2.2 Artificial neural networks
Artificial neural networks (ANNs) are a set of mathematical algorithms that are able to capture complex relationships between the input variables and response variables. According to the universal approximation theorem [50], an ANN of enough size can approximate any function with any accuracy as defined by the user. This makes ANNs potentially useful for approximating complex multi-dimensional and non-linear input-output relationships of QSP models. They have shown to be an efficient tool for model-order reduction of various types of models in fields such as systems engineering and control [51].
ANNs are particularly useful in nonparametric model-order reduction in situations where it is hard to find an appropriate empirical function to approximate a given input-output relationship. For example, when there is a large number of response variables or highly correlated independent variables to be considered. ANNs have been shown to produce fast but accurate reduced-order models that approximate nonlinear dynamical systems [26]. There are currently no published stduies on the use of ANNs for QSP models. Unpublished work (by the authors) illustrated the use of an ANN surrogate models to approximate the heparin dose-response relationship in children which was 10,000-fold faster for simulation than the original full-order QSP model. Such a speed boost could enable use of complex QSP models in simulation, estimation, and potentially control purposes.