Model validation in dynamic systems for time‐course data with complex error structures

Abstract

Dynamic systems with ordinary differential equations have been widely used to describe dynamic processes in various fields such as chemistry, biology, and physics. The dynamic systems are usually constructed using time‐course data measured from experiments at discrete time points. Such experimental time‐course data typically have complex error structures while the dynamic systems are mathematical and deterministic models without random errors. Because of the inflexible nature of mathematical models, the model fits might not cover the whole range of data variations, and there might be a discrepancy between the models and real processes. Moreover, since those experiments typically yield sparse data with high variation, for more accurate prediction, dynamic systems should be statistically validated in terms of observed data. Thus, this study proposes a validation method for dynamic systems. In particular, the proposed method focuses on models from time‐course data with complex error structures such as heteroscedasticity, correlations between objects, and time dependence.