Hybrid Physics-Informed Neural Inference for Computer Agriculture Irrigation Scheduling Under Unmodeled Root-Zone Conductance: An Artificial Intelligence Residual-Bound Evaluation

Physics-informed neural networks (PINNs) promise irrigation schedules that respect soil-water balance while learning residual dynamics from data. Their reliability, however, depends on how the network's unmodeled component interacts with the physical constraint, and no bound currently exists for the inference error that this interaction induces when root-zone conductance is misspecified. The soil-water balance is written as a constrained operator equation in which the learned residual is projected onto the orthogonal complement of the physical flux space; the projection defines an inference error whose magnitude is controlled by the conductance misspecification and the Lipschitz constant of the residual network. A formal bound is derived (Theorem 3.1) and tightened for the practically relevant case of bounded conductance error (Corollary 3.2). The bound is then evaluated in a replication-based design study of the before-after-control-impact estimator that would be used to validate such schedules in the field. Using a declared variance structure (between-cluster SD = 6.0, residual SD = 4.5, intraclass correlation = 0.64), power was estimated across 2000 design cells for cluster counts of 8, 16, 24 and 32 and effects of 3, 5 and 8 percentage points. Fifty-six clusters are required for 80% power at a 5-percentage-point effect. The residual bound is informative at realistic cluster counts only when the conductance error is below a threshold that the design study makes explicit, and it identifies the conditions under which hybrid inference is preferable to either a purely physical or a purely learned schedule.