Empirical dynamic modeling for mechanistic understanding and prediction of bioreactors

The overall goal of WP3 is to analyse the mechanisms underlying the productivity decreases in microalgal PBRs, identify early warning signals and evaluate, from the whole set of identified signals, those that meet the specified criteria of scalability, reliability, and affordability.

Natural systems are often complex and dynamic (i.e. nonlinear), and are difficult to understand using linear statistical approaches. Linear approaches are fundamentally based on correlation and are ill-posed for nonlinear dynamical systems, because in dynamical systems, not only can correlation occur without causation, but causation can also occur in the absence of correlation. Empirical dynamic modeling is specifically developed for studying nonlinear dynamical systems (such as bioreactors). These nonlinear statistical methods are rooted in State Space Reconstruction (SSR), i.e. lagged coordinate embedding of time series data  (see animation: tinyurl.com/EDM-intro). These methods do not assume any set of equations governing the system but recover the dynamics from time series data, thus called Empirical Dynamic Modeling (EDM).

EDM is especially suitable for analyzing time series data collected from reactors in the PRODIGIO project. EDM allows to 1) identify critical environmental variables affecting each target microbial taxon; 2) reconstruct time-varying interaction networks among microbial taxa; and 3) develop Early Warning Signal for anticipating critical transition (e.g., system collapse) in the reactors. As such, EDM can help maintain the stability and sustainability of systems.