Error Cancellation
Error cancellation is the reduction of error in a computed difference (a reaction energy, a relative adsorption energy, a formation energy) when the errors of the two quantities being subtracted are positively correlated. Because the variance of a difference is the sum of the individual variances minus twice their covariance, correlated errors partly cancel, while independent errors add in quadrature and amplify the error of the difference. Many practical conclusions in computational chemistry rely on this effect, since methods are often more accurate for relative than for absolute energies.
Error cancellation in GNN adsorption energy differences (2023)
Ock, Tian, Kitchin and Ulissi analyzed about 483 million pairs of adsorbate-catalyst systems from OC20-Dense and defined a subgroup error cancellation ratio (SECR), one minus the error standard deviation in a subgroup divided by that over all pairs (Ock et al. 2023). BEEF-vdW ensembles showed amplified error for unrelated pairs (about -3%) and 42% to 77% cancellation for chemically similar ones. Modern GNNs (DimeNet++ onward) also had positive SECR for every similar subgroup, up to 71% for configurations near the surface minimum, showing that their errors are not independent; but outside those near-minimum configuration pairs, their difference errors stayed larger than their individual-energy errors, unlike DFT, and SECR did not track the falling MAE across model generations. Summary: ock2023.