M. McKerns

T. J. Sullivan, M. McKerns, D. Meyer et al.

We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter sensitivities (McDiarmid diameters) and output deviation (or failure) probabilities. The solutions of these optimization problems depend non-trivially (even non-monotonically and discontinuously) upon the specified legacy data. Furthermore, the extreme values are often determined by only a few members of the data set; in our principal physically-motivated example, the bounds are determined by just 2 out of 32 data points, and the remainder carry no information and could be neglected without changing the final answer. We propose an analogue of the simplex algorithm from linear programming that uses these observations to offer efficient and rigorous UQ for high-dimensional systems with high-cardinality legacy data. These findings suggest natural methods for selecting optimal (maximally informative) next experiments.

A. Diaw, M. McKerns, I. Sagert et al.

Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are interested in finding a surrogate that provides valid predictions of any potential future model evaluations, we introduce an online learning method empowered by optimizer-driven sampling. The method has two advantages over current approaches. First, it ensures that all turning points on the model response surface are included in the training data. Second, after any new model evaluations, surrogates are tested and "retrained" (updated) if the "score" drops below a validity threshold. Tests on benchmark functions reveal that optimizer-directed sampling generally outperforms traditional sampling methods in terms of accuracy around local extrema, even when the scoring metric favors overall accuracy. We apply our method to simulations of nuclear matter to demonstrate that highly accurate surrogates for the nuclear equation of state can be reliably auto-generated from expensive calculations using a few model evaluations.