Fig. 2: The workflow of McMLP (Metabolite response predictor using coupled multilayer perceptrons).

We aim to predict endpoint metabolomic profiles (i.e., metabolomic profiles after the dietary interventions) based on the baseline microbial compositions (i.e., microbial compositions before the dietary intervention), dietary intervention strategy, and baseline metabolomic profiles. Here we used a hypothetical example with n = 5 training samples and 2 samples in the test set. For each sample, we considered \({N}_{{{{\rm{s}}}}}\) microbial species, \({N}_{{{{\rm{d}}}}}\) dietary resources, and \({N}_{{{{\rm{m}}}}}\) metabolites. Across three panels, microbial species and their relative abundances are colored blue, dietary resources and their intervention doses are colored green, and metabolites and their concentrations are colored red. Icons associated with baseline/endpoint data are bounded by solid black/dashed lines respectively. a The model architecture of McMLP. McMLP comprises two coupled MLPs (multilayer perceptrons). The first MLP at the top (step 1) predicts the endpoint microbial compositions based on the baseline data and the dietary intervention strategy. The predicted endpoint microbial compositions from the first MLP are then provided as input to the second MLP at the bottom (step 2). The second MLP combines the predicted endpoint microbial compositions, the dietary intervention strategy, and the baseline metabolomic profiles to finally predict the endpoint metabolomic profiles. The value of dietary intervention strategy is either binary to denote the presence/absence of each dietary resource or numeric to be proportional to the intervention dose. Details of both MLPs can be found in Supplementary Fig. 1 and “Methods”. b McMLP takes two types of baseline data (baseline microbial compositions and baseline metabolomic profiles) and the dietary intervention strategy as input variables and is trained to predict corresponding endpoint metabolomic profiles. During training, the endpoint microbial composition is needed to train the first MLP. By contrast, the second MLP directly takes the predicted endpoint microbial composition instead of the actual endpoint microbial composition. c The well-trained McMLP can generate predictions for metabolomic profiles for the test set. During testing, no endpoint microbial composition is needed because the second MLP directly takes the predicted endpoint microbial composition from the first MLP as the input.