72: On physics-informed neural networks for ecological diffusion modeling of wildlife diseases

Music City Center 

A physics-informed neural network (PINN) is a powerful deep learning algorithm that can approximate the solution of a partial differential equation (PDE). PINNs have been applied to ecological diffusion equations (EDEs) for statistical models in wildlife diseases and showed superior performance in forecasting and inference. However, there is a gap in the theoretical developments of PINNs for models using ecological diffusion as the underlying mechanism of observations. In this work, we derive a generalization error bound for PINNs solving forward problems for EDEs and we provide an error bound for approximating the expected value of a response variable with underlying spread mechanisms modeled as the solution of an EDE. Finally, we quantitatively compare the performance of PINNs with commonly used numerical solvers, showing that PINNs are accurate and provide important modeling flexibility.

physics-informed neural network

ecology

environmental statistics

spatiotemporal data

ecological diffusion equation

deep learning 

Section on Statistics and the Environment