Inference in a Partial Differential Equations Model of Pulmonary Arterial and Venous Blood Circulation Using Statistical Emulation

  • Umberto Noè
  • Weiwei Chen
  • Maurizio Filippone
  • Nicholas Hill
  • Dirk Husmeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10477)

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.

Keywords

Statistical inference Gaussian processes Emulation Simulator Global optimization Efficient global optimization Hidden constraints Nonlinear differential equations Pulmonary blood circulation Pulmonary hypertension 

Notes

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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Umberto Noè
    • 1
  • Weiwei Chen
    • 2
  • Maurizio Filippone
    • 3
  • Nicholas Hill
    • 1
  • Dirk Husmeier
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
  2. 2.Research Center for Regenerative MedicineGuangxi Medical UniversityNanningChina
  3. 3.Eurecom, Campus SophiaTechBiotFrance

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