Fast fitting of neural ordinary differential equations by Bayesian neural gradient matching to infer ecological interactions from time series data

1. Inferring ecological interactions is hard because we often lack suitable parametric representations to portray them. Neural ordinary differential equations (NODEs) provide a way of estimating interactions nonparametrically from time series data. NODEs, however, are slow to fit, and inferred interactions have not been truthed. 2. We provide a fast NODE fitting method, Bayesian neural gradient matching (BNGM), which relies on interpolating time series with neural networks, and fitting NODEs to the interpolated dynamics with Bayesian regularisation. We test the accuracy of the approach by inferring ecological interactions in time series generated by an ODE model with known interactions. We also infer interactions in experimentally replicated time series of a microcosm featuring an algae, flagellate, and rotifer population, as well as in the hare and lynx system. 3. Our BNGM approach allows us to cut down the fitting time of NODE systems to only a few seconds. The method provides accurate estimates of ecological interactions in the artificial system, as linear and nonlinear true interactions are estimated with minimal error. In the real systems, dynamics are driven by a mixture of linear and nonlinear ecological interactions, of which only the strongest are consistent across replicates. 4. Overall, NODEs alleviate the need for a mechanistic understanding of interactions, and BNGM alleviates the heavy computational cost. This is a crucial step availing quick NODE fitting, cross-validation, and uncertainty quantification, as well as more objective estimation of interactions, and complex context dependence, than parametric models.