Seminar – Fast fitting of NODEs by Bayesian neural gradient matching.

Speaker: Willem Bonnaffeé, Nuffield Department of Surgical Sciences, University of Oxford

Abstract: Neural ordinary differential equations (NODEs) allow us to nonparametrically infer ecological interactions from time series data. NODEs however are slow to fit. We developed a fitting method, Bayesian neural gradient matching (BNGM), which reduces NODEs fitting times to only a few seconds. We test the approach in an artificial tri-trophic system where true ecological interactions are known, as well as in an experimentally replicated time series of an algae, flagellate, and rotifer, and in the multi-species aquatic community of the Maizuru bay in Japan. We show that BNGM is faster and more accurate than standard NODEs, parametric ODEs, and convergent cross-mapping (CCM). Our results suggest that only main interactions are consistent across the replicated time series, and that dynamics of the Maizuru bay community are largely driven by a single species. Overall, this work shows that while NODEs alleviate the need for a mechanistic understanding of interactions, BNGM alleviates the heavy computational cost, thus greatly improving the usability of the approach.