  In this paper, we consider the problem of learning a predictive model for
population cell growth dynamics as a function of the media conditions. We first
introduce a generic data-driven framework for training operator-theoretic
models to predict cell growth rate. We then introduce the experimental design
and data generated in this study, namely growth curves of Pseudomonas putida as
a function of casein and glucose concentrations. We use a data driven approach
for model identification, specifically the nonlinear autoregressive (NAR) model
to represent the dynamics. We show theoretically that Hankel DMD can be used to
obtain a solution of the NAR model. We show that it identifies a constrained
NAR model and to obtain a more general solution, we define a causal state space
system using 1-step,2-step,...,{\tau}-step predictors of the NAR model and
identify a Koopman operator for this model using extended dynamic mode
decomposition. The hybrid scheme we call causal-jump dynamic mode
decomposition, which we illustrate on a growth profile or fitness prediction
challenge as a function of different input growth conditions. We show that our
model is able to recapitulate training growth curve data with 96.6% accuracy
and predict test growth curve data with 91% accuracy.
