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 Unpublished work (by the authors) illustrated the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.