A Differentiable dFBA Simulator for Scalable Bayesian Inference over Microbial Metabolic Models

Medium optimisation for bioprocess design remains challenging and costly: fermentation recipes typically contain ten or more components, the design space expands combinatorially as ingredients are added, and each batch experiment requires over 24 hours. High-throughput 96-well plate screening can reduce experimental cost, but extracting actionable predictions from growth curves requires a mechanistic model that links medium composition to cellular metabolism. In this paper, we present a differentiable simulator for dynamic flux balance analysis (dFBA) that enables scalable Bayesian inference over microbial metabolic models. A distinguishing feature is that inference is driven entirely by OD600 measurements, a simple optical proxy for biomass, without substrate or product assays; internal fluxes, substrate consumption, and secreted metabolite profiles are recovered as latent variables constrained by the metabolic network stoichiometry. We resolve the core differentiability barrier of classical dFBA by reformulating the per-step linear or quadratic programme (LP/QP) as a smooth continuous ODE (the Relaxed Interior-Point ODE, R-iODE), establishing the mathematical framework for end-to-end gradient propagation through long fermentation trajectories in JAX; full gradient validation is ongoing. The result is a framework for principled inference over thousands of batch fermentations, providing a path toward model-guided medium design, cross-strain parameter transfer, and scale-up prediction from plate data.