Fast predictive multi-fidelity prediction with models of quantized fidelity levels

• Published in: Journal of computational physics 2019-01, Vol.376, p.992-1008
• Main Authors: Razi, Mani, Kirby, Robert M., Narayan, Akil
• Format: Article
• Language: English
• Subjects: Computational physics; Computing time; Discrete systems; Markov analysis; Markov chains; Mathematical models; Model accuracy; Model-order reduction; Multi-fidelity models; Parameter estimation; Parameters; Polymers; Predictions; Surrogate modeling
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2018.10.025

In this paper, we introduce a novel approach for the construction of multi-fidelity surrogate models with “discrete” fidelity levels. The notion of a discrete level of fidelity is in contrast to a mathematical model, for which the notion of refinement towards a high-fidelity model is relevant to sending a discretization parameter toward zero in a continuous way. Our notion of discrete fidelity levels encompasses cases for which there is no notion of convergence in terms of a fidelity parameter that can be sent to zero or infinity. The particular choice of how levels of fidelity are defined in this framework paves the way for using models that may have no apparent physical or mathematical relationship to the target high-fidelity model. However, our approach requires that models can produce results with a common set of parameters in the target model. Hence, fidelity level in this work is not directly representative of the degree of similarity of a low-fidelity model to a target high-fidelity model. In particular, we show that our approach is applicable to competitive ecological systems with different numbers of species, discrete-state Markov chains with a different number of states, polymer networks with a different number of connections, and nano-particle plasmonic arrays with a different number of scatterers. The results of this study demonstrate that our procedure boasts computational efficiency and accuracy for a wide variety of models and engineering systems. •Construction of a multi-fidelity predictive model with quantized fidelity levels.•Identification of optimal sampling patterns using small-scale simulations.•Characterized by short analysis time and few number of expensive model evaluations.•Demonstration of the method for four benchmark examples in different areas.•Reasonable accuracy and computational efficiency of the constructed predictive models.