The increasing complexity of mathematical models of complex systems like living cells has created a need for methods to reduce computational demand, maintain overview of the capabilities and feasibility of the models, compare alternative models, and obtain more reliable and effective fitting of models to experimental data. Metamodeling-statistical modeling of the behavior of complex mathematical models, also called 'surrogate modeling'-is well established in many scientific disciplines, such as mechanical engineering and process simulation, and has recently also found use in computational biology, as well as other fields of bioscience. Many of these are based on partial least squares regression (PLSR) and various nonlinear and N-way extensions of the PLSR. This is a versatile family of multivariate data modeling methods that combines a simple, flexible model structure (low-rank bilinear subspace regression) and an intuitively attractive optimization criterion (maximized explained input-output covariance) to provide both predictive ability and graphical insight. This review summarizes the background for PLSR-based metamodeling, and the use of PLSR and related methods in the main application areas of metamodeling: reduction of computational demand, sensitivity analysis, model comparison, and parameterization of models in relation to measured data. The methodology is generic, but here illustrated by examples from computational biology. The advantages and limitations of metamodeling for analyzing complex model behavior are discussed.Conflict of interest: The authors have declared no conflicts of interest for this article. main application areas to date. Subsequently, methods for multivariate metamodeling are described, with particular focus on the partial least squares regression (PLSR) version of bilinear regression.Finally, examples of applications of multivariate metamodeling are shown, with special focus on the use of metamodeling in biology and medicine. These are fields where it is increasingly important to enable scientists to handle high-complexity systems with understandable and robust mathematical models. The Methods section gives technical details of the generic methodology, the Applications section provides illustrations of practical use of the metamodeling, while 440 Mathematical model behavior by partial least squares regression-based multivariate metamodeling behavior of model M(.) is observed under all relevant conditions. If model M(.) has K different Volume 6, November/December 2014 Overview and direct parameter estimation State trajectories/ calculated metrics Parameters = I(Metrics) Original model M Metrics = C(Parameters) Overview, sensitivity analysis, and computational speed-up Inputs Prediction Parameters, initial conditions Inverse metamodel, I Classical metamodel, C Prediction Measured metrics Outputs FIGURE 1 | Classical and inverse multivariate metamodeling of a mathematical model M(.). 2 While the classical metamodel C(.) has the same input-output direction as the original model, the inve...