Universal differential equations for ecology

As a postdoc at Oregon State University, I am developing machine learning tools for uncovering nonlinear ecological dynamics from time series data. My collaborators and I are building on a class of models called universal differential equations, which combine neural networks and known parametric functions to model how physical and ecological systems change over time. This allows researchers to incorporate known physical or biological processes into a model that uses flexible machine-learning tools to represent unknown mechanisms.

Although these new tools have many potential advantages for modeling ecosystems, they have primarily been applied to data from physical systems. In comparison, ecological data has many unique characteristics and limitations. Ecological data are often sampled frequently, and the measurements can be noisy. Furthermore, it is rare to observe all of the important mechanisms that cause changes in an ecosystem. Simply put, models of ecological models must be able to accommodate a high degree of uncertainty.

To address this limitation, we are developing a library in the Julia programming language that embeds universal differential equations within a state-space modeling framework. State space models are a class of time series models that account for imprecise observations and random variability, making them very useful for quantifying uncertinaty and fitting models to noisy data. Combining universal differential equations and state space models allows us to leverage this powerful new machine-learning technique in the context of noisy ecological data.

The code and documentation for the project are available on my Github!