Gaussian process emulation for discontinuous response surfaces with applications for cardiac electrophysiology models

Ghosh, Sanmitra; J. Gavaghan, David; R. Mirams, Gary

Abstract

Mathematical models of biological systems are beginning to be used for safety-critical applications, where large numbers of repeated model evaluations are required to perform uncertainty quantification and sensitivity analysis. Most of these models are nonlinear both in variables and parameters/inputs which has two consequences. First, analytic solutions are rarely available so repeated evaluation of these models by numerically solving differential equations incurs a significant computational burden. Second, many models undergo bifurcations in behaviour as parameters are varied. As a result, simulation outputs often contain discontinuities as we change parameter values and move through parameter/input space.
Statistical emulators such as Gaussian processes are frequently used to reduce the computational cost of uncertainty quantification, but discontinuities render a standard Gaussian process emulation approach unsuitable as these emulators assume a smooth and continuous response to changes in parameter values.
In this article, we propose a novel two-step method for building a Gaussian Process emulator for models with discontinuous response surfaces. We first use a Gaussian Process classifier to detect boundaries of discontinuities and then constrain the Gaussian Process emulation of the response surface within these boundaries. We introduce a novel `certainty metric' to guide active learning for a multi-class probabilistic classifier.
We apply the new classifier to simulations of drug action on a cardiac electrophysiology model, to propagate our uncertainty in a drug's action through to predictions of changes to the cardiac action potential. The proposed two-step active learning method significantly reduces the computational cost of emulating models that undergo multiple bifurcations.

Citation

Ghosh, S., J. Gavaghan, D., & R. Mirams, G. Gaussian process emulation for discontinuous response surfaces with applications for cardiac electrophysiology models

• Other Type: Other
• Deposit Date: Jan 14, 2020
• Publicly Available Date: Jan 15, 2020
• Keywords: Computation
• Public URL: https://nottingham-repository.worktribe.com/output/2465155
• Additional Information: This is an arXiv preprint.