Greedy nonlinear autoregression for multifidelity computer models at different scales

Abstract

Although the popular multi-fidelity surrogate models, stochastic collocation and nonlinear autoregression have been applied successfully to multiple benchmark problems in different areas of science and engineering, they have certain limitations. We propose a uniform Bayesian framework that connects these two methods allowing us to combine the strengths of both. To this end, we introduce Greedy-NAR, a nonlinear Bayesian autoregressive model that can handle complex between-fidelity correlations and involves a sequential construction that allows for significant improvements in performance given a limited computational budget. The proposed enhanced nonlinear autoregressive method is applied to three benchmark problems that are typical of energy applications, namely molecular dynamics and computational fluid dynamics. The results indicate an increase in both prediction stability and accuracy when compared to those of the standard multi-fidelity autoregression implementations. The results also reveal the advantages over the stochastic collocation approach in terms of accuracy and computational cost. Generally speaking, the proposed enhancement provides a straightforward and easily implemented approach for boosting the accuracy and efficiency of concatenated structure multi-fidelity simulation methods, e.g., the nonlinear autoregressive model, with a negligible additional computational cost.