Robustness to extensions of the BINN equation-learning setting

Investigate the robustness of the biologically-informed neural-network hyperparameter-selection workflow for partial differential equations with additional or different right-hand-side terms, including advection, and for right-hand-side terms that depend on covariates such as space, time, or background environmental factors.

Background

The workflow is developed and evaluated for reaction–diffusion systems in which the unknown diffusion and growth coefficient functions depend on density. The authors therefore do not establish whether the same architecture-ordered diagnostics and selection principles remain reliable when the governing equation includes other mechanisms or when the learned right-hand-side terms depend on variables beyond density.

The proposed extensions include partial differential equations with additional or different right-hand-side terms, such as advection, and coefficient functions involving space, time, or environmental covariates. These cases could alter the interaction between state-network capacity, right-hand-side-network capacity, and early stopping, making them a distinct unresolved problem.