Budget-limited distribution learning in multifidelity problems

Abstract

Multifidelity methods are widely used for statistical estimation of quantities of interest (QoIs) in uncertainty quantification using simulation codes of differing costs and accuracies. Many methods approximate numerical-valued statistics that represent only limited information of the QoIs. In this paper, we introduce a semi-parametric approach that aims to effectively describe the distribution of a scalar-valued QoI in the multifidelity setup. Under a linear model hypothesis, we propose an exploration-exploitation strategy to reconstruct the full distribution of a scalar-valued QoI using samples from a subset of low-fidelity regressors. We derive an informative asymptotic bound for the mean 1-Wasserstein distance between the estimator and the true distribution, and use it to adaptively allocate computational budget for parametric estimation and non-parametric reconstruction. Assuming the linear model is correct, we prove that such a procedure is consistent, and converges to the optimal policy (and hence optimal computational budget allocation) under an upper bound criterion as the budget goes to infinity. A major advantage of our approach compared to several other multifidelity methods is that it is automatic, and its implementation does not require a hierarchical model setup, cross-model information, or a priori known model statistics. Numerical experiments are provided in the end to support our theoretical analysis.

Artificial Intelligence for Earth System Predictability (AI4ESP) (2021 Workshop Report)

“…Fletcher, McNally, and Virgin (2021) and have shown that multifidelity training is feasible and can lead to improvements in accuracy for CAM4 and CAM5 examples. More recent approaches by Liu, Pareschi, and Zhu (2021) and Xu and Narayan (2021) seek to find efficient and mathematically rigorous ways of learning a surrogate model with bi-or multifidelity training sources, but these approaches have not yet been tested on global climate models.…”