Abstract
The present article addresses the problem of inference in a multiscale computational model of pulmonary arterial and venous blood circulation. The model is a computationally expensive simulator which, given specific parameter values, solves a system of nonlinear partial differential equations and returns predicted pressure and flow values at different locations in the arterial and venous blood vessels. The standard approach in parameter calibration for computer code is to emulate the simulator using a Gaussian Process prior. In the present work, we take a different approach and emulate the objective function itself, i.e. the residual sum of squares between the simulations and the observed data. The Efficient Global Optimization (EGO) algorithm [2] is used to minimize the residual sum of squares. A generalization of the EGO algorithm that can handle hidden constraints is described. We demonstrate that this modified emulator achieves a reduction in the computational costs of inference by two orders of magnitude.
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Notes
- 1.
Vascular rarefaction is an old finding in patients with hypertension, and represents the condition of having fewer blood vessels per tissue volume.
- 2.
See Eq. (4.14) in Rasmussen and Williams [9] Sect. 4.2.
- 3.
In this context, surrogate or metamodel are synonyms for GP posterior mean, and were generated by the engineering community.
- 4.
The presented results were obtained on a CentOS 7 machine using MATLAB®. Our code used to perform inference depends on the GPML toolbox by Rasmussen [9] and the standard MATLAB® Statistics Toolbox.
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Acknowledgment
UN is supported by a scholarship from the Biometrika Trust. SofTMech is a research centre for Multi-scale Modelling in Soft Tissue Mechanics, funded by EPSRC (grant no. EP/N014642/1).
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Noè, U., Chen, W., Filippone, M., Hill, N., Husmeier, D. (2017). Inference in a Partial Differential Equations Model of Pulmonary Arterial and Venous Blood Circulation Using Statistical Emulation. In: Bracciali, A., Caravagna, G., Gilbert, D., Tagliaferri, R. (eds) Computational Intelligence Methods for Bioinformatics and Biostatistics. CIBB 2016. Lecture Notes in Computer Science(), vol 10477. Springer, Cham. https://doi.org/10.1007/978-3-319-67834-4_15
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