Inference in a Partial Differential Equations Model of Pulmonary Arterial and Venous Blood Circulation Using Statistical Emulation
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  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.
KeywordsStatistical inference Gaussian processes Emulation Simulator Global optimization Efficient global optimization Hidden constraints Nonlinear differential equations Pulmonary blood circulation Pulmonary hypertension
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).
- 1.Gelbart, M.A., Snoek, J., Adams, R.P.: Bayesian optimization with unknown constraints. In: Uncertainty in Artificial Intelligence (UAI) (2014)Google Scholar
- 3.Kuss, M.: Gaussian process models for robust regression, classification, and reinforcement learning. Ph.D. thesis, Technische Universität, Darmstadt (2006)Google Scholar
- 6.Olufsen, M.S.: Structured tree outflow condition for blood flow in larger systemic arteries. Am. J. Physiol. Heart Circulatory Physiol. 276, 257–268 (1999)Google Scholar
- 11.Sasena, M.J.: Optimization of Computer Simulations via Smoothing Splines and Kriging Metamodels. MSc Thesis, University of Michigan (1998)Google Scholar
- 12.Snoek, J., Larochelle, H., Adams, R.P.: Practical bayesian optimization of machine learning algorithms. In: Advances in Neural Information Processing Systems, pp. 2951–2959 (2012)Google Scholar
- 13.Snoek, J.: Bayesian Optimization and Semiparametric Models with Applications to Assistive Technology. Ph.D. thesis, University of Toronto, Toronto, Canada (2013)Google Scholar