While the residual multi-fidelity framework presents several advantages, there are potential limitations and challenges associated with its implementation in practical applications. One challenge is related to determining an optimal balance between low- and high-fidelity models, ensuring that they are appropriately correlated without introducing biases or inaccuracies into the surrogate model. Additionally, selecting suitable hyperparameters for training neural networks within this framework can be complex and may require extensive experimentation to achieve optimal performance. Another limitation could arise from assumptions made about regularity conditions on target functions or network approximation errors which might not hold true in all real-world scenarios.
Furthermore, implementing this framework effectively requires access to sufficient training data across different fidelity levels which may not always be readily available or easy to obtain. The success of this approach also depends on accurately estimating discrepancies between models at various fidelity levels which could pose challenges if these discrepancies are not well understood or quantified beforehand.