Grigorian, Gevik; Volodina, Victoria; Ray, Samiran; Diaz De La O, Francisco; Black, Claire; (2025) Addressing model discrepancy in a clinical model of the oxygen dissociation curve. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences , 383 (2293) , Article 20240213.

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Abstract

Many mathematical models suffer from model discrepancy, posing a significant challenge to their use in clinical decision-making. In this article, we consider methods for addressing this issue. In the first approach, a mathematical model is treated as a black box system, and model discrepancy is defined as an independent and additive term that accounts for the difference between the physical phenomena and the model representation. A Gaussian Process (GP) is commonly used to capture the model discrepancy. An alternative approach is to construct a hybrid grey box model by filling in the incomplete parts of the mathematical model with a neural network. The neural network is used to learn the missing processes by comparing the observations with the model output. To enhance interpretability, the outputs of this non-parametric model can then be regressed into a symbolic form to obtain the learned model. We compare and discuss the effectiveness of these approaches in handling model discrepancy using clinical data from the ICU and the Siggaard–Andersen oxygen status algorithm. This article is part of the theme issue ‘Uncertainty quantification for healthcare and biological systems (Part 2)’.

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