Despite their success, the results of first-principles quantum mechanical calculations contain inherent numerical errors caused by various intrinsic approximations. We propose here a neural-network-based algorithm to greatly reduce these inherent errors. As a demonstration, this combined quantum mechanical calculation and neural-network correction approach is applied to the evaluation of standard heat of formation Delta(f)H(-) for 180 small- to medium-sized organic molecules at 298 K. A dramatic reduction of numerical errors is clearly shown with systematic deviation being eliminated. For example, the root-mean-square deviation of the calculated Delta(f)H(-) for the 180 molecules is reduced from 21.4 to 3.1 kcal mol(-1) for B3LYP/6-311+G(d,p) and from 12.0 to 3.3 kcal mol(-1) for B3LYP/6-311+G(3df,2p) before and after the neural-network correction. (C) 2003 American Institute of Physics.