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Intermediate Variable Emulation: using internal processes in simulators to build more informative emulators

Oughton, Rachel and Goldstein, Michael and Hemmings, John (2022) 'Intermediate Variable Emulation: using internal processes in simulators to build more informative emulators.', SIAM/ASA Journal on Uncertainty Quantification, 10 (1). pp. 268-293.


Complex systems are often modelled by intricate and intensive computer simulators. This makes their behaviour difficult to study, and so a statistical representation of the simulator is often used, known as an emulator, to enable users to explore the space more thoroughly. These have the disadvantage that they do not allow one to learn about the simulator’s behaviour beyond its role as a function from input to output variables. We take a new approach, by involving the internal processes modelled within the simulator in our emulator. We introduce a new technique, intermediate variable emulation, which enables a simulator to be understood in terms of the processes it models. This leads to advantages in simulator improvement and in calibration, as the simulator can be scrutinised in more detail and the physical processes can be used to refine the input space. The intermediate variable emulator also allows one to represent more complicated relationships within the simulator, as we show with a simple example. We demonstrate the method using a simulator of the ocean carbon cycle. Using an intermediate variable emulator we are able to discover unrealistic behaviour in the simulator that would not be noticeable using a standard input to output emulator, and reduce the input space accordingly. We also learn about the sub-processes that drive the output, and about the input variables driving each sub-process.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Date accepted:20 October 2021
Date deposited:11 November 2021
Date of first online publication:28 February 2022
Date first made open access:06 April 2022

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