The Creation of Surrogate Models for Fast Estimation of Complex Model Outcomes

A surrogate model is a black box model that reproduces the output of another more complex model at a single time point. This is to be distinguished from the method of surrogate data, used in time series. The purpose of a surrogate is to reduce the time necessary for a computation at the cost of rigor and generality. We describe a method of constructing surrogates in the form of support vector machine (SVM) regressions for the purpose of exploring the parameter space of physiological models. Our focus is on the methodology of surrogate creation and accuracy assessment in comparison to the original model. This is done in the context of a simulation of hemorrhage in one model, “Small”, and renal denervation in another, HumMod. In both cases, the surrogate predicts the drop in mean arterial pressure following the intervention. We asked three questions concerning surrogate models: (1) how many training examples are necessary to obtain an accurate surrogate, (2) is surrogate accuracy homogeneous, and (3) how much can computation time be reduced when using a surrogate. We found the minimum training set size that would guarantee maximal accuracy was widely variable, but could be algorithmically generated. The average error for the pressure response to the protocols was -0.05±2.47 in Small, and -0.3 +/- 3.94 mmHg in HumMod. In the Small model, error grew with actual pressure drop, and in HumMod, larger pressure drops were overestimated by the surrogates. Surrogate use resulted in a 6 order of magnitude decrease in computation time. These results suggest surrogate modeling is a valuable tool for generating predictions of an integrative model’s behavior on densely sampled subsets of its parameter space.