The proposed RMFNN algorithm offers a significant improvement over traditional methods in terms of both accuracy and efficiency. In traditional approaches, such as direct high-fidelity model sampling or using high-fidelity neural networks alone, the computational cost can be prohibitively high due to the need for a large number of expensive high-fidelity evaluations. On the other hand, the RMFNN algorithm leverages multi-fidelity information and residual modeling to construct a surrogate model that is accurate within small tolerances while dramatically reducing computational costs. By training two neural networks - one to learn the residual function and another to act as a surrogate for the high-fidelity quantity of interest - the RMFNN algorithm achieves higher accuracy with fewer expensive computations. This approach allows for efficient generation of synthetic high-fidelity data and results in dramatic savings in computational cost when compared to traditional methods.