Validation and uncertainty quantification play crucial roles in extrapolating the use of physics-based models. Bayesian analysis provides a natural framework for incorporating the uncertainties that undeniably exist in computational modeling. However, the ability to perform quality Bayesian and uncertainty analyses is often limited by the computational expense of first-principles physics models. In the absence of a reliable low-fidelity physics model, phenomenological surrogate or machine learned models can be used to mitigate this expense; however, these data-driven models may not adhere to known physics or properties. Furthermore, the interactions of complex physics in high-fidelity codes lead to dependencies between quantities of interest (QoIs) that are difficult to quantify and capture when individual surrogates are used for each observable. Although this is not always problematic, predicting multiple QoIs with a single surrogate preserves valuable insights regarding the correlated behavior of the target observables and maximizes the information gained from available data. A method of constructing a Gaussian Process (GP) that emulates multiple QoIs simultaneously is presented. As an exemplar, we consider Magnetized Liner Inertial Fusion, a fusion concept that relies on the direct compression of magnetized, laser-heated fuel by a metal liner to achieve thermonuclear ignition. Magneto-hydrodynamics (MHD) codes calculate diagnostics to infer the state of the fuel during experiments, which cannot be measured directly. The calibration of these diagnostic metrics is complicated by sparse experimental data and the expense of high-fidelity neutron transport models. The development of an appropriate surrogate raises long-standing issues in modeling and simulation, including calibration, validation, and uncertainty quantification. The performance of the proposed multi-output GP surrogate model, which preserves correlations between QoIs, is compared to the standard single-output GP for a 1D realization of the MagLIF experiment.
