Non-linear Multivariate Dynamics Modelled by PLSR

Information-rich high-speed, low-cost multi-channel measurements will increasingly become available for characterizing and quantifying chemical constituents and physical phenomena in e.g. biology. The question is how to parameterize, quantify and display and interpret this information. The paper discusses how bio-scientists can make use of PLS-based regression methods to explore multivariate non-linear dynamics of complex systems. A novel application of nominal-level PLSR modelling in the time domain is presented. It allows pragmatic modelling of empirical time series data in order to search for plausible mechanistic explanations of dynamics in terms of systems of local linear differential equation. A recently developed approach to develop non-linear mechanistic models is then employed in order to merge the PLS regression coefficients from the nominal-level local linear modelling into a global non-linear differential equation system. The approach is demonstrated on a simulated data set.