Non-Interfering Asymmetric AdamW Updates for Constrained Exploration of Equifinality in Hybrid Models

Abstract

Hybrid models let neural networks supply the unresolved parameters of a process-based simulator, and are fitted to observations that constrain aggregate fluxes and storages but not the internal partitioning that produces them. Such a fit is equifinal: configurations indistinguishable in the observed aggregates can disagree substantially about the unobserved internals, and therefore about the mechanism they attribute to the same data. We study evapotranspiration, whose total flux is observed while its split into transpiration and evaporation is not. A model ensemble built from random seeds alone spans only a narrow band of the partitionings the data admit. We produce the spread deliberately, training members under auxiliary repulsion on transpiration, subject to the fit to observations not degrading. Non-interference is usually arranged by making the auxiliary gradient orthogonal to the main one, but under AdamW the applied step is a preconditioned momentum direction, so orthogonality between raw gradients no longer implies it. We introduce Non-interfering Asymmetric Network Optimization (NANO), an update whose first-order effect on the main loss is exactly that of the main objective alone, whose auxiliary step is bounded, and which concentrates repulsion in the coordinates the main gradient leaves idle.