Moment Methods for Advection on Networks and an Application to Forest Pest Life Cycle Models

TL;DR

This paper introduces low-dimensional moment methods for advection problems on networks, effectively modeling complex biological processes like forest pest life cycles with fewer variables than traditional PDE methods.

Contribution

It develops a simple ODE-based moment method and an asymptotic-preserving scheme for advective PDEs on networks, applied to modeling invasive species like the spotted lanternfly.

Findings

The moment method accurately predicts pest establishment potential.

The approach significantly reduces computational complexity.

It successfully captures key dynamics with only three degrees of freedom per domain.

Abstract

This paper develops low-dimensional moment methods for advective problems on networks of domains. The evolution of a density function is described by a linear advection-diffusion-reaction equation on each domain, combined via advective flux coupling across domains in the network graph. The PDEs' coefficients vary in time and across domains but they are fixed along each domain. As a result, the solution on each domain is frequently close to a Gaussian that moves, decays, and widens. For that reason, this work studies moment methods that track only three degrees of freedom per domain -- in contrast to traditional PDE discretization methods that tend to require many more variables per domain. A simple ODE-based moment method is developed, as well as an asymptotic-preserving scheme. We apply the methodology to an application that models the life cycle of forest pests that undergo different life stages and developmental pathways. The model is calibrated for the spotted lanternfly, an invasive species present in the Eastern USA. We showcase that the moment method, despite its significant low-dimensionality, can successfully reproduce the prediction of the pest's establishment potential, compared to much higher-dimensional computational approaches.