Figure 4: The model selection process using time course measurements of three metabolites in yeast glycolysis.

(a) For each set of given initial conditions (open circles), a noisy measurement of the three observable concentrations (filled circles) is made at a single random time. Hidden variables (in grey) are not measured. In this example, we fit to N=40 in-sample conditions. (b) Models from an ordered class, with the illustrated connectivity, are fit and tested sequentially until , an approximation of the relative log-likelihood, decreases sufficiently from a maximum. (c) The selected model (large connectivity diagram) is used to make predictions about out-of-sample conditions. Here, we compare the output of the selected model (solid lines) with that of the model that created the synthetic data (dashed lines). (d) Performance versus computational and experimental effort. The mean out-of-sample correlation for three measured biochemical species from the range of initial conditions twice that used in training rises to over 0.6 using <5 × 10⁸ model evaluations and 40 in-sample measurements. In (ref. 14), inferring an exact match to the original seven-dimensional model used roughly 500 times as many measurements of all seven species (with none hidden). The approach also used 200 times as many model evaluations (Supplementary Note 4). Nonetheless, the accuracy of both approaches is comparable, and Sir Isaac additionally retains information about the phase of the oscillations. This illustrates that the problem of adaptively finding an approximation to the dynamics is, in fact, much simpler than the problem of inferring the detailed equations describing the dynamics.