Data-driven sensor placement with shallow decoder networks

The paper’s QR-with-SDN pipeline and its QR argument (maximizing a greedy volume surrogate via CPQR; Eq. 9–11) are standard and empirically supported, but largely heuristic without formal risk guarantees; its pruning results are also empirical and explained qualitatively (sensor clustering) . The model’s solution correctly reconstructs the CPQR logic and adds reasonable conditioning and noise-propagation analyses, but it implicitly assumes generalization when claiming SDN cannot underperform the linear POD map for fixed Φ, and it moves from MSE to relative-error ordering via an upper bound only—both require additional assumptions not present in the paper or proof sketch. Hence, both are incomplete: the paper for lack of formal performance guarantees, the model for unspoken assumptions about training and generalization.