Abstract
Various real-world applications involve modeling complex systems with immense uncertainty and optimizing multiple objectives based on the uncertain model. Quantifying the impact of the model uncertainty on the given operational objectives is critical for designing optimal experiments that can most effectively reduce the uncertainty that affect the objectives pertinent to the application at hand. In this paper, we propose the concept of mean multi-objective cost of uncertainty (multi-objective MOCU) that can be used for objective-based quantification of uncertainty for complex uncertain systems considering multiple operational objectives. We provide several illustrative examples that demonstrate the concept and strengths of the proposed multi-objective MOCU. Furthermore, we present a real-world example based on the mammalian cell cycle network to demonstrate how the multi-objective MOCU can be used for quantifying the operational impact of model uncertainty when there are multiple, possibly competing, objectives.
Highlights
Investigating real-world systems and phenomena typically requires complex models that involve a large number of parameters
While finding a reliable point estimate of the parameter vector may not be possible in such a case, it may be possible to identify the parameter ranges based on the available data and/or prior system knowledge, or in a more general setting, we may assume a joint distribution of the model parameters
This naturally places the uncertain model in a Bayesian framework, where the likelihood of every possible model in the uncertainty class is described by a prior distribution that could be constructed from prior system knowledge and/or existing data
Summary
Investigating real-world systems and phenomena typically requires complex models that involve a large number of parameters. As MOCU enables objective-based uncertainty quantification, it provides an effective means of quantifying the expected impact of potential experiments on reducing model uncertainty that directly affects operator performance. For this reason, MOCU has been recently utilized in various application domains for optimal experimental design (OED), where examples include controlling uncertain gene regulatory networks (GRNs) [5, 6], synchronization of uncertain Kuramoto oscillator models [7], designing materials with targeted functional properties [8], optimal sequential sampling [9], and active learning for optimal Bayesian classification [10, 11]. V, we conclude the paper with further discussions on the significance of the proposed multi-objective MOCU, relation to other existing methods, and potential future applications
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