Data-driven model discovery and model selection for noisy biological systems
Fig 2
Evaluation of hybrid dynamical model fits on the Lotka-Volterra model.
A. The Lotka-Volterra system describes predator-prey relationships in an ecosystem, here parameterized by (α, β, γ, δ). B. Example simulation with parameters (1 . 3, 0 . 9, 0 . 8, 1 . 8). The population dynamics oscillate at a stable limit cycle. C and D. To evaluate model discovery methods, additive or multiplicative noise is added to the underlying deterministic dynamics at different noise levels. The mean trajectories of 200 samples for each noise model are shown; ribbons represent ± 3 s.d. E and F. Comparison of fits using hybrid dynamical models. In setting 1, good fits to the data were not obtained (high validation loss). Training parameters: learning rate 0.001; window size 10; batch size 10. In setting 2, a good fit to the data was obtained. Training parameters: learning rate 0.01; window size 5; batch size 5.