Speaker
Description
Identifying tipping points in spatially distributed ecosystems is critical for conservation but remains challenging due to the complexity of nonlinear dynamics, spatial connectivity, and limited observational data. We present a framework combining Universal Differential Equations (UDEs) with a novel dynamic gradient matching algorithm to learn ecosystem dynamics from large-scale remotely sensed time series. Dynamic gradient matching extends existing gradient matching approaches by simultaneously fitting linear spline smoothing functions and UDE parameters via a joint loss function, eliminating the need for ODE solvers during training while accounting for both process and observation error. This enables efficient scaling to datasets with many state variables. We evaluate four UDE model formulations on simulated spatially distributed kelp forest dynamics with emergent Allee effects, testing their ability to detect and quantify tipping points. The models achieve low false positive rates (0.5–6.2%) and moderate to high true positive rates (58.5–91.5%) for threshold detection, with performance depending on the proximity of the system to the tipping point and spatial correlation of environmental forcing. We further demonstrate the approach on satellite-derived kelp abundance data from central California using the Kelp Watch database, incorporating sea surface temperature as a covariate and estimating dispersal kernels. Results highlight the potential of UDE-based approaches for data-driven identification of critical transitions in spatially extended ecosystems.
