Bayesian Calibration of Inertial Confinement Fusion Models with Very Expensive Data
Calibrating computer simulations against experimental data is a ubiquitous problem in science and is particularly difficult when experimental data are expensive or diffi- cult to collect. In inertial confinement fusion experiments, where a single data point can cost 10 5 –10 6 USD, calibration of large-scale design calculations is particularly challenging. We present a framework that aims to provide calibrated predictions far from the available data that can be trained using a small number of data points. The approach aims to retain as much of the physics (summarized by the simulation code) as possible and is based on a truncated polynomial chaos expansion in the space of simulation inputs, augmented with a non-parametric correction for higher distribution modes. Due to the difficulty of the problem, understanding the sources of uncertainty in the model is essential; we demonstrate this through an application of our approach to a series of 6 experimental laser shots. As a result, we validate our approach, show that the uncertainties in our predictions of experimental performance are dominated by shot-shot fluctuations and regression uncertainties, and discuss paths towards an improved prediction model.