  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.
