Understanding the responses of ecosystems to environmental change and increased stochasticity is the need of the hour. The difficulty in studying ecology is rooted mainly in the fact that ecosystems are made up of many complex highly interacting parts. Theoretical models are the best ways to make progress in such complex systems where data are limited and dynamics are high-dimensional.
Modeling many-species systems as coupled differential equations is a common approach among theoreticians. However, real-world situations pose the following challenges - 1) The structure of the underlying dynamics is not known, and 2) we only have data on a partial set of variables. Empirical dynamic modeling (EDM) offers a solution to the first problem, wherein the dynamics are constructed purely from the available data. Time-delay embedding (TDE) offers a solution to the second problem by reproducing the multi-variable dynamics using lags from the observed time-series as surrogates for the unobserved variables. Through algebraic restructuring of the time-delay embedding equation, we show that a recurrent neural network is well-placed to approximate the the dynamics of a non-linear system.
Results/Conclusions
We compare the performances of Gaussian process regression (GPR) versus recurrent neural network (RNN) approaches to model the non-linear dynamics of both simulated and real-world ecosystems. We show the error bounds for both approaches and highlight the scenarios where GPR or RNN works better. We will discuss ways in which hybrid approaches - where mechanistic models are given enough degrees of freedom to employ EDM approaches and fill the gaps of our mechanistic understanding of the underlying process - can be employed to improve both our understanding and predictability of partially observed ecosystems.