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This paper develops low-dimensional moment methods for advective problems onnetworks of domains. The evolution of a density function is described by alinear advection-diffusion-reaction equation on each domain, combined viaadvective flux coupling across domains in the network graph. The PDEs'coefficients vary in time and across domains but they are fixed along eachdomain. As a result, the solution on each domain is frequently close to aGaussian that moves, decays, and widens. For that reason, this work studiesmoment methods that track only three degrees of freedom per domain -- incontrast to traditional PDE discretization methods that tend to require manymore variables per domain. A simple ODE-based moment method is developed, aswell as an asymptotic-preserving scheme. We apply the methodology to anapplication that models the life cycle of forest pests that undergo differentlife stages and developmental pathways. The model is calibrated for the spottedlanternfly, an invasive species present in the Eastern USA. We showcase thatthe moment method, despite its significant low-dimensionality, can successfullyreproduce the prediction of the pest's establishment potential, compared tomuch higher-dimensional computational approaches.

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