A tabular foundation model finds higher-biomass media with limited experimental feedback in simulated culture-medium optimization

Culture-medium optimization is constrained by the duration of each culture cycle, which limits opportunities for experimental feedback. We evaluated TabPFN, a tabular foundation model, against Gaussian-process models for simulated medium optimization under a fixed experimental budget. Campaigns of five 96-well plates were simulated using a kinetic growth model with 8 to 120 components and 20 randomly parameterized growth scenarios. Under a shared batch-selection rule, TabPFN achieved mean relative gains in best-discovered biomass of 8.6% and 20.5% over a dimension-scaled Gaussian process at 80 and 120 components, respectively. Observed performance was comparable to that of the dimension-scaled Gaussian process at 8 to 40 components and when an eight-component growth model was embedded in a 120-variable search space. An exploratory factorial simulation suggested that relative performance varies with essential-component probability and contribution-weight concentration. Essential components were coupled through Liebig's law of the minimum, suggesting switching nutrient limitation as a candidate mechanism underlying the observed performance differences. These simulation results show that TabPFN can improve best-discovered biomass under a fixed plate budget in media with many components, while maintaining comparable observed performance in the lower-component settings examined. The findings provide a basis for future laboratory evaluation of tabular foundation models for medium optimization with limited experimental feedback. Code, simulation results and analysis scripts are available at https://github.com/sesejun/PlatePrior and archived at https://doi.org/10.5281/zenodo.23200480.