Fig 1.
Lotka-Volterra observation data.
Simulated data used for network identification. Log-Normal noise is added to the true trajectory, and measurement frequency is changed to show the uncertainty in posteriors.
Table 1.
Library of ansatz reactions for the Lotka-Voltera model.
Fig 2.
Lotka-Volterra estimated reactions.
(a) Estimated parameters using Eq (6). Reactions correspond to the reactions specified in Table 1 (b) Estimated parameters using Reactive SINDy at different measurement frequencies as well as using noise-less measurements.
Fig 3.
(a) Using posterior samples from Eq (6). Even at smaller observation frequencies, the observed data is accurately captured, though (as expected) with greater uncertainty. (b) As Reactive SINDy estimates derivatives, errors in the numerical methods lead to large deviations in the reconstructed trajectories as sampling frequency and noise increase. Although a single trajectory at dt = 0.2 may capture the oscillating behavior, it is clearly biased away from the true observations.
Fig 4.
Lotka-Volterra: Posterior distributions of non-zero reactions using the proposed model.
As expected, uncertainty in the parameters decreases as the measurement frequency decreases, but all are concentrated in relatively the same area. Only a single network is consistently identified given this data, indicating that identifiabiltiy is not a problem for this system.
Fig 5.
Identified trajectories and posterior from partial observations.
The true network can still be captured using only observations of Y however the credible intervals are significantly higher due to the loss of observations of P.
Fig 6.
Identified trajectories and posterior from additive.
Similar to the case of observing only one Y, the true network can still be recovered in this example however credible intervals are significantly larger.
Fig 7.
Prokaryotic auto-regulation observation data.
Simulated data used for the prokaryotic auto-regulation model. Log-normal observational noise is added to the true trajectory.
Table 2.
Selected recovered networks for prokaryotic auto-regulation system.
The first 4 reactions are assumed to be known and the remaining reactions are to be inferred by the method.
Fig 8.
Dynamics from the identified networks.
The dynamics from both recovered networks are different from the truth and each other, but still manage to produce plausible dynamics when compared to the noisy data. This points to an unidentifiability in the system, caused by noise in the data and structural identifiability issues.
Fig 9.
Posterior distributions over non-zero reaction rates.
Pair plots of the two distinct reaction networks inferred by the model. Reaction rates within each network exhibit are relatively well determined. This indicates a distinct multi-modality or unidentifiability in the problem.