Impact of Data Assimilation on Cost-Accuracy Tradeoff in Multifidelity Models

Abstract

Observable phenomena can often be described by alternative models with different degrees of fidelity. Such models typically contain uncertain parameters and forcings, rendering predictions of the state variables uncertain as well. Within the probabilistic framework, solutions of these models are given in terms of their probability density functions (PDFs). In the presence of data, the latter can be treated as prior distributions. Uncertainty and assimilation of measurements into model predictions, e.g., via Bayesian updating of solution PDFs, pose a question of model selection: Given a significant difference in computational cost, is a lower-fidelity model preferable to its higher-fidelity counterpart? We investigate this question in the context of multiphase flow in heterogeneous porous media whose hydraulic properties are uncertain. While low-fidelity (reduced-complexity) models introduce a model error, their moderate computational cost makes it possible to generate more realizations, which reduces the (e.g., Monte Carlo) sampling error. These two errors determine the model with the smallest total error. Our analysis suggests that assimilation of measurements of a quantity of interest (a medium's saturation, in our example) influences both types of errors, increasing the probability that the predictive accuracy of a reduced-complexity model exceeds that of its higher-fidelity counterpart.

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