<p>Overview of the proposed modeling framework.</p>

In particular, active and dormant cell states can influence system-level behavior but are rarely resolved from standard fermentation measurements. In this study, we present a hybrid modeling framework that combines structured population-state reconstruction with sparse identification of nonlinear dynamics (SINDy) to analyze a <i>Clostridium acetobutylicum</i>-<i>Clostridium ljungdahlii</i> coculture under perfusion mode.

The framework estimates active and biomass-equivalent trajectories from observable biomass and activity measurements, reconstructs dormant populations as model-constrained latent states, and uses these states to identify extracellular metabolite dynamics. After accounting for first-principles perfusion transport, SINDy identified sparse biological reaction terms associated with organic acid turnover, solvent formation, and acetone-to-isopropanol conversion.